Question

For which of the following processes, \[\Delta {\text{S}}\] is negative?
A.\[{{\text{N}}_2}({\text{g}},273{\text{K}}) \to {{\text{N}}_2}({\text{g}},300{\text{K}})\]
B.\[{{\text{N}}_2}({\text{g}},1{\text{ atm}}) \to {{\text{N}}_2}({\text{g}},5{\text{ atm}})\]
C.\[{\text{C}}({\text{diamond}}) \to {\text{C}}({\text{graphite}})\]
D.\[{{\text{H}}_2}({\text{g}}) \to 2{\text{H}}({\text{g}})\]

Answer 1

Hint: \[\Delta {\text{S}}\] represents change in entropy. Entropy increases as we increase the temperature and it decreases as the temperature decreases. With increase in pressure the entropy decreases. While dissociation entropy increases.

Complete step by step solution:
Entropy is the degree of randomness or disorder of the system. The freer a particle is free to move or the more disturbed state it is the more is the entropy. If in a reaction the final entropy of the system is more that the initial then entropy change will be positive.
Let us look at each of the processes one by one:
\[{{\text{N}}_2}({\text{g}},273{\text{K}}) \to {{\text{N}}_2}({\text{g}},300{\text{K}})\]
Here the temperature of the system is increased. We have known in case of gas, as the temperature increases their kinetic energy increases. Hence they will move more freely and there will be more disorder in the system. So final entropy increases and hence the entropy change is positive.
\[{{\text{N}}_2}({\text{g}},1{\text{ atm}}) \to {{\text{N}}_2}({\text{g}},5{\text{ atm}})\]
In the above reaction, we are increasing the pressure of the system. If we increase the pressure, the volume of the system will decrease because according to Boyle’s law the pressure and volume are inversely proportional to each other. When volume decreases then particles will come closer to each other and have less randomness. So the final entropy of the system decreases. Here change in entropy will be negative.
\[{\text{C}}({\text{diamond}}) \to {\text{C}}({\text{graphite}})\]
In the above conversion, carbon in the form of diamond is heated to a very high temperature to convert into carbon in the form of graphite, here also entropy increases.
\[{{\text{H}}_2}({\text{g}}) \to 2{\text{H}}({\text{g}})\]
One mole of hydrogen gas is getting converted to 2 moles of hydrogen atoms. The increase in the number of atoms also increases entropy.

Thus, the correct option is B.

Note: Entropy is a thermodynamic function and is a state function. Entropy is represented by S. it is an extensive property that means it depends upon the number or size and not nature of substance. Entropy of gas is higher than liquid and liquid have higher entropy than solid.