Question

Which of the following is the correct pair of inequality for standard molar entropy?
A. $NO(g) < N{O_2}(g)$
B. ${C_2}{H_2}(g) > {C_2}{H_6}(g)$
C. $C{H_3}COOH(l) < HCOOH(l)$
D. $C{O_2}(g) < CO(g)$

Answer 1

Entropy is a measure of the degree of disorder of a substance. In other words, it gives us a value for the randomness of a molecule.So, it tends to increase with molecular mass. Thus, when we are given compounds with the same atoms, the compound with the higher molecular mass will have higher standard molar entropy. In each option here, we just have to compare molecular masses and check if the equality given is correct.

Complete step by step answer:
As we know, entropy is a measure of the degree of disorder/randomness of a particle. And the standard molar entropy is the entropy content of one mole of pure substance under a standard state, usually the standard state being room temperature and pressure. As it is a measure of randomness, more particles and more mass in a molecule will mean that there is more randomness, as the number of states and directions in which the molecules get arranged will increase with the addition of every new atom. Thus, for compounds with similar atoms, standard molar entropy will be higher for the compound with higher molecular mass.
In option A, we see that $N{O_2}$ has a higher molecular mass than $NO$, so it is marked correctly.
In option B, since ${C_2}{H_6}$ has a higher molecular mass than ${C_2}{H_2}$, the higher standard molar entropy should’ve been for ${C_2}{H_6}$, making this option incorrect.
In option C, since $C{H_3}COOH$ has a higher molecular mass than $HCOOH$, the higher standard molar entropy should’ve been for $C{H_3}COOH$, making this option incorrect.
In option D, since $C{O_2}$ has a higher molecular mass than $CO$, the higher standard molar entropy should’ve been for $C{O_2}$, making this option incorrect.

So, the correct answer is “Option A”.

Note: The third law of thermodynamics states that the entropy of a perfectly crystalline solid at absolute zero is zero. This means that entropy decreases as temperature decreases, since the energy possessed by molecules decreases. Also note that the standard molar entropy of gases is more than liquids, which in turn have higher entropy values than solids. This is because the ordering of molecules decreases as we go from solid state to gaseous state, so the entropy increases accordingly.