Basic Physical Chemistry

Written by me, Richard Purvey, in the year 2012 and dedicated to my parents, Patricia and David

Chapter 1 of 6: ∆G

For a balanced chemical reaction;

a/6.022x10^23 A + b/6.022x10^23 B ↔ c/6.022x10^23 C + d/6.022x10^23 D,

∆G = kTln(([C]^c[D]^d/[A]^a[B]^b)/([C]eq^c[D]eq^d/[A]eq^a[B]eq^b)).

∆G is the reaction Gibbs free energy change per: c building units of the chemical product C produced, d building units of the chemical

product D produced, a building units of the chemical reactant A reacted and b building units of the chemical reactant B reacted. k is the

Boltzmann constant which is per building unit and T is the particular temperature. ln means the natural logarithm of and ^ means

to the power of.

[C], [D], [A] and [B] are the actual concentrations of the chemical products C and D and of the chemical reactants A and B, respectively, at a given time and

[C]eq, [D]eq, [A]eq and [B]eq are any set of concentrations of the chemical products C and D and of the chemical reactants A and B, respectively, which constitutes chemical equilibrium at the particular temperature, T.

NB: For this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, ∆G must be less than 0 which, because ∆G = kTln(([C]^c[D]^d/[A]^a[B]^b)/([C]eq^c[D]eq^d/[A]eq^a[B]eq^b)), means that for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, kTln(([C]^c[D]^d/[A]^a[B]^b)/([C]eq^c[D]eq^d/[A]eq^a[B]eq^b)) must be less than 0 and so for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, ln(([C]^c[D]^d/[A]^a[B]^b)/([C]eq^c[D]eq^d/[A]eq^a[B]eq^b)) must be less than 0 and so for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, ([C]^c[D]^d/[A]^a[B]^b)/([C]eq^c[D]eq^d/[A]eq^a[B]eq^b) must be less than 1 and so for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, [C]^c[D]^d/[A]^a[B]^b must be less than [C]eq^c[D]eq^d/[A]eq^a[B]eq^b.

Chapter 2 of 6: Chemical Reactions and ∆G

For a balanced chemical reaction; a A + b B ↔ c C + d D, where the values: a, b, c and d are any set of stoichiometric coefficients which balances the chemical equation, ∆G = RTln(Q/K). ∆G is the reaction Gibbs free energy change per: c moles of building units of the chemical product C

produced, d moles of building units of the chemical product D produced, a moles of building units of the chemical reactant A

reacted and b moles of building units of the chemical reactant B reacted. R, equal to 6.022x10^23k, is the gas constant which is per mole of building units and T is the particular temperature.

Q = [C]^c[D]^d/[A]^a[B]^b where [C], [D], [A] and [B] are the actual concentrations of the chemical products C and D and of the chemical reactants A and B, respectively, at a given time and Q is the chemical reaction quotient and

K = [C]eq^c[D]eq^d/[A]eq^a[B]eq^b

where [C]eq, [D]eq, [A]eq and [B]eq are any set of concentrations of the chemical products C and D and of the chemical reactants A and B, respectively, which constitutes chemical equilibrium at the particular temperature, T and K is the chemical equilibrium constant.

NB: For this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, ∆G must be less than 0 which, because ∆G = RTln(Q/K), means that for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, RTln(Q/K) must be less than 0 and so for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, ln(Q/K) must be less than 0 and so for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, Q/K must be less than 1 and so for this forward chemical reaction to spontaneously proceed until chemical equilibrium is reached, Q must be less than K.

And when the value of the chemical reaction quotient reaches the value of the chemical equilibrium constant, i.e. when the value of Q reaches the value of K, chemical equilibrium has been reached. Because ∆G = RTln(Q/K), this means that, at chemical equilibrium,

