Ch.14 - Chemical Kinetics

Problem 51b

Chapter 14, Problem 51b

(b) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

Verified step by step guidance

Understand the relationship between temperature and reaction rate: The rate of a chemical reaction typically depends on the temperature at which the reaction is carried out.

Recall the Arrhenius Equation: This equation, given by \( k = A e^{-\frac{E_a}{RT}} \), 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, describes how the rate constant changes with temperature.

Analyze the effect of increasing temperature: Increasing the temperature \( T \) in the Arrhenius equation results in a decrease in the value of the exponent \( -\frac{E_a}{RT} \), making the entire exponent larger (less negative).

Examine the exponential term: As the exponent becomes larger, the value of \( e^{-\frac{E_a}{RT}} \) increases because the negative exponent becomes less negative.

Conclude the effect on rate constant: Since the exponential term increases with an increase in temperature, the rate constant \( k \) also increases.

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Key Concepts

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

Rate Constant

The rate constant (k) is a proportionality factor in the rate equation of a chemical reaction, indicating the speed at which the reaction occurs. It is specific to a particular reaction at a given temperature and is influenced by factors such as temperature, concentration, and the presence of catalysts.

Arrhenius Equation

The Arrhenius equation describes how the rate constant of a reaction changes with temperature. It is expressed as k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation shows that an increase in temperature generally leads to an increase in the rate constant.

Activation Energy

Activation energy (Ea) is the minimum energy required for reactants to undergo a chemical reaction. Higher temperatures provide more kinetic energy to the molecules, increasing the likelihood that they will overcome the activation energy barrier, thus enhancing the reaction rate and increasing the rate constant.

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Related Practice

Textbook Question

The gas-phase decomposition of NO₂, 2 NO₂(g) → 2 NO(g) + O₂(g), is studied at 383°C, giving the following data:

Time (s) [NO₂] (M)

0.0 0.100

5.0 0.017

10.0 0.0090

15.0 0.0062

20.0 0.0047

(a) Is the reaction first order or second order with respect to the concentration of NO₂?

(c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050 M NO₂.

Textbook Question

Sucrose 1C12H22O112, commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 C and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose: Time (min) 3C12H22o11 4 1M2 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 (a) Is the reaction first order or second order with respect to 3C12H22O114?

Textbook Question

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction?

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Textbook Question

Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.

Textbook Question

(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.6) is 160 kJ>mol. Calculate the fraction of methyl isonitrile molecules that has an energy equal to or greater than the activation energy at 500 K. (b) Calculate this fraction for a temperature of 520 K. What is the ratio of the fraction at 520 K to that at 500 K?

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