Thermochemistry

Most chemical changes that we observe occur at constant pressure. The enthalpy change in reactions D_rH or D_rxnH is a quantitative measure of the heat released or absorbed during the chemical change. Thermochemistry is the branch of thermodynamics that concerns the measurement (and calculation) of the heat of chemical reactions. We can define two categories of reactions

Exothermic reactions release heat

Endothermic reactions absorb heat

By definition D_rH = H_products – H_reactants.

For an exothermic reaction H_products < H_reactants and therefore D_rH < 0.

For an endothermic reaction H_products > H_reactants and therefore D_rH > 0.

Following McQuarrie and Simon we consider two reactions:

The combustion of methane (exothermic)

CH₄ (g) + 2 O₂ (g) ® CO₂ (g) + 2 H₂O (g)

D_rH = - 890 kJ/mole

The water-gas reaction (endothermic)

C (s) + H₂O (g) ® CO (g) + H₂ (g)

D_rH = + 131 kJ/mole

The enthalpy is a state function. Therefore, enthalpies are additive in chemical equations. We can consider individual steps in the formation of CO₂. Each of them has an associated enthalpy

C (s) + ½ O₂ (g) ® CO (g) D_rH = - 110 kJ/mole

CO (g) + ½ O₂ (g) ® CO₂ (g) D_rH = - 283 kJ/mole

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C (s) + O₂ (g) ® CO₂ (g) D_rH = - 393 kJ/mole

The additivity is known as Hess’ Law. If the values of D_rH(1) and D_rH(2) are known then we do not need to measure D_rH(3) provided D_rH(1) + D_rH(2) = D_rH(3).

Hess’ Law also leads to the result that

D_rH(reverse) = -D_rH(forward)

The standard reaction enthalpy D_rH^o refers to the enthalpy change associated with one mole of a specified reagent when all reactants and products are in their standard states. For a gas the standard state is defined as one bar of pressure and the temperature of interest. The standard state of a solid is the pure crystalline substance at one bar of pressure and the temperature of interest.

The standard enthalpy of formation D_fH^o is the standard reaction enthalpy for the formation of one mole of a molecule from its constituent elements. The degree superscript tell us that all of the elements are in their standard states.

Standard reaction enthalpies can be calculated from standard heats of formation using Hess’ Law. In general for a reaction with stoichiometric coefficients a, b, g, d.

aA + bB ® gC + dD

D_rH^o = gD_fH^o(C) + dD_fH^o(D) - aD_fH^o(A) + bD_fH^o(B)

While enthalpy is an extensive quantity D_rH in general, the standard reaction enthalpy D_rH is molar quantity and is intensive. It is intensive because it is defined on a “per mole” basis.

There are subscripts to define the enthalpy change for various processes. Examples of these are

vap vaporization

sub sublimation

fus fusion, melting

mix mixing of fluids

ads adsorption

c combustion

f formation

The temperature dependence of D_rH is given in terms of the heat capacities of the products and reactants. For the general reaction written above aA + bB ® gC + dD, we can express D_rH at temperature T as follows

D_rH(T) = g[D_cH(T) - D_cH(0)] + d[D_dH(T) - D_dH(0)]

- a[D_aH(T) - D_aH(0)] + b[D_bH(T) - D_bH(0)].

For each temperature dependent enthalpy term we can write

As we saw above. Thus, the temperature dependence of the enthalpy of the reaction can be expressed compactly as

DC_p(T) = gC_p,c(T) + dC_p,d(T) - aC_p,a(T) + bC_p,b(T)

Example: The Metabolism of Glycine

The biochemical reactions necessary to sustain life in a person produce about 6000 kJ/day of heat at constant pressure. This is the basal metabolic rate. Depending on level of activity 8000 to 12,000 kJ/day may be required in the form of food to replenish a person’s energy requirement (a nutrionist’s Cal is a chemist’s kcal = 4.184 kJ). Each gram of protein or carbohydrate provides about 15 kJ/g and fat provides about 35 kJ/g.

Let us consider the energy that can be extracted from the metabolism of the amino acid glycine (NH₂CH₂COOH). The oxidation of solid glycine at 25^o C to form CO₂, NH₃, and H₂O is given below:

(1) 3 O₂ (g) + 2 NH₂CH₂COOH (s) ® CO₂ (g) + 2 H₂O (l) + 2 NH₃(g) DH₁ = -1163.5 kJ/mol

The standard enthalpy for the hydrolysis of urea is:

(2) H₂O (l) + H₂NCONH₂ (s) ® CO₂ (g) + 2 NH₃ (g) DH₂ = 133.3 kJ/mol

If we subtract these two reactions, treating them as thermochemical reactions we obtain

(3) 3 O₂ + 2 NH₂CH₂COOH (s) ® H₂NCONH₂ (s) + 3 CO₂ (g) + 3 H₂O (l) DH₃ = -1296.8 kJ/mol

The above equation is of biochemical interest, because urea rather than ammonia is the main oxidative product of amino acid metabolism. However, the biological reaction does not involve solid glycine and solid urea but rather aqueous solutions. Therefore, we note that standard enthalpy of solution of urea and glycine.

(4) NH₂CH₂COOH (s) ® NH₂CH₂COOH (aq) DH₄ = +15.7 kJ/mol

(5) H₂NCONH₂ (s) ® H₂NCONH₂ (aq) DH₅ = +13.9 kJ/mol

Note that we have used the limiting enthalpy of solution which implies that the solid substances are dissolved in an infinite amount of liquid water. It is assumed that these enthalpies do not depend strongly on concentration.

We now subtract two times equation (4) and add equation (5) to equation (3). Note that there are two moles of glycine on the left-hand side of the equilibrium in (3) so that to apply Hess’s Law we must multiply the molar reaction in Eqn. 4 by the factor 2.

Solvated Equation for Biological Oxidation of Glycine = Eqn. (3) – 2 x Eqn. (4) + Eqn. (5)

(6) 3 O₂ + 2 NH₂CH₂COOH (aq) ® H₂NCONH₂ (aq) + 3 CO₂ (g) + 3 H₂O (l)

DH₆ = DH₃ –2 DH₄ + DH₅ =(-1296.8 kJ/mol) – 2(15.7 kJ/mol) + (13.9 kJ/mol)

DH₆ = -1314.3 kJ/mol

Do not be confused by the stoichiometric coefficients in the reactions. The enthalpies given refer to the heat released or absorbed per mole for the reaction as written. For example, Eqn. 3 is written in terms of moles of urea produced and therefore two moles of glycine are consumed in this reaction. We could have written it instead in terms of the number of moles of glycine consumed, however, we would need to modify the enthalpy by the appropriate factor in order to obtain the correct amount of heat released.

3/2 O₂ + NH₂CH₂COOH (s) ® ½ H₂NCONH₂ (s) + 3/2 CO₂ (g) + 3/2 H₂O (l) ½ DH₆ = -648.4 kJ/mol