Question

The following data were obtained during the first order thermal decomposition of $SO_{2}Cl_{2}$ at a constant volume.
$SO_{2}Cl_{2 \left(g\right)} \rightarrow SO_{2 \left(g\right)}+Cl_{2 \left(g\right)}$

Experiment	Time / $s$	Total pressure/atm
1	0	0.5
2	100	0.6

What is the rate of reaction when total pressure is 0.65 atm?

• A. $0.35$ atm $s^{- 1}$
• B. $2.235\times 10^{- 3}$ atm $s^{- 1}$
• C. $7.8\times 10^{- 4}$ atm $s^{- 1}$
• D. $1.55\times 10^{- 4}$ atm $s^{- 1}$

Answer 1

Answer: (C)

$SO_{2}Cl_{2 \left(g\right)} \rightarrow SO_{2 \left(g\right)}+Cl_{2 \left(g\right)}$
$k=\frac{2.303}{t}\log \frac{p_{0}}{2 p_{0} - P_{t}}$
$=\frac{2.303}{100}\log \frac{0.5}{2 \times 0.5 - 0.6}=\frac{2.303}{100}log ⁡ 1.25$
$=2.2318\times 10^{- 3}s^{- 1}$
Pressure of $SO_{2}Cl_{2}$ at time t $\left(p_{S O_{2} C l_{2}}\right)$
$=2p_{0}-P_{t}=2\times 0.50-0.65$ atm
$=0.35$ atm
Rate of that time $=k\times p_{S O_{2} C l_{2}}$
$=\left(2.2318 \times 1 0^{- 3}\right)\times \left(0.35\right)=7.8\times 10^{- 4}$ atm $s^{- 1}$