Q.The decomposition of $Cl_2O_7$ at 500 K in the gas phase to $Cl_2$ and $O_2$ is a first order reaction. After 1 minute at 500 K, the pressure of $Cl_2O_7$ falls from 0.08 to 0.04 atm. Calculate the rate constant in $s^{-1}$.

A first order reaction has $\text{Rate}=k[A]^1$. Integrating $-d[A]/dt=k[A]$ gives $\ln\dfrac{[A]_0}{[A]}=kt$, or in base-10 form, $k=\dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}$ -- the single most-used formula in this chapter. Rearranged as $\ln[A]=-kt+\ln[A]_0$, a plot of $\ln[A]$ against time is a straight line with NEGATIVE slope $-k$, the standard test for first order behaviour. Real examples include decomposition of $N_2O_5$, $SO_2Cl_2$ and $H_2O_2$, and cyclopropane's isomerisation. …