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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th 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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Arrhenius Equation

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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Activity Series Chart

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

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) Cl2(g) → 2 Cl(g)

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Textbook Question

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

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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

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