Question

The correct order of molar heat capacities measured at 298 K and 1 bar is :

• A. Copper(s) >Bromine(l) >Helium(g)
• B. Bromine(l) >Copper(s) >Helium(g)
• C. Helium(g) >Bromine(l) >Copper(s)
• D. Helium(g) >Bromine(l) $=$ Copper(s)

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Molar heat capacity ($C_m$) depends on the degrees of freedom available to the substance in its current phase (solid, liquid, or gas) and its molecular complexity.
Step 2: Detailed Explanation:
1. Helium (g): Helium is a monatomic gas. Its molar heat capacity at constant pressure ($C_{p,m}$) is approximately $\frac{5}{2}R \approx 20.8 \text{ J mol}^{-1}\text{ K}^{-1}$.
2. Copper (s): According to the Dulong-Petit Law, the molar heat capacity of most solid elements is approximately $3R \approx 24.9 \text{ J mol}^{-1}\text{ K}^{-1}$.
3. Bromine (l): Bromine is a liquid at room temperature and is diatomic ($Br_2$). Liquids generally have much higher molar heat capacities than solids or gases because they possess many vibrational, translational, and rotational modes, along with strong intermolecular interactions. For Bromine (l), $C_{p,m} \approx 75.7 \text{ J mol}^{-1}\text{ K}^{-1}$.

Comparing the values: $75.7>24.9>20.8$.
Therefore, the order is Bromine(l) >Copper(s) >Helium(g).
Step 3: Final Answer:
The correct order of molar heat capacities is Bromine(l) >Copper(s) >Helium(g).