Exploring Engineering

Chapter 5

Chemical energy

What You Will LearnChemical formulae

Atomic and molecular masses The mole/mol and Avogadro’s

number Basic combustion reactions Stoichiometry Tabular method of determining

stoichiometric cfts. Tabular method of solving

combustion problems

The “Mole/Mol” Concept Atoms are the building blocks of matter and

irreducible by chemical methods. A molecule is the smallest possible piece of a

chemical compound. Molecules are made of two or more atoms. Since molecules are extremely small entities,

and so we use large units called “mole or mol” and “kilo-mole or kmol” The unit* is the mole and its symbol is the mol – in

practice used synonymously

* Same concept as force in newtons or N

The Mole In chemical reactions, the identity and

number of atoms, but not molecules, remains constant E.g., S + O2 SO2

For engineering purposes, per atom or molecule basis is way too small

Use either g mole (abbreviated mole or mol) or kg mole (abbreviated kmole or kmol )

We’ll usually use kmol

The Mole The “gram mole” or “mol” is defined to

be the amount of substance containing as many "elementary entities" as there are atoms in exactly 0.012 kg of pure carbon‑12. (The “kmol” is a factor 103 larger)

The relative masses of atoms is called “molecular mass” and commonly but incorrectly “molecular weight”

Molecular massesAtom Molecular

massAtom Molecular

mass

H 1.00 N 14.0

He 4.00 S 32.1

C 12.0 Cl 35.5

O 16.0 Ar 40.0

• All to 3 significant figures

All the atoms: The Periodic Table

Avogadro’s Number The “elementary entities” in pure C-12 are atoms of

carbon defined as exactly mass 12. In exactly 1 mol any “elementary entity” (atoms,

molecules, ions, electrons, etc.) there are 6.0221367 x 1023 atoms. This is Avogadro’s number A kmol is 103 larger. These are sizes interesting

to engineers. Avogadro’s number is to mols as a dozen eggs

is to 12 eggs - a shorthand notation. Just as a dozen eggs may include 5 turkey and 6

chicken eggs and 1 dinosaur egg, the “elementary entities” can include mixtures of molecules, atoms, electrons, neutrons, etc.

Example:

How many kg are there in 1.00 kmol of CO2? How many kmols, mols, and lbm moles are there in 11.0 lbm of CO2?

Need: m (mass) and n (moles) in specified CO2

Know: Atomic masses of C = 12.0, O = 16.0; also 11.0 lbm = 5.00 kg. (Courtesy of Convert.exe)

How: n = m/M where M = molecular mass of CO2

Example: Concluded Solve: M for CO2 = 12.0 + 2 x16.0 = 44.0 kg/kmol or

44.0 lbm/lbm mole, or 44.0 tons/ton mole etc.

Thus 1.00 kg CO2 = 1.00/44.0 [kg][kmol/kg] = 2.27

10-2 kmol

5.00 kg (from 11.0 lbm) into kmols, n = 5.00/44.0 [kg][kmol/kg] = 0.114 kmol or 114 mols

11.0 lbm mols, n = 11.0/44.0 [lbm][lbm mole/lbm] = 0.251 lbm mole

Stoichiometry How much of “A” reacts with “B” according to a

stipulated chemical combustion reaction?

E.g., C2H5OH + aO2 bCO2 + cH2O

C2H5OH is called “ethanol” or “ethyl alcohol” and

popularly just plain “alcohol”.

We are completely combusting the alcohol to carbon dioxide and to water (vapor) in this example.

We need to find unique values of a,b & c that satisfy this equation and preserve the number of C, H and O atoms

This leads to three equations and three unknowns

The Tabular methodC2H5OH + aO2 bCO2 + cH2O. To

solve, the following tabular method is used in this course:

Atoms LHS RHS Solution

C 2 b b = 2

H 6 2c c = 3

O 1 + 2a 2b + c a = 2 + 3/2 - 1/2 = 3

C2H5OH + 3O2 2CO2 + 3H2O

– Visually check that this is correct!

StoichiometryA stoichiometric method is an essential

starting place to calculate fuel-to-air ratios in combustion applications Air is considered to be 79% N2 and 21% O2

in most combustion problems. This works out to 3.76 kmols of N2 per kmol of O2

The mixture of 3.76 kmols of N2 and 1.00

kmol of O2 is 4.76 kmols of air containing

4.76 NAvg (Avogadro’s number)

Energetics of combustionHow much energy released when a fuel

(such as a hydrocarbon) is burned?

Fuel Heating value, kJ/kg

Methane, CH4 55,650 Propane, C3H8 46,390 Isobutane, C4H10 45,660 Gasoline, “C8H18” 45,560 Diesel fuel, “C16H34” 43,980 Benzene, “C6H6” 42,350 Toluene, “C6H5CH3” 42,960

Energetics of combustionFor most simple hydrocarbons with 3 or

more carbon atoms/molecule assume heat of combustion is 45,500 J/mol

Example: If 1.00 kg of gasoline is burned, what is 1) the stoichiometric equation, how many lbm of CO2 is produced and how much heat is generated?

Simplified Combustion Example

Need: For 1 lbm of gasoline combusted what’s stoichiometry. How much CO2

produced and how much thermal energy?

Know: Gasoline modeled by isooctane C8H18 and it produces 45.5 kJ/mol heat

How: C8H18 + aO2 = bCO2 + cH2O

C8H18 + aO2 = bCO2 + cH2O

Atoms LHS RHS Solution

C 8 b b = 8

H 18 2c c = 9

O 2a 2b + c a = 8 + 9 /2 = 25/2

C8H18 + 12.5O2 = 8CO2 + 9H2O CO2 = 8 44.0 = 352 lbm.

Energetics

Item LHS LHS RHS RHS Molar quantities C8H18 O2(g) CO2(g) H2O(g) Mass, kg 114 12.5 32.0 8 44.0 9 18.0 Mass m, kg/kg of fuel 1.00 3.51 3.09 1.42 H, kJ/kg 45.5 0.00 0.00 0.00 m × H kJ/kg of fuel 45.5 0.000 0.00 0.00

Heating Value = Energy in fuel and oxidizer - Energy in the products of combustionHeating value = 45.5 kJ

Simplified Combustion Example

Because we asserted that the heat of combustion was 45.5 kJ/kg the energetics table was mostly filled with zeros But many fuels do not obey this rule and

instead use heats of formation

Heats of formationSubstance kJ/kg Carbon, C (s) 0 Nitrogen, N2 (g) 0 Oxygen, O2 (g) 0 Hydrogen, H2 (g) 0 Carbon Monoxide, CO (g) -3,946 Carbon Dioxide, CO2 (g) -8,942 Water, H2O (g) -13,423 Methane, CH4 (g) -4667 Acetylene, C2H2 (g) +8,720 Hexane, C6H14 (g) -1,945 Ethanol, C2H5OH (l) -5,771 Benzene, C6H6(l) +629

The values in the last column are not uniform in sign.The use of the matrix table in the last example is then Invaluable.

Summary “Elementary entities” means atoms,

molecules, even sub-nuclear particles Every mol has the same enormous number

of such particles (Avogadro’s number) Includes mixtures of molecules such as air

Stoichiometry based on conservation of atoms in a reacting mixture The tabular matrix method allows a solution

of stoichiometric coefficients. A related tabular matrix method allows a

solution of thermal energetics