I am trying to determine the activation energy of the decomposition of hydrogen peroxide with iron(III) chloride added as a catalyst. To do that, I need to find the rate constant, but I am not sure what to do exactly.
What would the rate equation be in this case for me to be able to calculate this?
You should take steps to measure the volume ${V(t)}$ of the oxygen gas $\ce{O2}$ produced by the decomposition reaction vs. time. Do this up to the time when you consider that this volume will not increase any more. This final volume ${V_∞}$ is proportional to the initial $\ce{H2O2}$ concentration, called $c_o$. Now calculate all differences $\Delta V(t) = V_∞ - V(t)$ for all volume measurements. This $\Delta V(t)$ is proportional to the $\ce{H2O2}$ concentration at time $t$.
Then report the successive values of log$\Delta V(t)$ on the $Oy$ axis, and the time $t$ on $Ox$ axis. The points should be alined, and the slope gives you the first order rate constant $k_1$. Repeat the same measurements at different temperatures. If the points are not well alined, report the inverse $1/V(t)$ vs. the time $t$. If this time the points are alined, the reaction is second order with a slope equal to the rate constant $k_2$
When these series of measurements are finished, report the log of the different $k_1$ or $k_2$ values vs. ${1/T}$, where $T$ is the absolute temperature in Kelvin. You should obtain a line with a slope equal to $E_a/R$, where $E_a$ is the activation energy of the reaction.
