Question

From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.
(A) $3N{{O}_{\left( g \right)}}\to {{N}_{2}}{{O}_{\left( g \right)}},\text{ }Rate=k{{\left[ NO \right]}^{2}}$
(B) ${{H}_{2}}O_{2\left( aq \right)}^{{}}+3I_{\left( aq \right)}^{-}+2{{H}^{+}}\to 2{{H}_{2}}{{O}_{\left( l \right)}}+3I,~~~Rate=k\left[ {{H}_{2}}{{O}_{2}} \right]\left[ {{I}^{-}} \right]$
(C) $C{{H}_{3}}CH{{O}_{\left( g \right)}}\to C{{H}_{4\left( g \right)}}+C{{O}_{\left( g \right)}},~~~Rate=k{{\left[ C{{H}_{3}}CHO \right]}^{3/2}}$
(D) ${{C}_{2}}{{H}_{5}}C{{l}_{\left( g \right)}}\to {{C}_{2}}{{H}_{4\left( g \right)}}+HC{{l}_{\left( g \right)}},~~~Rate=k\left[ {{C}_{2}}{{H}_{5}}Cl \right]$

Answer 1

Hint : We know that the unit of rate constants changes with change in order. For a second order reaction, the rate is directly proportional to the square of concentration of reactant. Rearranging the formula and putting units of respective known variables we will get the answer.

Complete Step By Step Answer:
Rate of the reaction is defined as the change in concentration of reactant or product per unit time. As the reaction proceeds the concentration of the reactant decreases and the concentration of product increases. The rate of reaction is always positive. We generally study zero to third order reactions. For a zero order reaction the unit of rate and rate constant is the same. Rate of a chemical reaction depends on the concentrations of reactants or products and the time required to complete the chemical change. Rate of a chemical reaction can be defined as the change in concentration of a reactant or product in unit time. Thus, rate of a chemical reaction can be expressed on the basis of following points: The rate of decrease in concentration of any one of the reactants or the rate of increase in concentration of any one of the products Time taken in the change in concentration.
1. $3N{{O}_{\left( g \right)}}\to {{N}_{2}}{{O}_{\left( g \right)}},\text{ }Rate=k{{\left[ NO \right]}^{2}}$
Order w.r.t $NO$ is two and overall order is two and dimensions of the rate constant $\dfrac{mol\text{ }{{L}^{-1}}}{s}=k{{\left( mol\text{ }{{L}^{-1}} \right)}^{2}}$
$\Rightarrow k=mo{{l}^{-1}}{{L}^{1}}{{s}^{-1}}$
2. ${{H}_{2}}O_{2\left( aq \right)}^{{}}+3I_{\left( aq \right)}^{-}+2{{H}^{+}}\to 2{{H}_{2}}{{O}_{\left( l \right)}}+3I,~~~Rate=k\left[ {{H}_{2}}{{O}_{2}} \right]\left[ {{I}^{-}} \right]$
Order w.r.t ${{H}_{2}}{{O}_{2}}$ ​ is one, order w.r.t ${{I}^{-}}$ is one and overall order is two and dimensions of the rate constant;
$\dfrac{mol\text{ }{{L}^{-1}}}{s}=k{{\left( mol\text{ }{{L}^{-1}} \right)}^{2}}$
$\Rightarrow k=mo{{l}^{-1}}{{L}^{1}}{{s}^{-1}}$
3. $C{{H}_{3}}CH{{O}_{\left( g \right)}}\to C{{H}_{4\left( g \right)}}+C{{O}_{\left( g \right)}},~~~Rate=k{{\left[ C{{H}_{3}}CHO \right]}^{3/2}}$
Order w.r.t $C{{H}_{3}}CHO$ is $\dfrac{3}{2}$ and overall order is $\dfrac{3}{2}$ and dimensions of the rate constant:
$\dfrac{mol\text{ }{{L}^{-1}}}{s}=k{{\left( mol\text{ }{{L}^{-1}} \right)}^{\dfrac{3}{2}}}$
$~\Rightarrow k=mo{{l}^{-\dfrac{1}{2}}}\text{ }{{L}^{\dfrac{1}{2}}}\text{ }{{s}^{-1}}$
4. ${{C}_{2}}{{H}_{5}}C{{l}_{\left( g \right)}}\to {{C}_{2}}{{H}_{4\left( g \right)}}+HC{{l}_{\left( g \right)}},~~~Rate=k\left[ {{C}_{2}}{{H}_{5}}Cl \right]$
Order w.r.t $~{{C}_{2}}{{H}_{5}}Cl$ is one, and overall order is one and dimensions of the rate constant $\dfrac{mol\text{ }{{L}^{-1}}}{s}=k{{\left( mol\text{ }{{L}^{-1}} \right)}^{1}}$
$\Rightarrow k={{s}^{-1}}$

Note :
Remember that the rate constant is a constant of proportionality. It depends upon the nature of reaction and temperature. At a constant temperature and at a particular reaction rate constant remains fixed.