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(a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature? (c) Which factor is most sensitive to changes in temperature-the frequency of collisions, the orientation factor, or the fraction of molecules with energy greater than the activation energy?

Short Answer

Expert verified
(a) Activation energy and molecular orientation, (b) Increase, (c) Fraction of molecules with energy greater than activation energy.

Step by step solution

01

Understand Collision Theory

According to collision theory, for a chemical reaction to occur, reacting molecules must collide with sufficient energy and proper orientation. The factors determining whether a collision will lead to a reaction include the energy of the collision, known as the activation energy, and the orientation of the molecules during the collision.
02

Analyze Temperature's Effect on Rate Constant

The rate constant of a chemical reaction generally increases with an increase in temperature. This is because higher temperatures provide more energy to the molecules, increasing the number of collisions that have sufficient energy to surpass the activation energy barrier.
03

Assess Sensitivity to Temperature Changes

The factor most sensitive to changes in temperature is the fraction of molecules with energy greater than the activation energy. As temperature increases, the Maxwell-Boltzmann distribution shows that a larger fraction of molecules possess the necessary energy to overcome the activation energy, leading to more successful reactions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Activation Energy
Activation energy is the minimum amount of energy that colliding molecules must have for a chemical reaction to occur. This energy acts as a barrier that the reacting molecules must overcome.

Think of activation energy as the initial push required to start a rolling ball down a hill. Without this push, the ball stays put. Similarly, molecules need a certain amount of energy, the activation energy, to transform into products.

The activation energy can vary depending on the nature of the substances involved and the conditions of the reaction. In the context of collision theory, only collisions that have energy exceeding the activation energy and occur with proper molecular orientation will lead to a chemical reaction.

To sum up, the activation energy is a crucial factor in determining the likelihood of a reaction when two molecules collide.
Reaction Rate Constant
The reaction rate constant, often noted as k, is a crucial aspect of understanding how fast a chemical reaction proceeds. As a core parameter in the rate law of reactions, it provides significant insight into the kinetics of the reaction process.

But what influences the rate constant? Primarily, the temperature and the presence of catalysts. When the temperature rises, the rate constant typically increases. This is due to more molecules having sufficient energy to exceed the activation energy, thus leading to more effective collisions. A crucial formula that shows this relationship is the Arrhenius equation:
  • k=Ae^{-Ea/RT}
In this equation:
  • A represents the frequency factor, accounting for the number of collisions with the correct orientation.
  • Ea is the activation energy.
  • R is the gas constant.
  • T is the temperature in Kelvin.
Catalysts can also increase the rate constant by providing an alternative pathway with a lower activation energy, enhancing the reaction rate even without a change in temperature. So, the reaction rate constant is a dynamic quantity that plays a critical role in defining how rapidly a reaction occurs.
Temperature Effect on Reactions
Temperature significantly impacts the rate of chemical reactions due to its influence on molecular energy. As temperature increases, molecules move with greater kinetic energy, leading to more frequent and forceful collisions.

One consequence of raised temperatures is a heightened fraction of molecules possessing energy that exceeds the activation energy. According to the Maxwell-Boltzmann distribution, higher temperatures shift the energy distribution curve, allowing more molecules to participate in successful collisions with sufficient energy.

Additionally, other factors like the frequency of collisions and the orientation during those collisions are affected by temperature changes. However, these are less sensitive compared to the fraction of molecules overcoming the activation energy barrier, which is the most temperature-sensitive factor.

Consequently, an increase in temperature generally boosts the rate of chemical reactions, and understanding this relationship serves as a cornerstone for predicting and controlling reaction kinetics in various fields of chemistry.

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Most popular questions from this chapter

Consider the hypothetical reaction \(2 \mathrm{~A}+\mathrm{B} \longrightarrow 2 \mathrm{C}+\mathrm{D}\) The following two-step mechanism is proposed for the reaction: $$ \begin{array}{l} \text { Step } 1: A+B \longrightarrow C+X \\ \text { Step } 2: A+X \longrightarrow C+D \end{array} $$ \(\mathrm{X}\) is an unstable intermediate. (a) What is the predicted rate law expression if Step 1 is rate determining? (b) What is the predicted rate law expression if Step 2 is rate determining? (c) Your result for part (b) might be considered surprising for which of the following reasons: (i) The concentration of a product is in the rate law. (ii) There is a negative reaction order in the rate law. (iii) Both reasons (i) and (ii). (iv) Neither reasons (i) nor (ii).

The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows: \begin{tabular}{ll} \hline Temperature \((\mathrm{K})\) & Rate Constant \(\left(\mathrm{s}^{-1}\right)\) \\ \hline 300 & \(3.2 \times 10^{-11}\) \\ 320 & \(1.0 \times 10^{-9}\) \\ 340 & \(3.0 \times 10^{-8}\) \\ 355 & \(2.4 \times 10^{-7}\) \\ \hline \end{tabular} From these data, calculate the activation energy in units of \(\mathrm{kJ} / \mathrm{mol}\).

Consider the following reaction between mercury(II) chloride and oxalate ion: $$ 2 \mathrm{HgCl}_{2}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \longrightarrow 2 \mathrm{Cl}^{-}(a q)+2 \mathrm{CO}_{2}(g)+\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s) $$ The initial rate of this reaction was determined for several concentrations of \(\mathrm{HgCl}_{2}\) and \(\mathrm{C}_{2} \mathrm{O}_{4}{ }^{2-}\), and the following rate data were obtained for the rate of disappearance of \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}:\) \begin{tabular}{llll} \hline Experiment & {\(\left[\mathrm{HgCl}_{2}\right](M)\)} & {\(\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right](M)\)} & Rate \((M / \mathrm{s})\) \\ \hline 1 & 0.164 & 0.15 & \(3.2 \times 10^{-5}\) \\ 2 & 0.164 & 0.45 & \(2.9 \times 10^{-4}\) \\ 3 & 0.082 & 0.45 & \(1.4 \times 10^{-4}\) \\ 4 & 0.246 & 0.15 & \(4.8 \times 10^{-5}\) \\ \hline \end{tabular} (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of \(\mathrm{HgCl}_{2}\) is \(0.100 \mathrm{M}\) and that of \(\mathrm{C}_{2} \mathrm{O}_{4}{ }^{2-}\) is \(0.25 \mathrm{M}\) if the temperature is the same as that used to obtain the data shown?

(a) Consider the combustion of hydrogen, \(2 \mathrm{H}_{2}(g)+\) \(\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) .\) If hydrogen is burning at a rate of \(0.5 \mathrm{~mol} / \mathrm{s},\) what is the rate of consumption of oxygen? What is the rate of formation of water vapor? (b) The reaction \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)\) is carried out in a closed vessel. If the partial pressure of NO is decreasing at the rate of \(60 \mathrm{kPa} / \mathrm{min},\) what is the rate of change of the total pressure of the vessel?

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism: $$ \begin{aligned} \mathrm{Cl}(g)+\mathrm{O}_{3}(g) & \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \\ \mathrm{ClO}(g)+\mathrm{O}(g) & \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ (a) What is the overall equation for this process? (b) What is the catalyst in the reaction? (c) What is the intermediate in the reaction?

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