How long will it take for 90% of the CH3CN to convert to CH3NC at 500 °C given the tabulated data: Time (h) [CH3CN] (M) 0.0 1.000, 5.0 0.794, 10.0 0.631, 15.0 0.501, 20.0 0.398, 25.0 0.316?

Verified step by step guidance

Determine the order of the reaction by analyzing the concentration data over time.

Use the integrated rate law for the determined order to find the rate constant, k.

Calculate the concentration of CH3CN when 90% has converted to CH3NC, which is 10% of the initial concentration.

Use the integrated rate law with the calculated concentration and rate constant to solve for the time required for 90% conversion.

Verify the calculated time by checking if it aligns with the trend observed in the tabulated data.

Key Concepts

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

Reaction Kinetics

Reaction kinetics is the study of the rates of chemical processes. It involves understanding how different factors, such as concentration, temperature, and catalysts, affect the speed of a reaction. In this question, analyzing the concentration of CH3CN over time allows us to determine the rate at which it converts to CH3NC, which is essential for calculating the time required for 90% conversion.

First-Order Reactions

First-order reactions are characterized by a rate that is directly proportional to the concentration of one reactant. The integrated rate law for a first-order reaction can be expressed as ln([A]0/[A]) = kt, where [A]0 is the initial concentration, [A] is the concentration at time t, k is the rate constant, and t is time. Understanding whether the reaction between CH3CN and CH3NC follows first-order kinetics is crucial for accurately predicting the time for 90% conversion.

Half-Life of Reactions

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is constant and independent of concentration. Knowing the half-life can help estimate the time needed for a specific percentage of reactant conversion, such as 90% in this case, by using the relationship between half-lives and the desired concentration reduction.

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First-Order Half-Life

Related Practice

Textbook Question

Suppose that the reaction A¡products is exothermic and has an activation barrier of 75 kJ/mol. Sketch an energy diagram showing the energy of the reaction as a function of the progress of the reaction. Draw a second energy curve showing the effect of a catalyst.

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Open Question

Suppose that a catalyst lowers the activation barrier of a reaction from 125 kJ/mol to 55 kJ/mol. By what factor would you expect the reaction rate to increase at 25 °C? (Assume that the frequency factors for the catalyzed and uncatalyzed reactions are identical.)

Textbook Question

The activation barrier for the hydrolysis of sucrose into glucose and fructose is 108 kJ/mol. If an enzyme increases the rate of the hydrolysis reaction by a factor of 1 million, how much lower must the activation barrier be when sucrose is in the active site of the enzyme? (Assume that the frequency factors for the catalyzed and uncatalyzed reactions are identical and a temperature of 25 °C.)

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Textbook Question

The tabulated data were collected for this reaction at 500 °C: CH₃CN(g) → CH₃NC( g) a. Determine the order of the reaction and the value of the rate constant at this temperature.

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Textbook Question

The tabulated data were collected for this reaction at 500 °C: CH₃CN(g) → CH₃NC( g) b. What is the half-life for this reaction (at the initial concentration)?

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Open Question

What is the half-life for this reaction at the initial concentration?