∆G = RTln(K/K) and so, at chemical equilibrium, ∆G = RTln1 and so, at chemical equilibrium, ∆G = 0. NB: If [C]^c[D]^d = [A]^a[B]^b then [C]^c[D]^d/[A]^a[B]^b = 1.And because Q = [C]^c[D]^d/[A]^a[B]^b, this means that if [C]^c[D]^d = [A]^a[B]^b then Q = 1.And because ∆G = RTln(Q/K), this means that if [C]^c[D]^d = [A]^a[B]^b then ∆G = RTln(1/K) and so if [C]^c[D]^d = [A]^a[B]^b then ∆G = - RTlnK.∆G, in this case, is known as the standard reaction Gibbs free energy change per: c moles of building units of the chemical product C produced, d moles of building units of the chemical product D produced, a moles of building units of the chemical reactant A reacted and b moles of building units of the chemical reactant B reacted and is given the symbol ∆Go. REDOX CHEMICAL REACTIONS; For redox chemical reactions, as well as ∆G being the reaction Gibbs free energy change per: c moles of building units of the chemical product C produced, d moles of building units of the chemical product D produced, a moles of building units of the chemical reactant A reacted and b moles of building units of the chemical reactant B

reacted, ∆G is also the reaction Gibbs free energy change per n moles of electrons transferred. And the equation relating ∆G to these n moles of electrons transferred is ∆G = - nFE where n is this number of moles of electrons transferred in this redox chemical reaction when these a moles of building units of the chemical reactant A and these b moles of building units of the chemical

reactant B react producing these c moles of building units of the chemical product C and these d moles of building units of the chemical product D. F is the Faraday constant which is in units of C per mole of electrons and E is the cell potential which is in units of V. NB: Because for this forward redox chemical reaction to spontaneously proceed until chemical equilibrium is reached, ∆G must be less than 0, this means that for this forward redox chemical reaction to spontaneously proceed until chemical equilibrium is reached, - nFE must be less than 0 and so for this forward redox chemical reaction to spontaneously proceed until chemical equilibrium is reached, - E must be less than 0 and so for this forward redox chemical reaction to spontaneously proceed until chemical equilibrium is reached, E must be greater than 0.

NB: F is the charge per mole of electrons and so is equivalent to 6.022x10^23e where e is the charge per electron.

nFE = welect where welect is the electrical work available from the redox chemical reaction. This is exactly the same type of equation as qV = welect where welect is the electrical work available, q is the charge which is in units of C and V is the voltage which is in units of V. Because, for redox chemical reactions, as well as ∆G being equal to RTln(Q/K), ∆G is also equal to - nFE, for redox chemical reactions, - nFE = RTln(Q/K) and so, for redox chemical reactions,E = RTln(Q/K)/(-nF) and so, for redox chemical reactions, E = - RTln(Q/K)/nF and so, for redox chemical reactions, E = RTln(K/Q)/nF.And because when the value of the chemical reaction quotient reaches the value of the chemical equilibrium constant, i.e. when the value of Q reaches the value of K, chemical equilibrium has been reached, this means that for a redox chemical reaction, at chemical equilibrium, E = RTln(K/K)/nF and so for a redox chemical reaction, at chemical equilibrium,E = RTln1/nF and so for a redox chemical reaction, at chemical equilibrium,E = 0/nF and so for a redox chemical reaction, at chemical equilibrium,E = 0 and so for a redox chemical reaction, at chemical equilibrium, as well as ∆G being equal to 0, E is also equal to 0.NB: Because if [C]^c[D]^d = [A]^a[B]^b then Q = 1, it also means that, for a redox chemical reaction, if [C]^c[D]^d = [A]^a[B]^b then E = RTln(K/1)/nF and so, for a redox chemical reaction, if [C]^c[D]^d = [A]^a[B]^b thenE = RTlnK/nF.E, in this case, is known as the standard cell potential and is given the symbol Eo (just as ∆G, in this case, is given the symbol ∆Go).

Chapter 3 of 6: Chemical Reaction Rates

In a chemical reaction where some chemical reactant A and some chemical reactant B react

producing some chemical product C and some chemical product D, the balanced chemical reaction

is;

a A + b B → c C + d D.

And within any time interval during this chemical reaction, (the decrease in the concentration of the chemical reactant A)/a, (the decrease in the concentration of the chemical reactant B)/b, (the increase in the concentration of the chemical product C)/c and (the increase in the concentration of the chemical product D)/d are all equal.

