At 1990 K and 1 atm pressure, there are equal number of Cl₂, molecules and Cl atoms in the reaction mixture. The value of Kₚ for the reaction Cl 2 (g) ⇌ 2Cl (g) under the above conditions is x × 10⁻¹.
The value of x is _______. (Rounded off to the nearest integer)

Solution

Chemistry ma’am · 3 steps

Equal numbers means equal mole fractions, so at 1 atm each gas is at exactly half an atmosphere.

1. Mole fractions. The mixture has equal numbers of Cl₂ molecules and Cl atoms. So each mole fraction is 1/2.
2. Partial pressures. Partial pressure is mole fraction times total pressure. With a total of 1 atm, p_(Cl) = p_(Cl₂) = 0.5 atm.

   Kₚ = (p_(Cl))²/p_(Cl₂) = (0.5)²/0.5 = 0.5 atm

3. So. Kₚ = 0.5 = 5 × 10⁻¹, so x = 5.

The common slip: 10. Forgetting to square p_(Cl) for the coefficient 2 gives Kₚ = 1 = 10 × 10⁻¹, so x = 10, not 5.

The idea to keep. Turn a particle ratio into mole fractions, multiply by the total pressure to get partial pressures, then raise each one to its stoichiometric coefficient in Kₚ.

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