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Ch.15 - Chemical Kinetics
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.15 - Chemical KineticsProblem 104a
Chapter 15, Problem 104a

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?

Verified step by step guidance
1
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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Key Concepts

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

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.
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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.
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Related Practice
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?

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Textbook Question

This reaction has an activation energy of zero in the gas phase: CH3 + CH3 → C2H6

a. Would you expect the rate of this reaction to change very much with temperature?

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Textbook Question

The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)

C2H5Br(aq) + OH- (aq) → C2H5OH(l) + Br- (aq)

Temperature (°C) k (L,mol •s)

25 8.81⨉10-5

35 0.000285

45 0.000854

55 0.00239

65 0.00633

b. Determine the rate constant at 15 °C.

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Textbook Question

Consider the two reactions:

O + N2 → NO + N Ea = 315 kJ/mol

Cl + H2 → HCl + H Ea = 23 kJ/mol

a. Why is the activation barrier for the first reaction so much higher than that for the second?

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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

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

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