Sulfuryl chloride is in equilibrium with sulfur dioxide and chlorine gas: so2cl2 (g) so2 (g) + cl2 (g) a system with a volume of 1.00 l is in equilibrium at a certain temperature with p (so2cl2) = 1.00 bar and p (so2) = p (cl2) = 0.10 bar. by how much will the number of moles of so2cl2 at equilibrium change if the volume is reduced to 0.50 l? (a) increase 1-10% (b) increase 11-50% (c) decrease 1-10% (d) decrease 11-50%

Sulfuryl chloride decreases by - 1/21 (-4.76%) (option c)

Explanation:

Denoting

sc = so2cl2 (g)

s=so2 (g)

c=cl2 (g)

Assuming that the compression is an isothermal process, then reaction equilibrium constant in terms of pressure does not change

Kp = psc/ps*pc =

where p = partial pressures

Assuming ideal behaviour, then from Dalton's law,

Xsc₁=psc₁/P₁ = psc₁/P₁ = 1 bar / (1 bar + 0.1 bar + 0.1 bar) = 5/6

Xs=ps₁/P₁ = 0.1/1.2=1/12

Xc=pc₁/P₁ = 0.1/1.2=1/12

since Xs=Xc → the reaction started as pure Sulfuryl chloride. Then representing ξ as the extent of reaction and n as the moles

nsc=nsc₀ * (1-ξsc), ns=nsc₀*ξsc, nc=nsc₀*ξsc → n=nsc + ns + nc = nsc₀ * (1+ξsc)

therefore

Xs₁=ns₁/n₁=ξsc₁ / (1+ξsc₁) → Xs₁*ξsc₁+Xs₁=ξsc₁ → ξsc₁=Xs₁ / (1-Xs₁) = (1/12) / (11/12) = 1/11

then from the ideal gas law

ps₁*V₁=ns₁*R*T

after the reduction

ps₂V₂=ns₂*R*T

dividing both equations

(ps₂/ps₁) * (V₂/V₁) = (ns₂/ns₁) = nsc₀*ξsc₂ / (nsc₀*ξsc₁) = ξsc₂/ξsc₁

ps₂ = ps₁ * (V₁/V₂) * (ξsc₂/ξsc₁)

since

psc₁*V₁=nsc₁*R*T, psc₂V₂=nsc₂*R*T → psc₂ = psc₁ * (V₁/V₂) * (1-ξsc₂) / (1-ξsc₁)

also knowing that

Kp = psc₁/ps₁² = psc₂/ps₂²

psc₂/ps₂² = psc₁/ps₁² * (V₁/V₂) * (1-ξsc₂) / (1-ξsc₁) / [ (V₁/V₂) * (ξsc₂/ξsc₁) ]² =

1 = (V₂/V₁) (1-ξsc₂) * ξsc₁ / [ (1-ξsc₁) * ξsc₂]

replacing ξsc₁ = 1/11

1 = (V₂/V₁) (1-ξsc₂) / ξsc₂ * (1/10)

10 = (V₂/V₁) * (1/ξsc₂-1) → ξsc₂ = 1 / (10 * (V₁/V₂) + 1)

therefore the extent of reaction varies with the volume reduction according to

ξsc₂ = 1 / (10 * (V₁/V₂) + 1)

since V₁/V₂=2

ξsc₂ = 1 / (10*2+1) = 1/21

therefore the decrease in moles of Sulfuryl chloride is

Δnsc/nsc₁ = (ξsc₂-ξsc₁) / (1-ξsc₁) = (1/21-1/11) / (10/11) = (11/21-1) / 10 = - 1/21 (-4.76%)