Ch.14 - Chemical Kinetics

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.14 - Chemical Kinetics

Problem 62

Chapter 14, Problem 62

The rate constant of a reaction at 32 °C is 0.055 s⁻¹. If the frequency factor is 1.2 × 10¹³ s⁻¹, what is the activation barrier?

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

Verified step by step guidance

Identify the Arrhenius equation: \(k = A e^{-\frac{E_a}{RT}}\), where \(k\) is the rate constant, \(A\) is the frequency factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin: \(T = 32 + 273.15\).

Rearrange the Arrhenius equation to solve for the activation energy \(E_a\): \(E_a = -RT \ln\left(\frac{k}{A}\right)\).

Substitute the known values into the equation: \(R = 8.314 \text{ J/mol·K}\), \(k = 0.055 \text{ s}^{-1}\), \(A = 1.2 \times 10^{13} \text{ s}^{-1}\), and the calculated \(T\) in Kelvin.

Calculate the natural logarithm and multiply by \(-RT\) to find the activation energy \(E_a\).

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 the temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation helps in understanding how temperature influences reaction rates.

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 transform into products. A higher activation energy indicates a slower reaction rate, while a lower activation energy suggests a faster reaction, making it a crucial factor in reaction kinetics.

Frequency Factor (A)

The frequency factor, also known as the pre-exponential factor, is a constant that reflects the frequency of collisions and the orientation of reactants in a chemical reaction. It is a component of the Arrhenius equation and indicates how often reactants collide with sufficient energy to react. A higher frequency factor typically correlates with a faster reaction rate.

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Related Practice

Textbook Question

The diagram shows the energy of a reaction as the reaction progresses. Label each blank box in the diagram.

a. reactants b. products c. activation energy (E_a) d. enthalpy of reaction (ΔH_rxn)

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Textbook Question

The data shown here were collected for the first-order reaction: N₂O(g) → N₂(g) + O(g) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.

Temperature (K) Rate Constant (1 , s)

800 3.24⨉10^{- 5}

900 0.00214

1000 0.0614

1100 0.955

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Textbook Question

The half-life for the radioactive decay of C-14 is 5730 years and is independent of the initial concentration. If a sample of C-14 initially contains 1.5 mmol of C-14, how many millimoles are left after 2255 years?

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Textbook Question

The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5⨉10¹¹/ s. Calculate the rate constant of the reaction at 25 °C.

The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1/T (in K) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.

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