Question

The rate constant for an isomerization reaction, $A\to B$ is $4.5\times {10}^7{s}^{-1}$ at ${100}^{\circ }C$. Evaluate the Arrehenius parameters A and $E_a$:

• A. A = 0.7633 M, $E_a$=$3.435\times {10}^{-3}mol{L}^{-1}{s}^{-1}$
• B. A = 7.633 M, $E_a$=$3.435\times {10}^{-4}mol{L}^{-1}{s}^{-1}$
• C. A = 76.33 M, $E_a$=$3.435\times {10}^{-5}mol{L}^{-1}{s}^{-1}$
• D. None of these

Answer 1

Answer: (A)

A = 0.7633 M, $E_a$=$3.435\times {10}^{-3}mol{L}^{-1}{s}^{-1}$

For a first-order reaction

$k=\frac{2.303}{t}log\frac{a}{a-x}=\frac{2.303}{60}log\frac{A_0}{A}$

or $4.5\times {10}^{-3}=\frac{2.303}{60}log\frac{1}{A}$

or A = 0.7633 M

Rate = k[A] = $4.5\times {10}^{-3}\times 0.7633$

Rate = $3.435\times {10}^{-3}mol{L}^{-1}{s}^{-1}$

Hence, the correct option is $\text{A}$