And because a decrease is equivalent to a negative increase, the decrease in the concentration of the chemical reactant A = - (the "increase" in the concentration of the chemical reactant A) and the decrease in the concentration of the chemical reactant B = - (the "increase" in the concentration of the chemical reactant B) and so this means that, within any time interval during this chemical reaction, - (the "increase" in the concentration of the chemical reactant A)/a, - (the "increase" in the concentration of the chemical reactant B)/b, (the increase in the concentration of the chemical product C)/c and (the increase in the concentration of the chemical product D)/d are all equal.

The "increase" in the concentration of the chemical reactant A = the change in the concentration of the chemical reactant A, the "increase" in the concentration of the chemical reactant B = the change in the concentration of the chemical reactant B, the increase in the concentration of the chemical product C = the change in the concentration of the chemical product C and the increase in the concentration of the chemical product D = the change in the concentration of the chemical product D and so this means that, within any time interval during this chemical reaction, - (the change in the concentration of the chemical reactant A)/a, - (the change in the concentration of the chemical reactant B)/b, (the change in the concentration of the chemical product C)/c and (the change in the concentration of the chemical product D)/d are all equal.

In other words,

- ∆[A]/a∆t = - ∆[B]/b∆t = ∆[C]/c∆t = ∆[D]/d∆t where ∆[A], ∆[B], ∆[C] and ∆[D] are the changes in the concentrations of the chemical reactants A and B and of the chemical products C and D, respectively, within the time interval, ∆t during this chemical reaction.

A chemical reaction takes place from start to finish continuously with respect to time and so this means that

(-1/a)(d[A]/dt) = (-1/b)(d[B]/dt) = (1/c)(d[C]/dt) = (1/d)(d[D]/dt) at time, t during this chemical reaction.

And this value: (-1/a)(d[A]/dt), (-1/b)(d[B]/dt), (1/c)(d[C]/dt) and (1/d)(d[D]/dt) is the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction (it is usually just referred to as the unique instantaneous rate of chemical reaction at time, t), and is in units of L^(-1)s^(-1).

A chemical reaction takes place through a sequence of elementary chemical reactions. And, at a particular temperature, the unique instantaneous rate of an elementary chemical reaction with respect to time at time, t during this elementary chemical reaction is directly proportional to (the respective concentrations, at the time, of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction multiplied together)/x where x is the stoichiometric coefficient in this balanced elementary chemical reaction.

For example, at a particular temperature, for a balanced elementary chemical reaction of the type;

xA' + xB' → xC' + xD',

where A' and B' are the elementary chemical reactants and C' and D' are the elementary chemical products in this elementary chemical reaction,

(-1/x)(d[A']/dt) = (-1/x)(d[B']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) is directly proportional to [A'][B']/x and so

- d[A']/dt = - d[B']/dt = d[C']/dt = d[D']/dt is directly proportional to [A'][B']

where [A'] and [B'] are the concentrations, at the time, of the elementary chemical reactants A' and B' respectively.

In other words, at a particular temperature, the unique instantaneous rate of an elementary chemical reaction with respect to time at time, t during this elementary chemical reaction = k multiplied by (the respective concentrations, at the time, of each of the elementary chemical reactants in

the elementary chemical equation for this elementary chemical reaction multiplied together)/x.

The value of the constant, k, therefore, depends upon the particular temperature. And the equation relating k to the particular temperature, T is k = Ae^(-Eminimum/RT) where e is the mathematical constant, e. Whatever units this constant, A is in, the constant, k is in these units too. The value of the constant, e^(-Eminimum/RT) depends upon the particular temperature, T and the higher the particular temperature, T, the higher the value of this constant, e^(-Eminimum/RT). e^(-Eminimum/RT) represents the fraction of the elementary chemical reactants colliding where there is enough non relativistic kinetic energy to form the elementary chemical products. The value of the constant, A also depends upon the particular temperature, T because A determines the frequency of the collisions between the elementary chemical reactants which depends upon the average relative speed amongst the elementary chemical reactants which, in turn, depends upon the particular temperature, T. And the higher the particular temperature, T, the higher the average relative speed amongst the elementary chemical reactants and so the higher the value of the constant, A. Because the higher the particular temperature, T, the higher the value of the constant, e^(-Eminimum/RT) and because the higher the particular temperature, T, the higher the value of the constant, A, the higher the particular temperature, T, the higher the value of the constant, k.

