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Chemistry Question 55 – JEE-MAIN 2026

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

Consider how the phase (gas, liquid, solid) and molecular complexity affect the available degrees of freedom for energy storage.

Step 1: Identify Substances and Phases✦ Active

We need to compare the molar heat capacities (Cp) of Copper(s), Bromine(l), and Helium(g) at 298 K and 1 bar. These represent a solid metal, a diatomic liquid, and a monatomic gas, respectively.

Step 2: Estimate Molar Heat Capacities○ Expand

1. For Helium(g) (monatomic ideal gas), the molar heat capacity at constant pressure is Cp=52R. Using R=8.314 J mol−1 K−1, Cp(He(g))=2.5×8.314≈20.785 J mol−1 K−1. 2. For Copper(s) (metallic solid), according to the Dulong-Petit law, the molar heat capacity is approximately 3R. So, Cp(Cu(s))≈3×8.314≈24.942 J mol−1 K−1. (The actual value for Cu(s) at 298K is around 24.4 J mol−1 K−1). 3. For Bromine(l) (liquid), liquids generally have significantly higher molar heat capacities than simple gases and many solids. This is due to stronger intermolecular forces and more complex vibrational and rotational modes in the liquid phase. The actual Cp for Br2(l) at 298K is approximately 75.7 J mol−1 K−1.

💡 Teacher's Secret Hint

Remember that the Dulong-Petit law is an approximation for solids at room temperature, and ideal gas heat capacities are theoretical values.

Step 3: Determine the Order○ Expand

Comparing the approximate values: Cp(Bromine(l))≈75.7 J mol−1 K−1 Cp(Copper(s))≈24.4 J mol−1 K−1 Cp(Helium(g))≈20.8 J mol−1 K−1 Therefore, the correct order is Bromine(l) > Copper(s) > Helium(g).

💡 Teacher's Secret Hint

The general trend is often Cp(liquid)>Cp(solid)>Cp(gas) when comparing different substances, especially for polyatomic liquids vs. monatomic gases.

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