Question

What is the enthalpy change for the reaction?
$2A + B \to 2C + 2D$
Use the following data:
Substance $\Delta H_f^0$ (kJ/mol)
A -231
B -393
C +187
D -475

Answer 1

For solving this question we’ll use the Hess Law which states that the enthalpy of a reaction is the difference of the sum of the enthalpies of the product and the sum of the enthalpies of formation of the reactants. The enthalpies are the standard enthalpies of formation denoted by $\Delta H_f^0$

Complete answer:
The reaction given to us is: $2A + B \to 2C + 2D$
The enthalpies of formation given to us are the standard enthalpies of formation of the respective species. Standard enthalpies of formation is the measure when one mole of each of these compounds are formed from one mole of their constituent elements in their pure states. The enthalpy thus obtained is in kilojoules per mole i.e. kJ/mol
The standard enthalpies of formation given to us are:
$A \to - 231kJ/mol$
$B \to - 393kJ/mol$
$C \to + 187kJ/mol$
$D \to - 475kJ/mol$
The overall enthalpy of formation can be found by subtracting the enthalpies of the product with the reactants, this is known as the Hess Law. The enthalpy change can be given by using each individual enthalpy of formation for the products and reactants. Mathematically it can be given as:
$\Delta H_{rxn}^0 = \sum {(n \times \Delta H_{f(products)}^0) - } (m \times \Delta H_{f(reactants)}^0)$
In here, n and m are the no. of moles of each product and reactant respectively. In the given reaction there are 2 moles of C and 2 moles of D formed from 2 moles of A and 1 mol of B.
Substituting the values in the equation we get the overall enthalpy as:
$\sum {\Delta H_{f(product)}^0 = 2 \times 187 + 2 \times ( - 475) = - 576kJ/mol}$
$\sum {\Delta H_{f(reactant)}^0 = 2 \times ( - 231) + 1 \times ( - 391) = - 853kJ/mol}$
Therefore, the overall enthalpy $\Delta H_{rxn}^0 = - 576 - ( - 853)kJ/mol = + 277kJ/mol$
Hence the required answer is +277 kJ/mol.

Note:
If various processes are given to us such as enthalpy of formation, dissociation enthalpy, electron gain enthalpy, etc. then the overall lattice energy is also found by using the Hess Law itself, which will be the sum of all the energies given to us.