The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5×10−2s−1.?

a)
For the reaction is first order:
ln[P(SO₂Cl₂)ₒ / P(SO₂Cl₂)] = (4.5 × 10⁻² s⁻¹) t

When P(SO₂Cl₂)ₒ = 420 torr and t = 63s :
ln[(420 torr) / P(SO₂Cl₂)] = (4.5 × 10⁻² s⁻¹) × (63s)
(420 torr) / P(SO₂Cl₂) = e^(4.5 × 10⁻² × 63)
P(SO₂Cl₂) = 420 / e^(4.5 × 10⁻² × 63) torr
P(SO₂Cl₂) = 24.7 torr

Partial pressure of SO₂Cl₂ at 63 s = 24.7 torr


b)
When P(SO₂Cl₂) = (1/10) P(SO₂Cl₂)ₒ :
P(SO₂Cl₂)ₒ / P(SO₂Cl₂) = 10

As ln[P(SO₂Cl₂)ₒ / P(SO₂Cl₂)] = (4.5 × 10⁻² s⁻¹) t
ln(10) = (4.5 × 10⁻² s⁻¹) t
t = ln(10) / (4.5 × 10⁻² s⁻¹)
t = 51.2 s