Order of Molar Heat Capacities at Standard Conditions

To determine the correct order of molar heat capacities at constant pressure ($C_{p,m}$) measured at standard conditions ($298\text{ K}$ and $1\text{ bar}$), we analyze the degrees of freedom and heat capacity values for each substance:

1. Helium gas ($\text{He}, g$): Helium is a monoatomic ideal gas. It possesses only 3 translational degrees of freedom. Its molar heat capacity at constant pressure is given by: $C_{p,m}(\text{He}, g) = \frac{5}{2} R = 2.5 \times 8.314\text{ J mol}^{-1}\text{K}^{-1} \approx 20.79\text{ J mol}^{-1}\text{K}^{-1}$

2. Copper solid ($\text{Cu}, s$): According to the Dulong–Petit Law, the molar heat capacity of simple monoatomic solids near room temperature is approximately $3R$: $C_{p,m}(\text{Cu}, s) \approx 3R \approx 3 \times 8.314\text{ J mol}^{-1}\text{K}^{-1} \approx 24.47\text{ J mol}^{-1}\text{K}^{-1}$

3. Bromine liquid ($\text{Br}_2, l$): Liquid bromine consists of diatomic $\text{Br}_2$ molecules. Liquids possess translational, rotational, vibrational, and significant structural/intermolecular degrees of freedom. Consequently, liquids generally exhibit higher heat capacities than monoatomic gases and crystalline solids. The experimental molar heat capacity of liquid bromine is: $C_{p,m}(\text{Br}_2, l) \approx 75.7\text{ J mol}^{-1}\text{K}^{-1}$

Comparing the molar heat capacities: $75.7\text{ J mol}^{-1}\text{K}^{-1} > 24.47\text{ J mol}^{-1}\text{K}^{-1} > 20.79\text{ J mol}^{-1}\text{K}^{-1}$

Therefore, the correct order of molar heat capacity is: $\text{Bromine}(l) > \text{Copper}(s) > \text{Helium}(g)$

Hence, the correct option is B.