Temperature Dependence of Rate Constant — Prelims Questions

For a first-order reaction, the rate constant at $27^{\circ}\text{C}$ is $2.0 \times 10^{-3} \text{ s}^{-1}$. If the activation energy for the reaction is $50 \text{ kJ mol}^{-1}$, what will be the rate constant at $37^{\circ}\text{C}$? (Given: $R = 8.314 \text{ J mol}^{-1}\text{ K}^{-1}$, $\ln 10 = 2.303$)

A plot of $\ln k$ versus $1/T$ for a reaction gives a straight line with a slope of $-1.5 \times 10^4 \text{ K}$. What is the activation energy ($E_a$) for this reaction? (Given: $R = 8.314 \text{ J mol}^{-1}\text{ K}^{-1}$)

Which of the following statements is INCORRECT regarding the effect of temperature on reaction rate?

For a reaction, the rate constant $k$ is given by $\ln k = 15 - \frac{25000}{T}$. What is the activation energy ($E_a$) for this reaction? (Given: $R = 8.314 \text{ J mol}^{-1}\text{ K}^{-1}$)

The rate constant of a reaction increases by a factor of 10 when the temperature is increased from $27^{\circ}\text{C}$ to $47^{\circ}\text{C}$. Calculate the activation energy ($E_a$) of the 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?