Textbook Question
The addition of NO accelerates the decomposition of N2O, possibly by the following mechanism: NO1g2 + N2O1g2¡N21g2 + NO21g2 2 NO21g2¡2 NO1g2 + O21g2 (b) Is NO serving as a catalyst or an intermediate in this reaction?
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Ch.14 - Chemical Kinetics
Chapter 14, Problem 85
The enzyme carbonic anhydrase catalyzes the reaction CO2(g) + H2O(l) ↔ HCO3⁻(aq) + H⁺(aq). In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s⁻¹ at 25 _x001E_C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 * 10⁶ s⁻¹ at 25 _x001E_C. Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.
Verified step by step guidance1
Identify the Arrhenius equation: k = A * e^(-Ea/(RT)), where k is the rate constant, A is the pre-exponential factor (collision factor), Ea is the activation energy, R is the gas constant (8.314 J/(mol*K)), and T is the temperature in Kelvin.
Since the collision factor (A) is the same for both reactions, use the Arrhenius equation to set up the ratio of the rate constants: k1/k2 = e^((Ea2 - Ea1)/(RT)), where k1 and k2 are the rate constants for the uncatalyzed and catalyzed reactions, respectively.
Take the natural logarithm of both sides of the equation to solve for the difference in activation energies: ln(k1/k2) = (Ea2 - Ea1)/(RT).
Substitute the given rate constants (k1 = 0.039 s⁻¹ and k2 = 1.0 * 10⁶ s⁻¹) and the temperature (T = 25°C = 298 K) into the equation: ln(0.039 / (1.0 * 10⁶)) = (Ea2 - Ea1)/(8.314 * 298).
Solve the equation for the difference in activation energies (Ea2 - Ea1) by multiplying both sides by (8.314 * 298) to isolate (Ea2 - Ea1).
Related Practice
Textbook Question
Many metallic catalysts, particularly the precious-metal ones, are often deposited as very thin films on a substance of high surface area per unit mass, such as alumina 1Al2O32 or silica 1SiO22. (b) How does the surface area affect the rate of reaction?
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Open Question
(b) Automobile catalytic converters have to work at high temperatures, as hot exhaust gases stream through them. In what ways could this be an advantage? In what ways a disadvantage? (c) Why is the rate of flow of exhaust gases over a catalytic converter important?
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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