(Solved): Learning Goal: To use the Arrhenius equation to calculate the activation energy. As temperature ris ...

Learning Goal: To use the Arrhenius equation to calculate the activation energy. As temperature rises, the average kinetic energy of molecules increases. In a chemical reaction, this means that a higher percentage of the molecules possess the required activation energy, and the reaction goes faster. This relationship is shown by the Arrhenius equation $$k=A{e}^{?E_{\mathrm{a}}/RT}$$ where $$k$$ is the rate constant, $$A$$ is the frequency factor, $$E_{\mathrm{a}}$$ is the activation energy, $$R=8.3145\mathrm{J}/(\mathrm{K}?\mathrm{mol})$$ is the gas constant, and $$T$$ is the Kelvin temperature. The following rearranged version of the equation is also useful: $$\ln \left(\frac{k_2}{k_1}\right)=\left(\frac{E_{\mathrm{a}}}{R}\right)\left(\frac{1}{T_1}?\frac{1}{T_2}\right)$$ where $$k_1$$ is the rate constant at temperature $$T_1$$, and $$k_2$$ is the rate constant at temperature $$T_2$$. The rate constant of a chemical reaction increased from $$0.100{\mathrm{s}}^{?1}$$ to $$3.20{\mathrm{s}}^{?1}$$ upon raising the temperature from $$25.0^{?}\mathrm{C}$$ to $$39.0{}^{?}\mathrm{C}$$. Calculate the value of $$\left(\frac{1}{T_1}?\frac{1}{T_2}\right)$$ where $$T_1$$ is the initial temperature and $$T_2$$ is the final temperature. Express your answer numerically. $$x$$ Incorrect; Try Again This is the difference between the temperatures, not between their reciprocal values. What is the activation energy of the reaction? Express your answer numerically in kilojoules per mole. * Incorrect; Try Again You may have made a conversion error.