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.

검증된 단계별 안내

Identify that the problem involves determining the rate constant at a different temperature using the Arrhenius equation.

The Arrhenius equation is given by: k = A * e^(-Ea/(RT)), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant (8.314 J/mol*K), and T is the temperature in Kelvin.

To find the rate constant at 15 °C, first convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature.

Use the given rate constants at different temperatures to plot ln(k) versus 1/T (in Kelvin) and determine the slope, which is equal to -Ea/R.

Once the activation energy (Ea) is determined, use the Arrhenius equation to calculate the rate constant at 15 °C by substituting the values of Ea, R, and the temperature in Kelvin into the equation.

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주요 개념

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

Reaction Order

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. In this case, the reaction is first order in each reactant, meaning the rate is directly proportional to the concentration of each reactant. Understanding reaction order is crucial for determining how changes in concentration affect the reaction rate.

Arrhenius Equation

The Arrhenius equation describes how the rate constant (k) of a reaction changes with temperature. It is expressed as k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This relationship allows us to estimate the rate constant at different temperatures, which is essential for solving the given problem.

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 and is specific to each reaction. In this question, determining the rate constant at 15 °C requires understanding how k changes with temperature, which can be inferred from the provided data.