Chapter 12, Problem 12.56SP

(a)

Interpretation Introduction

Interpretation:

The molarity of butadiene $\left({\text{C}}_{\text{4}}{\text{H}}_{\text{6}}\right)$ after $\text{1}\text{.00 hour}$ reaction time has to be calculated.

Concept introduction:

Integrated rate law for a second order reaction:

A second order reaction is defined as the reaction whose rate depends on the concentration of two reactants raised to the first power or of an only one reactant raised to the second power.

$\text{Rate}\text{=}\text{-}\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}\text{=}\text{k}{\left[\text{A}\right]}^{\text{2}}$

Integrated rate law for a second order reaction is given below

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

(b)

Interpretation Introduction

Interpretation:

The time required to reach the concentration of ${\text{C}}_{\text{4}}{\text{H}}_{\text{6}}$$\text{to}\text{0}\text{.0020}\text{M}$ has to be calculated

Concept introduction:

Integrated rate law for a second order reaction:

A second order reaction is defined as the reaction whose rate depends on the concentration of two reactants raised to the first power or of an only one reactant raised to the second power.

$\text{Rate}\text{=}\text{-}\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}\text{=}\text{k}{\left[\text{A}\right]}^{\text{2}}$

Integrated rate law for a second order reaction is given below

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