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Question: The rate constant for an isomerization reaction, \(A \to B\) is \(4.5 \times {10^7}{s^{ - 1}}\) at \...

The rate constant for an isomerization reaction, A→BA \to B is 4.5×107s−14.5 \times {10^7}{s^{ - 1}} at 100∘C{100^ \circ }C . Evaluate the Arrhenius parameters A and Ea{E_a} :
A.A=0.7633 M, Ea=3.435×10−2molL−1s−1{E_a} = 3.435 \times {10^{ - 2}}mol{L^{ - 1}}{s^{ - 1}}
B.A=7.633 M, Ea=3.435×10−4molL−1s−1{E_a} = 3.435 \times {10^{ - 4}}mol{L^{ - 1}}{s^{ - 1}}
C.A=76.33 M, Ea=3.435×10−5molL−1s−1{E_a} = 3.435 \times {10^{ - 5}}mol{L^{ - 1}}{s^{ - 1}}
D.None of these

Explanation

Solution

The rate constant is the proportionality constant in the equation which expresses the relation between rate of chemical reaction and the concentrations of the reacting substance. Arrhenius parameter is found by the isomerization reaction which is evaluated at the values at given temperature.

Complete step by step answer:
The order of reaction most probably useful to find the parameters.
For a first order reaction, we find out the value of A and Ea{E_a} .
Here the given value is k and temperature T.
The equation is given below,
k=2.303tlog⁡aa−x =2.30360log⁡AoA 4.5×10−3=2.30360log⁡1A  k = \dfrac{{2.303}}{t}\log \dfrac{a}{{a - x}} \\\ = \dfrac{{2.303}}{{60}}\log \dfrac{{{A_o}}}{A} \\\ 4.5 \times {10^{ - 3}} = \dfrac{{2.303}}{{60}}\log \dfrac{1}{A} \\\
Or A= 0.7633 M
Now we will find rate given as below:
Rate =K[A]=4.5×10−3×0.7633 = K[A]=4.5 \times {10^{ - 3}} \times 0.7633
Rate =3.435×10−3molL−1s−1 = 3.435 \times {10^{ - 3}}mol{L^{ - 1}}{s^{ - 1}}
Therefore, option (A) is the correct answer.

Additional information:
Isomerization is the chemical process which is a compound transformed into isomeric forms. Isomerization reaction is used to convert the reaction to gain the isomers. Isomerization can adopt two distinct confirmations which is cis and trans. It is defined by the transformation of a molecule into a different isomer. It is a chemical process which converts compounds into its optical or geometric isomers.

Note: We must remember that the Arrhenius equation is simple, but formula for the temperature dependence of the chemical reaction rate constant. This equation was derived for aqueous solutions and electrolytic dissociation which depends on temperature and reaction rate and describes the relation between rate of reaction and temperature.