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Ch.14 - Chemical Kinetics
Tro - Chemistry: A Molecular Approach 4th Edition
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Tutti i libri di testoTro 4th EditionCh.14 - Chemical KineticsProblema 99c
Capitolo 14, Problema 99c

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
c. If a reaction mixture is 0.155 M in C2H5Brand 0.250 M in OH-, what is the initial rate of the reaction at 75 °C?

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Identify the rate law for the reaction. Since the reaction is first order in each reactant and second order overall, the rate law is: \( \text{Rate} = k [\text{C}_2\text{H}_5\text{Br}] [\text{OH}^-] \).
Determine the rate constant \( k \) at 75 °C. Use the Arrhenius equation \( k = A e^{-E_a/(RT)} \) to extrapolate the rate constant at 75 °C from the given data.
Calculate the initial rate of the reaction using the rate law. Substitute the concentrations \([\text{C}_2\text{H}_5\text{Br}] = 0.155 \text{ M}\) and \([\text{OH}^-] = 0.250 \text{ M}\) into the rate law equation.
Substitute the extrapolated rate constant \( k \) at 75 °C into the rate law equation.
Solve the equation to find the initial rate of the reaction.

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Reaction Order

The order of a reaction indicates how the rate is affected by the concentration of reactants. In this case, the reaction is first order in each reactant, meaning that the rate is directly proportional to the concentration of each reactant. The overall order of the reaction is the sum of the individual orders, which is second order here, indicating that the rate depends on the concentrations of both reactants.
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00:36
Average Bond Order

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. It varies with temperature, which is crucial for calculating the initial rate of the reaction at different temperatures. The provided k values at various temperatures allow for the determination of how the reaction rate changes with temperature, following the Arrhenius equation.
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01:14
Equilibrium Constant K

Initial Rate of Reaction

The initial rate of a reaction is the rate measured at the very beginning of the reaction when the concentrations of reactants are at their highest. It can be calculated using the rate law, which incorporates the rate constant and the concentrations of the reactants. For this reaction, the initial rate at 75 °C can be determined by substituting the appropriate k value and the concentrations of C2H5Br and OH- into the rate equation.
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02:03
Average Rate of Reaction
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Domanda del libro di testo

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

a. Determine the activation energy and frequency factor for the reaction.

Domanda del libro di testo

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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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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The reaction 2 N2O5 → 2 N2O4 + O2 takes place at around room temperature in solvents such as CCl4. The rate constant at 293 K is found to be 2.35⨉10-4 s-1, and at 303 K the rate constant is found to be 9.15⨉10-4 s-1. Calculate the frequency factor for the reaction.

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