Question:
Determine the order of molar heat capacity \( \left(C_m\right) \) of \( \mathrm{Br_2(\ell) \), \( \mathrm{Cu(s)} \) and \( \mathrm{He(g)} \) at \( 298 \, \mathrm{K} \) and \( 1 \, \mathrm{atm} \).
Determine the order of molar heat capacity \( \left(C_m\right) \) of \( \mathrm{Br_2(\ell) \), \( \mathrm{Cu(s)} \) and \( \mathrm{He(g)} \) at \( 298 \, \mathrm{K} \) and \( 1 \, \mathrm{atm} \).
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For rough comparison of molar heat capacities at room temperature: monoatomic gases usually have the lowest values, solids are generally higher, and liquids often have the highest values due to additional intermolecular energy storage.
Updated On: Apr 7, 2026
- \( \mathrm{Br_2(\ell) > He(g) > Cu(s)} \)
- \( \mathrm{Br_2(\ell) > Cu(s) > He(g)} \)
- \( \mathrm{He(g) > Br_2(\ell) > Cu(s)} \)
- \( \mathrm{Cu(s) > Br_2(\ell) > He(g)} \)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding molar heat capacity.
Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by \( 1 \, \mathrm{K} \). Its value depends on the physical state of the substance and the number of ways in which the substance can store thermal energy. In general, gases with very few degrees of freedom have lower molar heat capacity, solids have moderate values, and liquids usually have higher values because of greater intermolecular interactions and more complex energy storage modes.
Step 2: Heat capacity of \( \mathrm{He(g)} \).
Helium is a monoatomic gas. For a monoatomic ideal gas, the molar heat capacity at constant pressure is: \[ C_m = C_P = \frac{5}{2}R \] This is comparatively small because helium atoms can store energy mainly in translational motion only. Therefore, \( \mathrm{He(g)} \) has the lowest molar heat capacity among the given substances.
Step 3: Heat capacity of \( \mathrm{Cu(s)} \) and \( \mathrm{Br_2(\ell)} \).
Copper is a solid metal. For many solid elements at room temperature, the molar heat capacity is close to: \[ C_m \approx 3R \] according to the Dulong--Petit law. So, \( \mathrm{Cu(s)} \) has a higher molar heat capacity than monoatomic helium gas.
Bromine in liquid state, \( \mathrm{Br_2(\ell)} \), has the highest molar heat capacity here. This is because liquid bromine molecules can absorb heat not only through translational, rotational, and vibrational modes, but also through intermolecular interactions present in the liquid state. Hence, liquids generally have greater molar heat capacities than gases and many solids.
Step 4: Comparing all the substances.
So, the correct decreasing order of molar heat capacity is: \[ \mathrm{Br_2(\ell) > Cu(s) > He(g)} \] Thus, option \( (B) \) is correct.
Final Answer: \( \mathrm{Br_2(\ell) > Cu(s) > He(g)} \).
Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by \( 1 \, \mathrm{K} \). Its value depends on the physical state of the substance and the number of ways in which the substance can store thermal energy. In general, gases with very few degrees of freedom have lower molar heat capacity, solids have moderate values, and liquids usually have higher values because of greater intermolecular interactions and more complex energy storage modes.
Step 2: Heat capacity of \( \mathrm{He(g)} \).
Helium is a monoatomic gas. For a monoatomic ideal gas, the molar heat capacity at constant pressure is: \[ C_m = C_P = \frac{5}{2}R \] This is comparatively small because helium atoms can store energy mainly in translational motion only. Therefore, \( \mathrm{He(g)} \) has the lowest molar heat capacity among the given substances.
Step 3: Heat capacity of \( \mathrm{Cu(s)} \) and \( \mathrm{Br_2(\ell)} \).
Copper is a solid metal. For many solid elements at room temperature, the molar heat capacity is close to: \[ C_m \approx 3R \] according to the Dulong--Petit law. So, \( \mathrm{Cu(s)} \) has a higher molar heat capacity than monoatomic helium gas.
Bromine in liquid state, \( \mathrm{Br_2(\ell)} \), has the highest molar heat capacity here. This is because liquid bromine molecules can absorb heat not only through translational, rotational, and vibrational modes, but also through intermolecular interactions present in the liquid state. Hence, liquids generally have greater molar heat capacities than gases and many solids.
Step 4: Comparing all the substances.
So, the correct decreasing order of molar heat capacity is: \[ \mathrm{Br_2(\ell) > Cu(s) > He(g)} \] Thus, option \( (B) \) is correct.
Final Answer: \( \mathrm{Br_2(\ell) > Cu(s) > He(g)} \).
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