The temperature dependence of the reaction rate constant is given by the equation: k = Ae^-Ea/RT Where: k = rate constant T = temperature A = frequency factor Ea = Energy of activation Use the rules for logarithms and exponents to write this equation in logarithmic form. NOTE: Write Ea as Ea for the answers below. Use ^ (caret) to enter superscripts. ln k =
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Step 1: Take the natural log of both sides of the equation: ln(k) = ln(Ae^(-Ea/RT)) Show more…
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David C.
Suppose a rate constant for an uncatalyzed reaction is described by the Arrhenius equation with an activation energy $E_{\mathrm{a}} .$ The introduction of a catalyst lowers the activation energy to the value $E_{\mathrm{a}}^{\prime}$ and thus increases the rate constant to the value $k^{\prime}$. Write the Arrhenius equation for both $k$ and $k^{\prime}$, and then derive an expression for the ratio $k^{\prime} / k$ in terms of $E_{\mathrm{a}}^{\prime}$ and $E_{\mathrm{a}} .$ Assume that the frequency factor $A$ and the temperature $T$ are constant. Use this equation to answer the next two questions.
The rate constant (k) for a reaction is measured as a function of temperature. A plot of ln k versus 1>T (in K) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.
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