In the case of a balanced elementary chemical reaction of the type; xA' + xB' → xC' + xD', where x moles of building units of the elementary chemical reactant A' and x moles of building units of the elementary chemical reactant B' react producing x moles of building units of the elementary chemical product C' and x moles of building units of the elementary chemical product D', Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant B' to react producing one mole of building units of the elementary chemical product C' and one mole of building units of the elementary chemical product D'. And, in this case, the quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant B' to react producing one building unit of the elementary chemical product C' and one building unit of the elementary chemical product D')/kT where this k is the Boltzmann constant.

Chapter 4 of 6: Rate Laws of Elementary Chemical Reactions

Because, at a particular temperature, the unique instantaneous rate of an elementary chemical reaction with respect to time at time, t during this elementary chemical reaction = k multiplied by (the respective concentrations, at the time, of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction multiplied together)/x and

because the equation relating k to the particular temperature, T is k = Ae^(-Eminimum/RT),

at a particular temperature, T, the unique instantaneous rate of an elementary chemical reaction with respect to time at time, t during this elementary chemical reaction = Ae^(-Eminimum/RT) multiplied by (the respective concentrations, at the time, of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction multiplied together)/x.

The constants, k and A are in units of L^(the number of elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction - 1)mol^(1 - the number

of elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction)s^(-1) and Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction to react producing one mole of building units of each of the elementary chemical products in the elementary chemical equation for this elementary chemical reaction. The quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction to react producing one building unit of each of the elementary chemical products in the elementary chemical equation for this elementary chemical reaction)/kT where this k is the Boltzmann constant.

For example, at a particular temperature, T, for a balanced elementary chemical reaction of the type;

xA' → xC' + xD',

where A' is the elementary chemical reactant and C' and D' are the elementary chemical products in this elementary chemical reaction,

(-1/x)(d[A']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A']/x and so

- d[A']/dt = d[C']/dt = d[D']/dt = Ae^(-Eminimum/RT) multiplied by [A']

where [A'] is the concentration, at the time, of the elementary chemical reactant A'.

In this case, the constants, k and A are in units of s^(-1) since there is only 1 elementary chemical reactant in the elementary chemical equation for this elementary chemical reaction and Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant A' to react producing one mole of building units of the elementary chemical product C' and one mole of building units of the elementary chemical product D'. And, in this case, the quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant A' to react producing one building unit of the elementary chemical product C' and one building unit of the elementary chemical product D')/kT where this k is the Boltzmann constant.

And, at a particular temperature, T, for a balanced elementary chemical reaction of the type;

xA' + xB' → xC' + xD',

where A' and B' are the elementary chemical reactants and C' and D' are the elementary chemical products in this elementary chemical reaction,

(-1/x)(d[A']/dt) = (-1/x)(d[B']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A'][B']/x and so

- d[A']/dt = - d[B']/dt = d[C']/dt = d[D']/dt = Ae^(-Eminimum/RT) multiplied by [A'][B']

where [A'] and [B'] are the concentrations, at the time, of the elementary chemical reactants A' and B' respectively.

In this case, the constants, k and A are in units of Lmol^(-1)s^(-1) since there are 2 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction and Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant B' to react producing one mole of building units of the elementary chemical product C' and one mole of building units of the elementary chemical product D'. And, in this case, the quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant B' to react producing one building unit of the elementary chemical product C' and one building unit of the elementary chemical product D')/kT where this k is the Boltzmann constant.

And, at a particular temperature, T, for a balanced elementary chemical reaction of the type;

xA' + xA' → xC' + xD',

where A' and A' are the elementary chemical reactants and C' and D' are the elementary chemical products in this elementary chemical reaction,

(-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A'][A']/x and so

(-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A']^2/x and so

- d[A']/dt = - d[A']/dt = d[C']/dt = d[D']/dt = Ae^(-Eminimum/RT) multiplied by [A']^2

where [A'] is the concentration, at the time, of the elementary chemical reactants A' and A'.

