For reaction : SO₂( g)+1/2O₂( g)⇌ SO₃( g)
Kₚ=2× 10¹² at 27°C and 1 atm pressure. The K_c for the same reaction is ____________ × 10¹³. (Nearest integer)
(Given R=0.082 L atm K⁻¹ mol⁻¹)

Solution

Chemistry ma’am · 4 steps

Find Δ n_g first. Here it is negative, so K_c comes out bigger than Kₚ.

1. Count gas moles. Products have 1 mol of gas. Reactants have 1 + 1/2 = 1.5 mol. So Δ n_g = 1 - 1.5 = -1/2.

   Kₚ = K_c (RT)^(Δ n_g) ⇒ K_c = Kₚ (RT)^(1/2)

2. Find RT. Convert to kelvin: T = 27 + 273 = 300 K. Then RT = 0.082 × 300 = 24.6, and √24.6 ≈ 4.96.
3. Put in numbers. K_c = 2 × 10¹² × 4.96 = 9.92 × 10¹² = 0.992 × 10¹³.
4. So. K_c ≈ 1 × 10¹³, and the answer is 1.

The common slip: 0. Taking Δ n_g as +1/2 divides by √RT instead of multiplying. That gives 4.0 × 10¹¹, which is 0 in units of 10¹³.

The idea to keep. Always count Δ n_g as gaseous products minus gaseous reactants, fractions included. If it is negative, K_c is larger than Kₚ.

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