Question

If the heat change at constant volume for decomposition of silver oxide is 80.25 kJ. What will be the heat change at constant pressure?

(A) 80.25 kJ
(B) > 80.25 kJ
(C) < 80.25 kJ
(D) 160.50 kJ

Answer 1

Hint: Write down the decomposition reaction of silver oxide to find the number of moles of gaseous products formed. Now apply the first law of thermodynamics to find the value of heat change at constant pressure. Heat change at constant pressure is the change in enthalpy for the reaction.
Formula: $\Delta \text{H = }\Delta U\text{ + }\Delta {{\text{n}}_{g}}\text{RT}$
Where,
$\Delta \text{H}$ is the change in enthalpy for the reaction,
$\Delta U$ is the change in internal energy,
$\Delta {{\text{n}}_{g}}$ is the difference of gaseous molecules on the product side and reactant side,
R is the universal gas constant,
T is the temperature at which the reaction is carried out.

Complete step by step answer:
The first law of thermodynamics is a version of the law of conservation of energy, applied for thermodynamic processes, distinguishing the two kinds of transfer of energy, namely heat and thermodynamic work, and relating them to a function of the body's state, called Internal energy.
The heat change at constant volume is equal to change in internal energy($\Delta U$). Similarly, the heat change at constant pressure is equal to change in enthalpy for the reaction($\Delta \text{H}$).
The decomposition reaction of silver oxide is given below:
$A{{g}_{2}}{{O}_{(s)}}\text{ }\to \text{ 2}A{{g}_{(s)}}\text{ + }\dfrac{1}{2}{{O}_{2}}_{(g)}$

$\Delta {{\text{n}}_{g}}$ for the above reaction is 0.5.
Substituting the values of $\Delta {{\text{n}}_{g}}$ and $\Delta U$, we get:
$\Delta \text{H = }\Delta U\text{ + }\Delta {{\text{n}}_{g}}\text{RT}$
$\Delta \text{H = 80}\text{.25 + 0}\text{.5RT}$

Since the terms on the right-hand side are positive, the value of $\Delta \text{H}$is greater than 80.25.
So, the correct answer is “Option B”.

Note: Before applying the first law of thermodynamics to a reaction, we make the following assumptions:
-Mass flows in or out of the system along one boundary of the system only.
-The rate of flow of mass into the system is taken as negative and mass flow out of the system is taken as positive.
-Mass can carry the internal energy into or out of the thermodynamic system.