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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 61
Chapter 14, Problem 61

(a) A certain first-order reaction has a rate constant of 2.75 * 10^-2 s^-1 at 20 _x001E_C. What is the value of k at 60 _x001E_C if Ea = 75.5 kJ/mol? (b) Another first-order reaction also has a rate constant of 2.75 * 10^-2 s^-1 at 20 _x001E_C. What is the value of k at 60 _x001E_C if Ea = 125 kJ/mol?

Verified step by step guidance
1
Step 1: Identify the Arrhenius equation, which relates the rate constant k to the temperature T and the activation energy Ea: 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: Convert the given temperatures from Celsius to Kelvin by adding 273.15 to each temperature. For example, 20°C becomes 293.15 K and 60°C becomes 333.15 K.
Step 3: Use the Arrhenius equation in its logarithmic form to find the new rate constant k2 at 60°C: ln(k2/k1) = -Ea/R * (1/T2 - 1/T1), where k1 is the initial rate constant at 20°C, T1 is the initial temperature in Kelvin, and T2 is the final temperature in Kelvin.
Step 4: Substitute the given values into the logarithmic form of the Arrhenius equation for part (a) with Ea = 75.5 kJ/mol, converting Ea to J/mol by multiplying by 1000.
Step 5: Repeat Step 4 for part (b) with Ea = 125 kJ/mol, again converting Ea to J/mol by multiplying by 1000. Solve for k2 in each case.

Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that if the concentration of the reactant doubles, the reaction rate also doubles. The rate law for a first-order reaction can be expressed as rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.
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First-Order Reactions

Arrhenius Equation

The Arrhenius equation describes how the rate constant (k) of a reaction depends on temperature (T) and activation energy (Ea). It is given by k = A * e^(-Ea/RT), where A is the pre-exponential factor, R is the universal gas constant, and T is the temperature in Kelvin. This equation allows us to calculate the rate constant at different temperatures if we know the activation energy.
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Arrhenius Equation

Activation Energy (Ea)

Activation energy (Ea) 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 activation energy means that fewer molecules have sufficient energy to react at a given temperature, resulting in a slower reaction rate. Understanding Ea is crucial for predicting how temperature changes affect reaction rates.
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Activity Series Chart
Related Practice
Textbook Question

Indicate whether each statement is true or false. (b) Exothermic reactions are faster than endothermic reactions.

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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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Textbook Question

Indicate whether each statement is true or false. (a) If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction.

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