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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Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature.

Use the Arrhenius equation: k = A * e^(-Ea/RT), where k is the rate constant, A is the collision factor, Ea is the activation energy, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.

Calculate the rate constant for the uncatalyzed reaction using the activation energy of 95 kJ/mol.

Calculate the rate constant for the catalyzed reaction using the activation energy of 55 kJ/mol.

Determine the factor by which the catalyst increases the rate by dividing the rate constant of the catalyzed reaction by the rate constant of the uncatalyzed reaction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. A higher activation energy means that fewer molecules have sufficient energy to react, resulting in a slower reaction rate. Conversely, lowering the activation energy, such as through the use of a catalyst, increases the likelihood of successful collisions between reactant molecules.

Catalysts

Catalysts are substances that increase the rate of a chemical reaction without being consumed in the process. They work by providing an alternative reaction pathway with a lower activation energy. This allows more reactant molecules to have enough energy to collide and react, thereby speeding up the reaction. Importantly, catalysts do not alter the equilibrium position of a reaction; they only affect the rate at which equilibrium is reached.

Arrhenius Equation

The Arrhenius equation describes how the rate constant of a reaction depends on temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation illustrates that as the activation energy decreases or the temperature increases, the rate constant increases, leading to a faster reaction rate.

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Arrhenius Equation

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Textbook Question

The enzyme urease catalyzes the reaction of urea, (NH₂CONH₂), 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. (b) If the rate of the catalyzed reaction were the same at 100°C as it is at 21°C, what would be the difference in the activation energy between the catalyzed and uncatalyzed reactions?

Textbook Question

The enzyme urease catalyzes the reaction of urea, (NH₂CONH₂), 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?

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

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.