gas mixtures because the gas laws apply to ideal gases, they also apply to gas mixtures. laws...

Gas MixturesBecause the gas laws apply to ideal gases, they also apply to gas mixtures. Laws frequently used:

• Ideal gas law

• Dalton’s Law for partial pressures(including mole fraction)

Collection of Gases By Water Displacement

Example: 2KClO3(g) 2KCl(s) + 3O2(g)

Dalton’s Law of Partial Pressures

Dalton’s Law (based on Avogadro’s Law)

For two gases in a mixture:

Ptotal = total gas pressure

PA = partial pressure of gas ‘A’ (etc.)

Ptotal = PA + PB + ....

The total pressure of a gas mixture is the sum of the partial pressures of the components of the gas.

Dalton’s Law

PN2 = 0.78 atm

PO2 = 0.21 atm

Example:• air is 78% N2, 21% O2, and 1% other gases. At 1 atm:

Example - 1

A mixture of gases in scuba diving tank: (at 25oC, 1atm)He...... 46 L O2...... 12 L tank

volume = 5.0 L

¿

(a)partial pressure of each gas?

(b)total pressure inside tank?

Strategy – for (a)

(i) to use PV = nRT, we need the number of moles of each.

(ii) then we can determine the partial pressure for each

A mixture of gases in scuba diving tank: (at 25oC, 1atm)He...... 46 L O2...... 12 L tank volume = 5.0 L

¿

(i) number of moles of each gas?

(ii) partial pressure of each gas?

(a) partial pressure of each gas?

A mixture of gases in scuba diving tank: (at 25oC, 1atm)He...... 46 L O2...... 12 L tank volume = 5.0 L

¿

(b) total pressure inside tank?

Ptotal = PA + PB + ....

Ptotal = 9.3 atm + 2.4 atm = 11.7 atm

Example - 2Potassium chlorate (KClO3) was heated in a test tube and decomposed by the following reaction:

¿Question:

a. What is the partial pressure of O2 in the gas collected?

b. What was the mass of KClO3 in the original sample?

2KClO3(s) 2KCl(s) + 3O2(g)

The oxygen is collected by water displacement at 22oC, at a total pressure of 754 torr, for a total volume of 0.650 L. (PH2O = 21 torr.)

¿

2KClO3(s) 2KCl(s) + 3O2(g)

(a) What is the PO2?

Ptotal = PO2 + PH2O

PO2 = 754 torr – 21 torr = 733 torr

¿

2KClO3(s) 2KCl(s) + 3O2(g)

(b) What was the mass of KClO3 in the original sample?

iii. Number of moles of O2

ii. Number of moles of KClO3 / i. Grams KClO3

Example - 3Two bulbs are separated by a valve.

¿

Bulb Gas Pinit Vinit

A Ne 1.09 atm 1.12 LB CO 0.773 atm 2.18 L

When the valves are opened, and the gases are allowed to reach equilibrium, what is the final pressure inside the bulbs?

(Assume constant temperature.)

¿

Strategy

(iv) Final pressure

(iii) pressure from PV = nRT (Ttotal = VA + VB + VC)

(ii) total number of moles (ntotal = nA + nB + nC)

(i) mole of each gas

¿

(i) mole of each gas:

(ii) total moles:

(We don’t know Temp, but RT will cancel when calculating Ptotal)

¿

(iii) PTotal:

Mole Fraction

The ratio of the number of moles of given component in a mixture to the total number of moles in the mixture.

for component gas, A:

Combining ideal gas laws for both, and cancelling out R, V and T, and rearrange:

The fraction is called the mole fraction of A (= XA)

PA = Xa

Ptotal