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?

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Identify that the reaction is zero order, which means the rate of reaction is constant and does not depend on the concentration of the reactant.

Use the zero-order rate equation: \[ [A] = [A]_0 - kt \] where \([A]\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, and \(k\) is the rate constant.

Substitute the given values into the equation: \([A]_0 = 8.9 \times 10^{16}\) molecules/cm\(^2\), \(k = 1.92 \times 10^{13}\) molecules/cm\(^2\)•s.

Calculate the concentration when half of the film has evaporated: \([A] = \frac{1}{2} \times 8.9 \times 10^{16}\) molecules/cm\(^2\).

Rearrange the zero-order rate equation to solve for \(t\): \[ t = \frac{[A]_0 - [A]}{k} \] and substitute the known values to find the time.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Zero-Order Kinetics

In zero-order kinetics, the rate of a reaction is constant and independent of the concentration of the reactants. This means that the rate of evaporation of the n-pentane film remains the same regardless of how much of the film is left. The rate constant, in this case, is given as 1.92×10^13 molecules/cm²•s, which allows us to calculate the time required for a specific change in concentration.

Half-Life in Zero-Order Reactions

The half-life of a zero-order reaction is determined by the initial concentration and the rate constant. It can be calculated using the formula t½ = [A]₀ / (2k), where [A]₀ is the initial concentration and k is the rate constant. This concept is crucial for determining how long it will take for half of the n-pentane film to evaporate, given the initial surface coverage.

Surface Coverage

Surface coverage refers to the number of molecules present on a surface per unit area, expressed in molecules/cm². In this scenario, the initial surface coverage of the n-pentane film is 8.9×10^16 molecules/cm². Understanding surface coverage is essential for calculating the time it takes for the film to evaporate, as it directly influences the rate of the zero-order reaction.

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?