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Ch.14 - Chemical Kinetics
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 63
Chapter 14, Problem 63

The rate of the reaction CH3COOC2H5(aq) + OH-(aq) → CH3COO-(aq) + C2H5OH(aq) was measured at several temperatures, and the following data were collected: Temperature (°C) k (M⁻¹ s⁻¹) 15 0.0521 25 0.101 35 0.184 45 0.332. Calculate the value of Ea by constructing an appropriate graph.

Verified step by step guidance
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Step 1: Understand the Arrhenius equation, which relates the rate constant k to the temperature T and the activation energy Ea. The equation is given by: k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.
Step 2: Rearrange the Arrhenius equation to a linear form for easier graphing: ln(k) = ln(A) - (Ea/R) * (1/T). This equation is in the form of y = mx + c, where y = ln(k), m = -Ea/R, x = 1/T, and c = ln(A).
Step 3: Convert the given temperatures from Celsius to Kelvin by adding 273.15 to each temperature value. This is necessary because the Arrhenius equation requires temperature in Kelvin.
Step 4: Calculate the natural logarithm of each rate constant (k) provided in the data. This will give you the y-values for your graph.
Step 5: Plot a graph of ln(k) (y-axis) versus 1/T (x-axis). The slope of the resulting line will be equal to -Ea/R. Use the slope to calculate the activation energy Ea by rearranging the slope formula: Ea = -slope * R.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to temperature and activation energy (Ea). It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, R is the universal gas constant, and T is the temperature in Kelvin. Understanding this equation is crucial for analyzing how temperature affects reaction rates and for calculating Ea from experimental data.
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Activation Energy (Ea)

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. A higher Ea indicates that a reaction is slower at a given temperature, while a lower Ea suggests a faster reaction. Calculating Ea from temperature-dependent rate constants helps in understanding the kinetics of the reaction.
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Graphical Analysis of Kinetics

Graphical analysis in chemical kinetics often involves plotting data to determine relationships between variables. In this case, a plot of ln(k) versus 1/T (in Kelvin) can be used to derive Ea from the slope of the resulting line, according to the linear form of the Arrhenius equation. This method allows for a visual interpretation of how the rate constant changes with temperature, facilitating the calculation of activation energy.
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Related Practice
Textbook Question

Based on their activation energies and energy changes and assuming that all collision factors are the same, rank the following reactions from slowest to fastest. (a) Ea = 45 kJ>mol; E = -25 kJ>mol (b) Ea = 35 kJ>mol; E = -10 kJ>mol (c) Ea = 55 kJ>mol; E = 10 kJ>mol

Textbook Question

The temperature dependence of the rate constant for a reaction is tabulated as follows: Temperature (K) k 1M 1 s1 2 600 0.028 650 0.22 700 1.3 750 6.0 800 23 Calculate Ea and A.

Textbook Question

(b) What is the difference between a unimolecular and a bimolecular elementary reaction?