Chapter 14.6, Problem 2CYU

(a)

Interpretation Introduction

Interpretation: The overall equation has to be given.

Concept introduction:

Molecularity: Elementary steps of a chemical reaction are classified by the number of reactant molecules (or ions, atoms, or free radicals) that come together.  The whole, positive number is called the molecularity of the elementary step.

Rate equations for elementary steps: The rate equation for elementary step is defined by its reaction stoichiometry.

  $\begin{array}{l}\text{Elementary}\text{step:}\text{A}\to \text{Product}\text{.}\\ \text{Rate}\text{equation:}\text{Rate}\text{=}\text{k[A]}\end{array}$

Answer to Problem 2CYU

The overall reaction is:$\text{overall:}{\text{2NH}}_{\text{3}}{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq)}}\stackrel{}{\to }{\text{ N}}_{\text{2}}{\text{H}}_{\text{4}}{}_{\text{(aq)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{ (l)}}{\text{+ Cl}}^{\text{-}}{}_{\text{(aq)}}$

Explanation of Solution

The overall reaction is given as,

  $\begin{array}{l}\text{Overall reaction:}Thesumofelementarysteps:\\ \underset{\_}{\begin{array}{l}\underset{\_}{\begin{array}{l}\text{Step}\text{1}:\text{Fast}{\text{NH}}_3{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq) }}\stackrel{}{\to }\cancel{{\text{NH}}_2{\text{Cl}}_{\text{(aq)}}}\text{ + }\cancel{{\text{OH}}^{-}{(aq)}_{}}\\ \text{Step}\text{2:}\text{Slow}\cancel{{\text{NH}}_2{\text{Cl}}_{\text{(aq)}}}{\text{ + NH}}_3{}_{\text{(aq)}}\to \cancel{{\text{N}}_2{\text{H}}_5^{+}{}_{\text{(aq)}}}\text{+ C}{l}^{-}{}_{\text{(aq)}}\\ \text{step 3: Fast }\cancel{{\text{N}}_2{\text{H}}_5^{+}{}_{\text{(aq)}}}+\cancel{{\text{OH}}^{-}{}_{\text{(aq)}}}\to {\text{ N}}_2{\text{H}}_4{}_{\text{(aq)}}{\text{ + H}}_2{\text{O }}_{\text{(l)}}\end{array}}\\ \text{overall:}2{\text{NH}}_3{}_{\text{(aq)}}\text{ + }OC{l}^{-}{}_{\text{(aq)}}\to {\text{ N}}_2{\text{H}}_4{}_{\text{(aq)}}{\text{ + H}}_2{\text{O}}_{\text{ (l)}}\text{+ C}{l}^{-}{}_{\text{(aq)}}\end{array}}\end{array}$

The overall reaction is:$\text{overall:}{\text{2NH}}_{\text{3}}{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq)}}\stackrel{}{\to }{\text{ N}}_{\text{2}}{\text{H}}_{\text{4}}{}_{\text{(aq)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{ (l)}}{\text{+ Cl}}^{\text{-}}{}_{\text{(aq)}}$

(b)

Interpretation Introduction

Interpretation: The rate determining step has to be given.

Concept introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time.  The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Answer to Problem 2CYU

Step 2 is the rate determining step.

Explanation of Solution

The overall reaction is given as,

  $\begin{array}{l}\text{Overall reaction:}Thesumofelementarysteps:\\ \underset{\_}{\begin{array}{l}\underset{\_}{\begin{array}{l}\text{Step}\text{1}:\text{Fast}{\text{NH}}_3{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq) }}\stackrel{}{\to }\cancel{{\text{NH}}_2{\text{Cl}}_{\text{(aq)}}}\text{ + }\cancel{{\text{OH}}^{-}{(aq)}_{}}\\ \text{Step}\text{2:}\text{Slow}\cancel{{\text{NH}}_2{\text{Cl}}_{\text{(aq)}}}{\text{ + NH}}_3{}_{\text{(aq)}}\to \cancel{{\text{N}}_2{\text{H}}_5^{+}{}_{\text{(aq)}}}{\text{+ Cl}}^{\text{-}}{}_{\text{(aq)}}\\ \text{step 3: Fast }\cancel{{\text{N}}_2{\text{H}}_5^{+}{}_{\text{(aq)}}}+\cancel{{\text{OH}}^{-}{}_{\text{(aq)}}}\to {\text{ N}}_2{\text{H}}_4{}_{\text{(aq)}}{\text{ + H}}_2{\text{O }}_{\text{(l)}}\end{array}}\\ \text{overall:}2{\text{NH}}_3{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq)}}\to {\text{ N}}_2{\text{H}}_4{}_{\text{(aq)}}{\text{ + H}}_2{\text{O}}_{\text{ (l)}}{\text{+ Cl}}^{\text{-}}{}_{\text{(aq)}}\end{array}}\end{array}$

