The molar heat capacity for an ideal gas at constant pressure is 20.785 J K⁻¹ mol⁻¹. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is ____________. [Nearest integer] (Given: R=8.314 J K⁻¹ mol⁻¹)

Solution

Chemistry ma’am · 3 steps

Internal energy always goes with Cᵥ, so first take R away from the Cₚ you are given.

1. Find Cv. For an ideal gas, Cₚ - Cᵥ = R. So Cᵥ = 20.785 - 8.314 = 12.471 J K⁻¹ mol⁻¹.

   Δ U = n Cᵥ Δ T

2. Put in numbers. Δ T = 500 - 300 = 200 K. Then n = 5000/(12.471 × 200) = 5000/2494.2 = 2.005.
3. So. The gas contains about 2.005 mol, which rounds to 2.

The common slip: 1. Using Cₚ directly in Δ U = nCΔ T gives n = 5000/(20.785 × 200) = 1.2, which rounds to 1, not 2.

The idea to keep. For an ideal gas, Δ U = nCᵥΔ T and Δ H = nCₚΔ T, whatever the process. If you are given Cₚ but asked about Δ U, use Cᵥ = Cₚ - R first.

Answer from the NTA final answer key. Solution by PrepWiser.