By Riti Gupta, Updated Mar 24, 2022

Understanding molar heat capacity is essential for thermodynamics calculations. It tells you how much energy is required to raise the temperature of one mole of a substance by one degree Celsius or Kelvin.

What Is Molar Heat Capacity?

Molar heat capacity (C) is defined as the amount of heat needed to raise the temperature of one mole of a substance by 1 K:

C = (specific heat) × (molar mass)

How to Compute It

1. Find the substance’s specific heat (J g⁻¹ K⁻¹).

2. Multiply by its molar mass (g mol⁻¹).

This yields C in units of J mol⁻¹ K⁻¹.

Example: Water

Specific heat of water = 4.18 J g⁻¹ K⁻¹.

Molar mass of water = 18.0 g mol⁻¹.

Therefore, C = 4.18 × 18.0 = 75.2 J mol⁻¹ K⁻¹.

Example: Methane (CH₄)

Specific heat = 2.20 J g⁻¹ K⁻¹; molar mass = 16.04 g mol⁻¹.

So, C = 2.20 × 16.04 = 35.3 J mol⁻¹ K⁻¹.

Using Molar Heat Capacity to Find Heat Energy

The heat (q) required to change temperature is given by:

q = n C ΔT

• n = number of moles
• C = molar heat capacity (J mol⁻¹ K⁻¹)
• ΔT = temperature change (K)

Example: Heating 5 mol of mercury by 10 K.

Specific heat of mercury = 27.8 J mol⁻¹ K⁻¹.

q = 5 mol × 27.8 J mol⁻¹ K⁻¹ × 10 K = 1 390 J.

Reversing the Equation: Finding Amount of Substance

If you know q, C, and ΔT, you can solve for n:

n = q / (C ΔT)

Example: A calcium carbonate sample absorbs 550 J when its temperature rises 5 K, with C = 82 J mol⁻¹ K⁻¹.

n = 550 J / (82 J mol⁻¹ K⁻¹ × 5 K) = 1.34 mol.

These equations allow you to determine any one of the four variables—q, n, C, ΔT—once the other three are known.