The rate determining step:

The rate of overall reaction is controlled by the slowest step in the mechanism. So, the step 2 is the slowest step which determines the rate of overall reaction.

(c)

Interpretation Introduction

Interpretation: The rate equation for the rate determining step has to be given.

Concept introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time.  The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of $\text{mol/(L}\text{.s)}$ .

The variation in concentration of reaction or product over a certain interval of time is called average reaction rate.

The equation that relates the reaction rate to the reactants concentrations that is raised to various powers is called as rate law.

Rate law can be determined by the slow step or otherwise called as rate-determining step.

Explanation of Solution

Rate equation for rate-determining step:

The overall reaction is given as,

  $\begin{array}{l}\text{Overall reaction:The sum of elementary steps:}\\ \underset{\_}{\begin{array}{l}\underset{\_}{\begin{array}{l}\text{Step}\text{1:}\text{Fast}{\text{NH}}_{\text{3}}{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq) }}\stackrel{}{\to }\cancel{{\text{NH}}_{\text{2}}{\text{Cl}}_{\text{(aq)}}}\text{ + }\cancel{{\text{OH}}^{\text{-}}{\text{(aq)}}_{}}\\ \text{Step}\text{2:}\text{Slow}\cancel{{\text{NH}}_{\text{2}}{\text{Cl}}_{\text{(aq)}}}{\text{ + NH}}_{\text{3}}{}_{\text{(aq)}}\stackrel{}{\to }\cancel{{\text{N}}_{\text{2}}{\text{H}}_{\text{5}}^{\text{+}}{}_{\text{(aq)}}}{\text{+ Cl}}^{\text{-}}{}_{\text{(aq)}}\\ \text{step 3: Fast }\cancel{{\text{N}}_{\text{2}}{\text{H}}_{\text{5}}^{\text{+}}{}_{\text{(aq)}}}\text{+}\cancel{{\text{OH}}^{\text{-}}{}_{\text{(aq)}}}\stackrel{}{\to }{\text{ N}}_{\text{2}}{\text{H}}_{\text{4}}{}_{\text{(aq)}}{\text{ + H}}_{\text{2}}{\text{O }}_{\text{(l)}}\end{array}}\\ \text{overall:}{\text{2NH}}_{\text{3}}{}_{\text{(aq)}}{\text{ + OCl}}^{\text{-}}{}_{\text{(aq)}}\stackrel{}{\to }{\text{ N}}_{\text{2}}{\text{H}}_{\text{4}}{}_{\text{(aq)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{ (l)}}{\text{+ Cl}}^{\text{-}}{}_{\text{(aq)}}\end{array}}\end{array}$

The rate determining step:

The rate of overall reaction is controlled by the slowest step in the mechanism. So, the step 2 is the slowest step which determines the rate of overall reaction.

The rate equation for the rate determining step is $Rate2:Rate=k\left[{\text{NH}}_2\text{Cl}\right]\left[{\text{NH}}_3\right]$.

(d)

Interpretation Introduction

Interpretation: The reaction intermediates has to be given.

Answer to Problem 2CYU

The reaction intermediates are ${\text{NH}}_2\text{Cl}$ and ${\text{N}}_2{\text{H}}_5^{+}$.

Explanation of Solution

Intermediates are the molecules that are formed from the reactants and reacts to give the products in a chemical reaction.  Hence, the two molecules that are generated in between the reaction and get turned to products are ${\text{NH}}_2\text{Cl}$ and ${\text{N}}_2{\text{H}}_5^{+}$.