The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128/s at 150 K. a. What is the half-life of the desorption reaction?-

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Identify that the desorption reaction is first order, which means the rate of reaction depends linearly on the concentration of the reactant.

Recall the formula for the half-life of a first-order reaction: \( t_{1/2} = \frac{0.693}{k} \), where \( k \) is the rate constant.

Substitute the given rate constant \( k = 0.128 \text{/s} \) into the half-life formula.

Calculate the half-life using the formula: \( t_{1/2} = \frac{0.693}{0.128} \).

Interpret the result to understand how long it takes for half of the n-butane to desorb from the aluminum oxide surface at 150 K.

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Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The mathematical representation of a first-order reaction is given by the equation: rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Half-Life

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 can be calculated using the formula: t1/2 = 0.693/k, where k is the rate constant. This property is significant because it allows for the prediction of how long it will take for a reaction to progress to a certain extent.

Rate Constant

The rate constant (k) is a proportionality factor in the rate law of a chemical reaction, which quantifies the speed of the reaction at a given temperature. It is specific to each reaction and varies with temperature and the presence of catalysts. In the context of first-order reactions, the rate constant is crucial for calculating the half-life and understanding the kinetics of the desorption process.

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Related Practice

Textbook Question

Consider the reaction in which HCl adds across the double bond of ethene: HCl + H₂C=CH₂ → H₃C-CH₂Cl The following mechanism, with the accompanying energy diagram, has been suggested for this reaction:

Step 1 HCl + H₂C=CH₂ → H₃C=CH₂⁺ + Cl^-

Step 2 H₃C=CH₂⁺ + Cl^- → H₃C-CH₂Cl

a. Based on the energy diagram, determine which step is rate limiting.

Textbook Question

Step 1 HCl + H₂C=CH₂ → H₃C=CH₂⁺ + Cl^-

Step 2 H₃C=CH₂⁺ + Cl^- → H₃C-CH₂Cl

b. What is the expected order of the reaction based on the proposed mechanism?

Textbook Question

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128/s at 150 K. b. If the surface is initially completely covered with n-butane at 150 K, how long will it take for 25% of the molecules to desorb (leave the surface)? For 50% to desorb?

Textbook Question

The evaporation of a 120-nm film of n-pentane from a single crystal of aluminum oxide is zero order with a rate constant of 1.92⨉1013 molecules/cm²•s at 120 K. a. If the initial surface coverage is 8.9⨉1016 molecules/cm², how long will it take for one-half of the film to evaporate?