Chapter 12, Problem 12.65SP

(a)

Interpretation Introduction

Interpretation:

The nitrous oxide decomposition is whether zeroth, first or second order reaction has to be determined by plotting appropriate graphs. The value of rate constant of nitrous oxide decomposition reaction has to be determined.

Concept Introduction:

Order of a reaction: Order of a reaction is defined as the sum of exponents of the concentrations in the rate law of the given reaction.

The rate of a reaction is defined by the change in concentration of substrate (reactant) or target (product) with change in time.

$\text{Rate}\text{=}\frac{\text{Concentration}\text{change}\left(\text{in}\text{reactant}\text{or}\text{product}\right)}{\text{Time}\text{change}}$

For a reaction,

• If the plot drawn between concentration of reactant and time is linear, then it is a zeroth order reaction
• If the plot drawn between ln[reactant] and time is linear, then it is a first order reaction
• If the plot drawn between 1/[reactant] and time is linear, then it is a second order reaction
• For the zeroth and first order reaction, the graph has a negative slope whereas the graph has a positive slope for a second order reaction.

(b)

Interpretation Introduction

Interpretation:

The molarity of AB after $\text{192 min}$ has to be calculated.

Concept introduction:

The rate law for a zero order reaction:

A zero order reaction is defined as the reaction whose rate which does not depend on the concentration the reactants.

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

(c)

Interpretation Introduction

Interpretation:

The time required when the AB concentration reaches a value of $0.0250M$ has to be calculated

Concept introduction:

The rate law for a zero order reaction:

A zero order reaction is defined as the reaction whose rate which does not depend on the concentration the reactants.

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