In this case, the constants, k and A are in units of Lmol^(-1)s^(-1) since there are 2 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction and Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant A' to react producing one mole of building units of the elementary chemical product C' and one mole of building units of the elementary chemical product D'. And, in this case, the quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant A' to react producing one building unit of the elementary chemical product C' and one building unit of the elementary chemical product D')/kT where this k is the Boltzmann constant.

And, at a particular temperature, T, for a balanced elementary chemical reaction of the type;

xA' + xA' + xB' → xC' + xD' ,

where A' and A' and B' are the elementary chemical reactants and C' and D' are the elementary chemical products in this elementary chemical reaction,

(-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (-1/x)(d[B']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A'][A'][B']/x and so

(-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (-1/x)(d[B']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A']^2[B']/x and so

- d[A']/dt = - d[A']/dt = - d[B']/dt = d[C']/dt = d[D']/dt = Ae^(-Eminimum/RT) multiplied by [A']^2[B']

where [A'] and [B'] are the concentrations, at the time, of the elementary chemical reactants A' and A' and B' respectively.

In this case, the constants, k and A are in units of L^2mol^(-2)s^(-1) since there are 3 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction and Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant B' to react producing one mole of building units of the elementary chemical product C' and one mole of building units of the elementary chemical product D'. And, in this case, the quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant B' to react producing one building unit of the elementary chemical product C' and one building unit of the elementary chemical product D')/kT where this k is the Boltzmann constant.

And, at a particular temperature, T, for a balanced elementary chemical reaction of the type;

xA' + xA' + xA' → xC' + xD',

where A' and A' and A' are the elementary chemical reactants and C' and D' are the elementary chemical products in this elementary chemical reaction,

(-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A'][A'][A']/x and so

(-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (-1/x)(d[A']/dt) = (1/x)(d[C']/dt) = (1/x)(d[D']/dt) = Ae^(-Eminimum/RT) multiplied by [A']^3/x and so

- d[A']/dt = - d[A']/dt = - d[A']/dt = d[C']/dt = d[D']/dt = Ae^(-Eminimum/RT) multiplied by [A']^3

where [A'] is the concentration, at the time, of the elementary chemical reactants A' and A' and A'.

In this case, the constants, k and A are in units of L^2mol^(-2)s^(-1) since there are 3 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction and Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant A' and one mole of building units of the elementary chemical reactant A' to react producing one mole of building units of the elementary chemical product C' and one mole of building units of the elementary chemical product D'. And, in this case, the quotient, - Eminimum/RT, is equivalent to - (the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant A' and one building unit of the elementary chemical reactant A' to react producing one building unit of the elementary chemical product C' and one building unit of the elementary chemical product D')/kT where this k is the Boltzmann constant.

Chapter 5 of 6: Rate Laws of Chemical Reactions

For some chemical reactions, at a particular temperature, T, the unique instantaneous rate of the chemical reaction with respect to time at time, t during this chemical reaction = a constant

multiplied by the respective concentrations, at the time, of elementary chemical reactants raised to corresponding positive powers and then multiplied together. The sum of these powers gives the overall chemical reaction order of this chemical reaction. The constant is in units of L^(the overall chemical reaction order of this chemical reaction - 1)mol^( - the overall chemical reaction order of this chemical reaction)s^(-1) and contains the constant, e^(-Ea/RT) where e is the mathematical constant, e and Ea is equal to the sum of each of the powers multiplied by the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the corresponding elementary chemical reactant to react.

And for other chemical reactions, at a particular temperature, T, the unique instantaneous rate of the chemical reaction with respect to time at time, t during this chemical reaction = a constant multiplied by (the respective concentrations, at the time, of elementary chemical reactants raised to corresponding positive powers and then multiplied together)/(the respective concentrations, at the time, of elementary chemical reactants raised to corresponding positive powers and then multiplied together). The sum of the powers in the numerator minus the sum of the powers in the denominator gives the overall chemical reaction order of this chemical reaction. The constant is again in units of L^(the overall chemical reaction order of this chemical reaction - 1)mol^( - the overall chemical reaction order of this chemical reaction)s^(-1) and contains the constant, e^(-Ea/RT) where e is the mathematical constant, e and Ea is equal to the sum of each of the powers in the numerator multiplied by the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the corresponding elementary chemical reactant to react minus the sum of each of the powers in the denominator multiplied by the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the corresponding elementary chemical reactant to react.

