Question

The following data were obtained during the first order thermal decomposition of $SO_2$ $Cl_2$ at a constant volume.
$SO_{2}Cl_{2\left(g\right)}\rightarrow SO_{2}+Cl_{2\left(g\right)}$

Experiment	Time/$s^{-1}$	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. $2.235\times10^{-3}$ atm $s^{-1}$
• C. $7.8\times10^{-4}$ atm $s^{-1}$
• D. $1.55\times10^{-4}$ atm $s^{-1}$

Answer 1

Answer: (C)

$SO_{2}Cl_{2}$ $\rightarrow$ $SO_{2}+Cl_{2}$
Initial pressure $\quad$ $p_{0}$ $\quad$ $0$ $\quad$$0$
Pressure at time $t$ $\quad$ $p_{0}-p$ $\quad$ $p$ $\quad$ $p$
Let initial pressure, $P_{0}$ $\propto$ $R_{0}$
Pressure at time $t$, $p_{t}$ $=p_{0}-p+p+p$ $=p_{0}+p$
Pressure of reactants at time $t$, $p_{0}-p$ $=2p_{0}-p_{t}\propto R$
$k=\frac{2.303}{t} log$ $\frac{p_{0}}{2p_{0}-p_{t}}$
$=\frac{2.303}{100} log$ $\frac{0.5}{2\times0.5-0.6}$ $=\frac{2.303}{100} log\, 1.25$
$=2.2318 \times10^{-3}$ $s^{-1}$
Pressure of $SO_{2}Cl_{2}$ at time $t$ $\left(p_{so_2cl_2}\right)$
$=2p_{0}-p_{t}$ $=2\times0.50$ $-0.65 \,atm$ $=0.35 \,atm$
Rate at that time$=k\times p_{so_2 cl_2}$
$=\left(2.2318\times10^{-3}\right)\times\left(0.35\right)$ $=7.8\times10^{-4}$ atm $s^{-1}$