Arrhenius Equation — Prelims Questions

For a first-order reaction, the rate constants at $27^circ\text{C}$ and $37^circ\text{C}$ are $2.0 \times 10^{-2},\text{s}^{-1}$ and $4.0 \times 10^{-2},\text{s}^{-1}$ respectively. Calculate the activation energy ($E_a$) for this reaction. (Given: $R = 8.314,\text{J mol}^{-1}\text{K}^{-1}$, $ln 2 = 0.693$)

For a reaction, the activation energy ($E_a$) is $60,\text{kJ mol}^{-1}$. If the rate constant at $300,\text{K}$ is $2.0 \times 10^{-3},\text{s}^{-1}$, what will be the approximate rate constant at $310,\text{K}$? (Given: $R = 8.314,\text{J mol}^{-1}\text{K}^{-1}$, $e^{0.77} approx 2.16$)

Which of the following statements is INCORRECT regarding the Arrhenius equation?

An Arrhenius plot of $ln k$ versus $1/T$ for a reaction gives a straight line with a slope of $-1.2 \times 10^4,\text{K}$. What is the activation energy ($E_a$) for this reaction? (Given: $R = 8.314,\text{J mol}^{-1}\text{K}^{-1}$)

A catalyst increases the rate of a reaction by a factor of $10^5$ at $300,\text{K}$. If the activation energy of the uncatalyzed reaction is $100,\text{kJ mol}^{-1}$, what is the activation energy of the catalyzed reaction? (Given: $R = 8.314,\text{J mol}^{-1}\text{K}^{-1}$, $ln 10 = 2.303$)

Which of the following plots correctly represents the Arrhenius equation for a typical chemical reaction?