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.

Chem 1C General Chemis... Self Assessment Quiz 5

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?

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