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Help! I'm really confused with this problem. I feel like i need to solve for k of the first reaction and then use that to solve for the activation energy of the second but I don't even know if that's right. Also, when they say that all other factors are equal, do they mean to each or to their values from the first reaction?
You need to solve for the ration if k catalyzed and k uncatalyzed. This ratio is given as 1000, so you set that equal to the Arrhenius equation of the catalyzed reaction divided by the Arrhenius equation of the uncatalyzed reaction. You then use algebra to get the equation Ea(cat) = Ea - RTln1000. When they say all other factors are equal, this means that the other values in the Arrhenius equation are equal to each other: A can be cancelled, R=8.314, T=298. The only value that is different is the activation energy.
You can set up a proportion of k of the catalyzed reaction and k of the uncatalyzed reaction with the formula k = Ae^-Ea/RT, like how you had to solve for problem #67. In this case, you would make the kcat/kuncat equal to 1000.
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