Chapter 12, Problem 12.128CHP

Interpretation Introduction

Interpretation:

The time required to drop the concentration of $N{O}_2$ to $0.0010M$ has to be calculated

Concept introduction:

Rate law: It is an equation that related to the dependence of the reaction rate on the concentration of each substrate (reactants).

For a reaction,

$\text{aA}\text{+}\text{bB}+cC\stackrel{}{\to }\text{Products}$

Where,

A and B are reactants

a and b are stoichiometric coefficients

$\text{Rate}\text{=}\text{-}\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}\text{=}\text{k}{\left[\text{A}\right]}^{\text{x}}{\left[\text{B}\right]}^{\text{y}}{\left[\text{C}\right]}^z$

Where,

k is the rate constant

Activation energy: The minimum amount of energy required to start a given chemical reaction is known as activation energy.

$\begin{array}{c}\text{ln}\left(\frac{{\text{k}}_{\text{2}}}{{\text{k}}_{\text{1}}}\right)\text{=}\left(\frac{-{\text{E}}_{\text{a}}}{\text{R}}\right)\left(\frac{\text{1}}{{\text{T}}_{\text{2}}}-\frac{\text{1}}{{\text{T}}_{\text{1}}}\right)\\ \\ where,\\ E_a=activationenergy \\ {\text{k}}_{\text{1}}{\text{ and k}}_{\text{2}}{\text{ are rate constants at temperatures T}}_{\text{1}}{\text{ and T}}_{\text{2}}\end{array}$

Rate constant: Rate constant is an expression used to relate the rate of a reaction to the concentration of reactants participating in the reaction.

A second order reaction is defined as the reaction whose rate depends on the concentration of both reactants.

$\begin{array}{l}\frac{\text{1}}{\left[\text{A}\right]}\text{=}\text{kt}\text{+}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}\\ \text{where,}\\ {\left[\text{A}\right]}_{\text{0}}\text{-}\text{concentration}\text{of}\text{A}\text{at}\text{time}\text{t}\text{=}\text{0}\\ \left[\text{A}\right]\text{-}\text{concentration}\text{of}\text{A}\text{after}\text{time}\text{t}\\ \text{k}\text{-}\text{rate}\text{constant}\end{array}$