Chapter 13, Problem 13.132CP

Interpretation Introduction

Interpretation:

The first order conversion of a reactant X to products in a reaction vessel with a constant volume of 1 L is being studied. Determine the minimum temperature required to convert all but 0.010 mol of X to products by 4:00 pm.

Concept Introduction:
First order reaction depends only on the concentration of the reactant (only on one reactant concentration). A first order reaction is a uni-molecular reaction which depends on the concentration of only one reactant; other reactants will be of zero order. Reaction of first order kinetics is as follows:
$A=A_o{e}^{-kt}$

Here, A is final rate, A_o is initial rate, k is rate constant and t is the time.
Activation energy ( $E_a$ ) can be defined as a minimum energy that is needed to start a chemical reaction and its formula is as follows:

  $\ln \frac{k_2}{k_1}=\frac{E_a}{R}\left[\frac{1}{T_1}-\frac{1}{T_2}\right]$

Here, $k_2$ is the rate constant at temperature $T_2$ and $k_1$ is rate constant at temperature $T_1$ and R is the gas constant.