Question

Consider the following first-order thermal decomposition of SO₂Cl₂ at a constant volume.

\[\ce{SO2Cl2_{(g)}->SO2_{(g)} + Cl2_{(g)}}\]

If the total pressure of the gases is found to be 200 torr after 10 seconds and 300 torr upon the complete decomposition of SO₂Cl₂. Calculate the rate constant.

(Given log 3 = 0.4771, log 2 = 0.3010)

Answer 1

Given log 3 = 0.4771, log 2 = 0.3010

\[\ce{SO2Cl2_{(g)}->SO2_{(g)} + Cl2_{(g)}}\]

t = 0	Pi	0	0
On completion	0	Pi	Pi
t = 10 sec	Pi − x	x	x

On completion:

P_T = P_i + P_i

P_T = 2P_i

P_i = `300/2`

= 150 torr

After 10 seconds:

P_T = P_i − x + x + x

x = P_T − P_i

x = 200 − 150

x = 50 torr

First-order integrated rate equation:

k = `2.0303/t  log  (P_i)/(P_i - x)`

= `2.0303/10  log  (150)/(150 - 50)`

= `2.0303/10  log  150/100`

= `2.0303/10  log  3/2`

= `2.0303/10  (log3 - log 2)`

= `2.0303/10  (0.4771 - 0.3010)`

= `2.0303/10 xx 0.1761`

= 0.040 s⁻¹