Question

sample problem: problem 12.20
entropy - qualitatively
for each of the following pairs of substances, determine which has the larger molar entropy at 298 k and state why.
(a) br₂ and cl₂
(b) ni and pt
(c) c₅h₁₂ and c₈h₁₈ (both liquids)
(d) sif₄ and ch₄ (both gases)

Explanation:

Step1: Consider molar - mass and molecular complexity

In general, for substances in the same physical state, the molar entropy increases with increasing molar mass and molecular complexity.

Step2: Analyze pair (a)

$Br_2$ has a larger molar mass than $Cl_2$. At 298 K, $Br_2$ is a liquid and $Cl_2$ is a gas. But considering just molar - mass and structure in the gaseous state (if both were gases), $Br_2$ would have a larger molar entropy due to its larger molar mass. Since $Br_2$ is a liquid and $Cl_2$ is a gas, $Cl_2$ has a larger molar entropy because gases have higher entropy than liquids due to greater freedom of motion.

Step3: Analyze pair (b)

$Pt$ has a larger molar mass than $Ni$. For metals, the molar entropy increases with increasing molar mass. So, $Pt$ has a larger molar entropy.

Step4: Analyze pair (c)

$C_8H_{18}$ has a more complex molecular structure and a larger molar mass than $C_5H_{12}$. For liquids with similar structures, the one with more atoms and higher molar mass has higher entropy. So, $C_8H_{18}$ has a larger molar entropy.

Step5: Analyze pair (d)

$SiF_4$ has a larger molar mass and more atoms than $CH_4$. For gases, the molar entropy increases with increasing molar mass and molecular complexity. So, $SiF_4$ has a larger molar entropy.

Answer:

(a) $Cl_2$ because gases have higher entropy than liquids and even if both were gases, $Br_2$ has a larger molar mass but the gas - phase entropy contribution dominates.
(b) $Pt$ due to its larger molar mass.
(c) $C_8H_{18}$ due to its greater molecular complexity and larger molar mass.
(d) $SiF_4$ due to its larger molar mass and more atoms.