Question

The decomposition of $Cl_2O_7$ at $400 K$ in the gas phase to $Cl_2$ and $O_2$ is a first order reaction. After $55$ seconds at $400 \,K$ the pressure of $CI_2O_7$ falls from $0.062$ to $0.044 \,atm.$ The rate constant and pressure of $CI_2O_7$ after $100$ sec of decomposition at this temperature are

• A. $5.2 \times 10^{-4} sec^{-1}; 0.05\,atm$
• B. $6.2 \times 10^{-3} sec^{-1}; 0.05\,atm$
• C. $5.8 \times 10^{-3} sec^{-1}; 0.05\,atm$
• D. $4.6 \times 10^{-3} sec^{-1}; 0.05\,atm$

Answer 1

Answer: (B)

The equation for first order reaction is
$K=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$
$\left(i\right)$ Here $a=0.062,a-x=0.044$
$k=\frac{2.303}{55}log\frac{0.062}{0.044}=6.2\times10^{-3}sec^{-1}$
$\left(ii\right)$ Here we are to find the value of $a - x$
$6.2\times10^{-3}=\frac{2.303}{100}log\frac{0.062}{a-x}$
log $\frac{0.062}{a-x}=2.69\times10^{-1}$
$\frac{0.062}{a-x}=1.86$
$a-x=\frac{0.062}{1.80}=0.033$ atm