Question

Calculate the rate constant of a reaction at 293K when the energy of activation is ${{103\,kJ}}\,{{mo}}{{{l}}^{{{ - 1}}}}$ and the rate constant at 273 K is \[{{7}}{{.87 \times 1}}{{{0}}^{{{ - 7}}}}{{{s}}^{{{ - 1}}}}{{, R = 8}}{{.314 \times 1}}{{{0}}^{{{ - 3}}}}{{kJmo}}{{{l}}^{{{ - 1}}}}{{{K}}^{{ - }}}^1\] .

Answer 1

Hint: The rate constant, or the specific rate constant, is the proportionality constant that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.
OR
The rate constant is defined as the proportionality constant that explains the relationship between the molar concentration of the reactants and the rate of a chemical reaction.
The rate constant is denoted by k and is also known as reaction rate constant for reaction rate coefficient. It is dependent on the temperature.

Complete step by step answer:
The Arrhenius equation is
${{log}}\dfrac{{{{{k}}_{{2}}}}}{{{{{k}}_{{1}}}}}{{ = }}\dfrac{{{{{E}}_{{a}}}}}{{{{2}}{{.303R}}}}{{[}}\dfrac{{{{{T}}_{{2}}}{{ - }}{{{T}}_{{1}}}}}{{{{{T}}_{{1}}}{{{T}}_{{2}}}}}{{]}}$
Given ${{{K}}_{{1}}}{{ = 7}}{{.87}}\times 1{{{0}}^{{{ - 7}}}}{{{s}}^{{{ - 1}}}}$
${{{E}}_{{a}}}{{ = 103\,kJmo}}{{{l}}^{{{ - 1}}}}$
${{R = 8}}{{.314 \times 1}}{{{0}}^{{{ - 3}}}}{{kJ}}\,{{mo}}{{{l}}^{{{ - 1}}}}\,{{{K}}^{{ - }}}^{{1}}$
${{{T}}_{{1}}}{{ = 273K}}\,{{and}}\,{{{T}}_{{2}}}{{ = 293K}}$
Substituting the values in Arrhenius equation
$\Rightarrow {{log}}\dfrac{{{{{k}}_{{2}}}}}{{{{7}}{{.87 \times 1}}{{{0}}^{{{ - 7}}}}}}{{ = }}\dfrac{{{{103 \times 20}}}}{{{{2}}{{.303 \times 8}}{{.314 \times 1}}{{{0}}^{{{ - 3}}}}{{ \times 293 \times 273}}}}{{ = 1345}}$
$\Rightarrow {{{K}}_{{2}}}{{ = 1}}{{.74 \times 1}}{{{0}}^{{{ - 5}}}}{{{s}}^{{{ - 1}}}}$

Note:
The reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution.
For a reaction of the type
${{aA + bB}} \to {{cC}}$
The reaction rate is often found to have the form
 ${{r = kT[A}}{{{]}}^{{m}}}{{{[B]}}^{{n}}}$
M and n are the partial orders of the reaction and are not dependent on the stoichiometric coefficients of the reactants (a and b) .they can be found experimentally and they depend on the reaction mechanism.