Any chemical reaction’s rate law is found using experimental data.

Examples;

For the balanced chemical reaction; 1/3NO(g) + 1/6O2(g) → 1/3NO2(g), it is found, using experimental

data, that, at a particular temperature, T, the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction, i.e. (-1/(1/3))(d[NO]/dt) = (-1/(1/6))

(d[O2]/dt) = (1/(1/3))(d[NO2]/dt) i.e. - 3d[NO]/dt = - 6d[O2]/dt = 3d[NO2]/dt, is equal to a constant multiplied by [NO]^2[O2] where [NO] and [O2] are the concentrations, at the time, of the elementary chemical reactants NO and O2 respectively.

This chemical reaction, then, is a chemical reaction where, at a particular temperature, T, the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction = a constant multiplied by the respective concentrations, at the time, of elementary chemical reactants raised to corresponding positive powers and then multiplied together, with the overall chemical reaction order of this chemical reaction equal to 2 plus 1, i.e. = 3, and with the constant in units of L^2mol^(-3)s^(-1) and containing the constant, e^(-Ea/RT) where e is the mathematical constant, e and Ea is equal to 2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary

chemical reactant O2 to react. And, in this case, the quotient, - Ea/RT, is equivalent to - (2 times the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant NO to react plus 1 times the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant O2 to react)/kT where this k is the Boltzmann constant.

And for the balanced chemical reaction; 1/4O3(g) → 3/8O2(g), it is found, using experimental data, that, at a particular temperature, T, the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction, i.e. (-1/(1/4))(d[O3]/dt) = (1/(3/8))(d[O2]/dt) i.e. - 4d[O3]/dt = (8/3)(d[O2]/dt), is equal to a constant multiplied by [O3]^2/[O2] where [O3] and [O2] are the

concentrations, at the time, of the elementary chemical reactants O3 and O2 respectively.

This chemical reaction, then, is a chemical reaction where, at a particular temperature, T, the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction = a constant multiplied by (the respective concentrations, at the time, of elementary chemical reactants raised to corresponding positive powers and then multiplied together)/(the respective concentrations, at the time, of elementary chemical reactants raised to corresponding positive powers and then multiplied together), with the overall chemical reaction order of this chemical reaction equal to 2 minus 1, i.e. = 1, and with the constant in units of mol^(-1)s^(-1) and containing the constant, e^(-Ea/RT) where e is the mathematical constant, e and Ea is equal to 2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3

to react minus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react. And, in this case, the quotient, - Ea/RT, is equivalent to - (2 times the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant O3

to react minus 1 times the minimum amount of non relativistic kinetic energy needed for one building unit of the elementary chemical reactant O2 to react)/kT where this k is the Boltzmann constant.

Chapter 6 of 6: Chemical Reaction Mechanisms

A chemical reaction takes place through a sequence of elementary chemical reactions and this sequence of elementary chemical reactions is known as the chemical reaction mechanism for this chemical reaction. However, there is no way of knowing, for sure, what the chemical reaction

mechanism for a chemical reaction is. You can only propose a chemical reaction mechanism for a chemical reaction after making sure that it is consistent with the experimental data for this chemical reaction.

Examples;

For the balanced chemical reaction; 1/3NO(g) + 1/6O2(g) → 1/3NO2(g), it is found, using experimental

data, that, at a particular temperature, T, the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction, i.e. (-1/(1/3))(d[NO]/dt) = (-1/(1/6))

(d[O2]/dt) = (1/(1/3))(d[NO2]/dt) i.e. - 3d[NO]/dt = - 6d[O2]/dt = 3d[NO2]/dt, is equal to a constant multiplied by [NO]^2[O2] where [NO] and [O2] are the concentrations, at the time, of the elementary chemical reactants NO and O2 respectively.

