The rate constant of a reaction is measured at different temperatures. A plot of the natural log of the rate constant as a function of the inverse of the temperature (in kelvins) yields a straight line with a slope of –8.55 103 K–1. What is the activation energy (Ea) for the reaction?

Question

The rate constant of a reaction is measured at different temperatures. A plot of the natural log of the rate constant as a function of the inverse of the temperature (in kelvins) yields a straight line with a slope of –8.55  103 K–1. What is the activation energy (Ea) for the reaction?

BlackTom AI · Accepted Answer

The question provides a slope from a plot of ln(k) versus 1/T (in kelvin) for an Arrhenius plot. In the Arrhenius equation, ln(k) = ln(A) − Ea/(R T), so the plot of ln(k) against 1/T has a straight-line form with slope equal to −Ea/R.

Step 1: Identify the slope. The slope is given as −8.55 × 10^3 K^−1.

Step 2: Relate slope to activation energy. Since slope = −Ea/R, we have Ea = −(slope) × R. The negative sign cancels because slope is negative.

Step 3: Use the gas constant R. For Ea in joules per mole, R = 8.314 J/(mol·K).

Step 4: Compute Ea.
Ea = (8.55 × 10^3 K^−1) × (8.314 J/(mol·K)) ≈ 71,085 J/mol ≈ 7.11 × 10^4 J/mol.
Converting to kilojoules per mole: Ea ≈ 71 kJ/mol.

Step 5: Compare with the given answer. The provided answer choice is 71 kJ, which matches the calculated activation energy when rounded to appropriate significant figures.

Note on missing options: The original data set shows an empty list for answer_options. If one were selecting an option, the proper choice would be the one stating Ea ≈ 71 kJ/mol. In this case, since no alternative options are presented, the numerical result and the reasoning remain valid for identifying Ea as approximately 71 kJ/mol.

Summary of key idea: The slope of a ln(k) vs 1/T plot equals −Ea/R, so Ea can be obtained by multiplying the slope’s magnitude by R, yielding Ea ≈ 71 kJ/mol in this scenario.

类似问题

Which energy difference in the energy profile below corresponds to the activation energy for the forward reaction?

No activation energy is required for an exergonic reaction

Activation energy is the:

In a one step reaction, the activation energy for the forward reaction is 20.0 kJ mol -1, and the enthalpy of the reaction is -30.0 kJ mol-1. Calculate the activation energy for the reverse reaction.

The energy diagram for the elementary reaction, X(g) + Y(g) ⇌ Z(g) + R(g) is shown below. What would happen if the kinetic energy of the reactants was not enough to provide the needed activation energy?

The rate constant of a reaction is measured at different temperatures. A plot of the natural log of the rate constant as a function of the inverse of the temperature (in kelvins) yields a straight line with a slope of –8.55 × 103 K–1. What is the activation energy (Ea) for the reaction?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单