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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 88
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Chapter 14, Problem 88

Suppose that a certain biologically important reaction is quite slow at physiological temperature 137 _x001E_C2 in the absence of a catalyst. Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a 1 * 10^5-fold increase in the reaction rate?

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Step 1: Understand the Arrhenius equation, which relates the rate constant k of a reaction to the temperature T and the activation energy E_a: k = A * e^(-E_a/(RT)), where A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin.
Step 2: Recognize that the problem asks for the change in activation energy (ΔE_a) needed to increase the reaction rate by a factor of 1 * 10^5. This means the new rate constant k' is 1 * 10^5 times the original rate constant k.
Step 3: Set up the ratio of the new rate constant to the original rate constant using the Arrhenius equation: k'/k = (A * e^(-E_a'/(RT))) / (A * e^(-E_a/(RT))) = e^((E_a - E_a')/(RT)).
Step 4: Substitute the given rate increase factor into the equation: 1 * 10^5 = e^((E_a - E_a')/(RT)).
Step 5: Solve for the change in activation energy ΔE_a = E_a - E_a' by taking the natural logarithm of both sides: ΔE_a = RT * ln(1 * 10^5).
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Textbook Question

The enzyme urease catalyzes the reaction of urea, 1NH2CONH22, with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 * 10-5 s-1 at 100 C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 * 104 s-1 at 21 C. (c) In actuality, what would you expect for the rate of the catalyzed reaction at 100 C as compared to that at 21 C?

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Textbook Question

The activation energy of an uncatalyzed reaction is 95 kJ/mol. The addition of a catalyst lowers the activation energy to 55 kJ/mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) 25 C

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Textbook Question

The activation energy of an uncatalyzed reaction is 95 kJ/mol. The addition of a catalyst lowers the activation energy to 55 kJ/mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (b) 125 °C?

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Textbook Question

Consider the reaction A + B → C + D. Is each of the following statements true or false? (b) If the reaction is an elementary reaction, the rate law is second order.

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Textbook Question

Consider the reaction A + B → C + D. Is each of the following statements true or false? (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order.

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Textbook Question

The reaction 2 NO(g) + O2(g) → 2 NO2 (g) is second order in NO and first order in O2. When [NO] = 0.040 M, and 3O24 = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10-5 M/s. (b) What is the value of the rate constant?

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