Heat of Reaction for Fumarase-Catalyzed Malate→Fumarate Conversion: 04-BS-13, December 2019, Q3

Question 3: Heat of Reaction for Fumarase-Catalyzed Malate→Fumarate Conversion (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Species	$\Delta h_c^\circ$ (kJ/gmol)
Malic acid, $C_4H_6O_5$ (reactant)	−1328.8
Fumaric acid, $C_4H_4O_4$ (product)	−1334.0
Liquid water (product)	0

Find. $\Delta H_{rxn}^\circ$ for malic acid $\rightarrow$ fumaric acid + water.

Approach. Apply Hess's law using heats of combustion: since combusting the reactants and combusting the products both end at the same fully-oxidized reference state (CO₂, H₂O), the heat of reaction is the heat released combusting the reactants minus the heat released combusting the products.

Hess's-law heat of reaction. $$\Delta H_{rxn}^\circ=\sum \Delta h_c^\circ(\text{reactants})-\sum \Delta h_c^\circ(\text{products})$$ $$\Delta H_{rxn}^\circ=(-1328.8)-\big[(-1334.0)+0\big]=-1328.8+1334.0=\boxed{+5.2\ \text{kJ/gmol}}.$$

Quantity	Result
Standard heat of reaction, malate → fumarate + water	+5.2 kJ/gmol (mildly endothermic)

Topic: Hess's-law heat-of-reaction calculation from tabulated heats of combustion.

Key relations: $\Delta H_{rxn}^\circ=\sum\Delta h_c^\circ(\text{reactants})-\sum\Delta h_c^\circ(\text{products})$; fully-oxidized end products (CO₂, liquid H₂O) have $\Delta h_c^\circ=0$ by definition, since they generate no further heat on combustion.

Why this works: both the direct reaction and the "combust everything to CO₂/H₂O" path connect the same reactant and product states to the same final reference state, so their enthalpy changes must be related by simple subtraction (Hess's law / state-function path independence).

Common pitfall: subtracting products minus reactants instead of reactants minus products when using heats of combustion specifically — this is the opposite sign convention from the far more common "heat of formation" version of Hess's law, and mixing the two conventions silently flips the sign of the answer.

Source: Shuler & Kargi, Bioprocess Engineering: Basic Concepts, Ch. 6 (energy balances via heats of combustion, Hess's law).

Question 3 of 9: Heat of Reaction for Fumarase-Catalyzed Malate→Fumarate Conversion

Question 3: Heat of Reaction for Fumarase-Catalyzed Malate→Fumarate Conversion (20 marks)