SO2Cl2 (g) → SO2 (g) + Cl2 (g)

Question

Sulfuroyl chloride (SO₂Cl₂) decomposes with a first order reaction with a rate constant of 0.0450/s at 660. K. If we start with a concentration of SO₂Cl₂ of 0.0200 M in 4.00 L container, how many minutes will it take for there to be 2.80 x 10^-4 mole of SO₂Cl₂ left?

Answer 1

t_1/2 for 1st order reaction = ln 2 / k

t_1/2 = 0.693 / 0.0450 s^-1

t_1/2 = 15.4 s

Also, for a 1st order reaction

Fraction Remaining (FR) = 0.5ⁿ where n = number of half lives exprired

Initial mols SO2Cl2 = 0.0200 mol/L x 4 L = 0.0800 mols

final mols = 2.8x10^-4 mols

FR = 2.8x10^-4 mols / 0.0800 mol = 3.5x10-3 = 0.00350

Solving for n we have...

0.00350 = 0.5ⁿ

n = 8.16 half lives expired

Since each half life = 15.4 s ...

total time = 8.16 half lives x 15.4 s / half life = 125.7 s x 1 min / 60 s = 2.09 minutes