And it can be shown that a possible chemical reaction mechanism for this balanced chemical reaction involves the 3 balanced elementary chemical reactions; 1/6NO + 1/6NO → 1/6N2O2, xN2O2 → xNO +

xNO and 1/6N2O2 + 1/6O2 → 1/6NO2 + 1/6NO2 and if this is the correct chemical reaction mechanism for this balanced chemical reaction then the constant equals 6k3k1/k2 where k1, k2 and k3 represent k, at the particular temperature, T, for these 3 balanced elementary chemical reactions; 1/6NO

+ 1/6NO → 1/6N2O2, xN2O2 → xNO + xNO and 1/6N2O2 + 1/6O2 → 1/6NO2 + 1/6NO2 respectively.

Note that;

Because k is in units of L^(the number of elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction - 1)mol^(1 - the number of elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction)s^(-1), k1 is in units of Lmol^(-1)s^(-1) since there are 2 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction, k2 is in units of s^(-1) since there is only 1 elementary chemical reactant in the elementary chemical equation for this elementary chemical reaction and k3 is in units of Lmol^(-1)s^(-1) since there are 2 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction.

And so k3k1/k2 is in units of Lmol^(-1)s^(-1) multiplied by units of Lmol^(-1)s^(-1) and divided by units of s^(-1) and so is in units of L^2mol^(-2)s^(-1).

The value, 6 in the formula 6k3k1/k2 is in units of mol^(-1) and so this means that 6k3k1/k2 is in units of mol^(-1) multiplied by units of L^2mol^(-2)s^(-1) and so, like the constant, is in units of L^2mol^(-3)s^(-1).

Also note that;

Because k = Ae^(-Eminimum/RT), k1 = A1e^(-E1minimum/RT), k2 = A2e^(-E2minimum/RT) and k3 = A3e^(-E3minimum/RT) and so 6k3k1/k2 = 6A3e^(-E3minimum/RT)A1e^(-E1minimum/RT)/A2e^(-E2minimum/RT), i.e. 6k3k1/k2 = 6A3A1e^(-E3minimum/RT)e^(-E1minimum/RT)/A2e^(-E2minimum/RT).

And because Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction to react producing one mole of building units of each of the elementary chemical products in the elementary chemical equation for this elementary chemical reaction, E1minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO and one mole of building units of the elementary chemical

reactant NO to react producing one mole of building units of the elementary chemical product N2O2,

E2minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react

producing one mole of building units of the elementary chemical product NO and one mole of building units of

the elementary chemical product NO and E3minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary

chemical reactant N2O2 and one mole of building units of the elementary chemical reactant O2 to react

producing one mole of building units of the elementary chemical product NO2 and one mole of building units of

the elementary chemical product NO2.

In other words, E1minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO and

one mole of building units of the elementary chemical reactant NO to react, E2minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react and E3minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 and one mole of building units of the elementary chemical reactant O2 to react.

In other words, E1minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO to

react plus the minimum amount of non relativistic kinetic energy which would be needed for

one mole of building units of the elementary chemical reactant NO to react, E2minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react and E3minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react plus the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react.

In other words, E1minimum is equal to 2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO to react, E2minimum is equal to 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react and E3minimum is equal to 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical

reactant O2 to react.

And because 6k3k1/k2 = 6A3A1e^(-E3minimum/RT)e^(-E1minimum/RT)/A2e^(-E2minimum/RT), this means that 6k3k1/k2 = 6A3A1e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical

reactant O2 to react)/RT)e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO

to react)/RT)/A2e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to

react)/RT) and so

6k3k1/k2 = 6A3A1e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to

react)/RT)e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one

mole of building units of the elementary chemical reactant O2 to react)/RT)/A2e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant N2O2 to react)/RT) and so

6k3k1/k2 = 6A3A1e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO to

react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react)/RT)/A2 and so

6k3k1/k2, like the constant, contains the constant e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant NO to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical

reactant O2 to react)/RT).

And for the balanced chemical reaction; 1/4O3(g) → 3/8O2(g), it is found, using experimental data, that, at a particular temperature, T, the unique instantaneous rate of this chemical reaction with respect to time at time, t during this chemical reaction, i.e. (-1/(1/4))(d[O3]/dt) = (1/(3/8))(d[O2]/dt) i.e. - 4d[O3]/dt = (8/3)(d[O2]/dt), is equal to a constant multiplied by [O3]^2/[O2] where [O3] and [O2] are the

concentrations, at the time, of the elementary chemical reactants O3 and O2 respectively.

