Determining the proportional rate constant for chemical reaction at specific temperature

Question

The main relation one can use to calculate the missing links is the Arrhenius equation: $k=k_0*e^{(-\frac{Ea}{R*T})}$, where $k_0$ is a rate constant of the chemical reaction, $k$ is a proportional constant at the temperature $T$, $Ea$ being the activation energy (doesn't change with temperature), $R$ the ideal gas constant, and $T$ temperature in Kelvin. I want to make sure if I am thinking correctly. The calculation problem is as follows: the task gives two proportional rate constants ($k_1, k_2$), each at its own temperatures ($T_1, T_2$) and demands to find the proportional rate constant at a third temperature ($T_3$). I have tried it like this: $ln(k_1)-ln(k_2)=\frac{Ea}{R*T_1}-\frac{Ea}{R*T_2}=\frac{Ea}{R}*(\frac{1}{T_1}-\frac{1}{T_2})$. From this step one can calculate the activation energy $Ea$. I continued with: $ln(k_0)=ln(k_1)+\frac{Ea}{R*T_1}$, from which one can calculate $k_0$ as $k_0=k_1*e^{\frac{Ea}{R*T_1}}$, and from that one can calculate the $k$ that is sought-after: $k=k_0*e^{-\frac{Ea}{R*T_k}}$. Is this procedure correct or am I doing something wrong?

Answer 1

This looks right. The plot of $ln(k)$ vs. $k$ is a straight line, so $k$ can be computed without explicitly computing $k_0$ or $E_a$.