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?

검증된 단계별 안내

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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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

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.

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.

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.