And it can be shown that a possible chemical reaction mechanism for this balanced chemical reaction involves the 3 balanced elementary chemical reactions; 1/8O3 → 1/8O2 + 1/8O, xO2 + xO → xO3 and

1/8O + 1/8O3 → 1/8O2 + 1/8O2 and if this is the correct chemical reaction mechanism for this balanced chemical reaction then the constant equals 8k3k1/k2 where k1, k2 and k3 represent k, at the particular temperature, T, for these 3 balanced elementary chemical reactions; 1/8O3 → 1/8O2 +

1/8O, xO2 + xO → xO3 and 1/8O + 1/8O3 → 1/8O2 + 1/8O2 respectively.

Note that;

Because k is in units of L^(the number of elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction - 1)mol^(1 - the number of elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction)s^(-1), k1 is in units of s^(-1) since there is only 1 elementary chemical reactant in the elementary chemical equation for this elementary chemical reaction, k2 is in units of Lmol^(-1)s^(-1) since there are 2 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction and k3 is in units of Lmol^(-1)s^(-1) since there are 2 elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction.

And so k3k1/k2 is in units of Lmol^(-1)s^(-1) multiplied by units of s^(-1) and divided by units of Lmol^(-1)s^(-1) and so is in units of s^(-1).

The value, 8 in the formula 8k3k1/k2 is in units of mol^(-1) and so this means that 8k3k1/k2 is in units of mol^(-1) multiplied by units of s^(-1) and so, like the constant, is in units of mol^(-1)s^(-1).

Also note that;

Because k = Ae^(-Eminimum/RT), k1 = A1e^(-E1minimum/RT), k2 = A2e^(-E2minimum/RT) and k3 = A3e^(-E3minimum/RT) and so 8k3k1/k2 = 8A3e^(-E3minimum/RT)A1e^(-E1minimum/RT)/A2e^(-E2minimum/RT), i.e. 8k3k1/k2 = 8A3A1e^(-E3minimum/RT)e^(-E1minimum/RT)/A2e^(-E2minimum/RT).

And because Eminimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of each of the elementary chemical reactants in the elementary chemical equation for this elementary chemical reaction to react producing one mole of building units of each of the elementary chemical products in the elementary chemical equation for this elementary chemical reaction, E1minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react producing one mole of building units of the

elementary chemical product O2 and one mole of building units of the elementary chemical product O,

E2minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 and one mole of

building units of the elementary chemical reactant O to react producing one mole of building units of the

elementary chemical product O3 and E3minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O and one mole of building units of the elementary chemical reactant O3 to react producing one mole

of building units of the elementary chemical product O2 and one mole of building units of the elementary

chemical product O2.

In other words, E1minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react,

E2minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 and one mole of

building units of the elementary chemical reactant O to react and E3minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O and one mole of building units of the elementary chemical reactant O3 to react.

In other words, E1minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react,

E2minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react plus the minimum amount of non relativistic kinetic energy which would be needed for one mole of

building units of the elementary chemical reactant O to react and E3minimum is the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the

elementary chemical reactant O to react plus the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react.

In other words, E1minimum is equal to 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react, E2minimum is equal to 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O to

react and E3minimum is equal to 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react.

And because 8k3k1/k2 = 8A3A1e^(-E3minimum/RT)e^(-E1minimum/RT)/A2e^(-E2minimum/RT), this means that 8k3k1/k2 = 8A3A1e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical

reactant O3 to react)/RT)e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3

to react)/RT)/A2e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react

plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O to react)/RT) and so

8k3k1/k2 = 8A3A1e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O to

react)/RT)e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react plus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one

mole of building units of the elementary chemical reactant O3 to react)/RT)/A2e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O to react)/RT)e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react)/RT) and so

8k3k1/k2 = 8A3A1e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to

react)/RT)/A2e^(-(1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react)/RT) and so

8k3k1/k2 = 8A3A1e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react

minus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react)/RT)/A2 and so

8k3k1/k2, like the constant, contains the constant e^(-(2 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O3 to react minus 1 times the minimum amount of non relativistic kinetic energy which would be needed for one mole of building units of the elementary chemical reactant O2 to react)/RT).