At -20°C and 1 atm pressure, a cylinder is filled with equal number of H₂,I₂ and HI molecules for the reaction H₂( g)+I₂( g)⇌ 2HI(g), the Kₚ for the process is x× 10⁻¹.
x= __________.
[Given : R=0.082 L atm K⁻¹ mol⁻¹]

Solution

Chemistry ma’am · 3 steps

Equal numbers of molecules mean equal partial pressures, so everything in Kₚ cancels to 1.

1. Equal partial pressures. Partial pressure is proportional to the number of molecules. With equal numbers of H₂, I₂ and HI at a total of 1 atm, each gas has p = 1/3 atm.

   Kₚ = p_(HI)²/(p_(H₂) p_(I₂)) = p²/(p × p) = 1

2. Temperature drops out. For H₂ + I₂ ⇌ 2HI, Δ n_g = 2 - 2 = 0. So Kₚ = K_c(RT)⁰ = K_c. Neither -20°C nor R = 0.082 changes the answer, and both are given only to distract you.
3. So. Kₚ = 1 = 10 × 10⁻¹, which gives x = 10, option (c).

The idea to keep. When Δ n_g = 0, the pressure terms cancel. Then Kₚ depends only on the ratio of amounts, and any T, P or R given in the question does not matter.

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