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Chapter 14: Problem 54

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) According to the collision model, why does temperature affect the value of the rate constant? (c) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

Short Answer

Expert verified
(a) Two main factors determine whether a collision between two molecules will lead to a chemical reaction: 1. Reactive orientation - molecules must collide with the correct orientation. 2. Activation energy - colliding molecules must possess sufficient energy to overcome the activation energy barrier. (b) According to the collision model, temperature affects the rate constant because an increase in temperature causes molecules to move faster, collide more frequently, and with greater energy, leading to a higher probability of effective collisions. This relationship is described by the Arrhenius equation: \(k = Ae^{\frac{-Ea}{RT}}\). (c) The rate constant for a reaction generally increases as the reaction temperature increases, as there are more effective collisions and the Arrhenius equation shows a direct relationship between temperature and the rate constant.

Step by step solution

01

(a) Factors determining whether a collision will lead to a chemical reaction

There are two main factors that determine whether a collision between two molecules will lead to a chemical reaction: 1. Reactive orientation: When two molecules collide, they need to be oriented in a particular manner, so that their reactive parts (atoms, functional groups, etc.) come into contact with each other. If the molecules collide in a non-reactive orientation, no reaction will take place. 2. Activation energy: For a chemical reaction to occur, the colliding molecules need to possess sufficient energy to overcome the potential energy barrier known as activation energy (Ea). In simple terms, the molecules need to have enough kinetic energy to break the existing chemical bonds and form new ones. Only those molecules with energy equal to or greater than the activation energy can undergo the reaction.
02

(b) Effect of temperature on rate constant according to the collision model

According to the collision model, an increase in temperature effectively increases the kinetic energy of the molecules, causing them to move faster. As a result, they collide more frequently and with greater energy. This leads to a higher probability of effective collision (collisions with the right orientation and sufficient energy to overcome the activation energy barrier). The rate constant (k) is directly related to the fraction of collisions that result in a successful chemical reaction. As the temperature increases, the rate constant also increases because of the higher number of effective collisions. This relationship between temperature and the rate constant is described by the Arrhenius equation: \[k = Ae^{\frac{-Ea}{RT}}\] In this equation, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
03

(c) The rate constant and reaction temperature

As the reaction temperature increases, the rate constant for a reaction generally increases. As mentioned in the explanation for question (b), an increase in temperature leads to a higher fraction of effective collision, thus increasing the value of the rate constant. The Arrhenius equation demonstrates that the rate constant (k) is directly related to the temperature (T), such that a higher temperature results in a higher value for the rate constant.

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Key Concepts

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

Reactive Orientation
When molecules collide, the way they are positioned matters a lot. This is called "reactive orientation."
For a reaction to happen, the molecules need to approach each other in a specific way, such that their reactive parts can interact. When molecules collide:
  • They need to be aligned in a position where the reactive groups or specific atoms are able to touch and interact.
  • If they hit each other in the wrong orientation, no reaction occurs even if they possess enough energy.
Imagine two puzzle pieces: they must be turned the right way to fit. Likewise, molecules need to meet in just the right way to react. Ensuring the right orientation is like setting the stage for the reaction to occur.
Activation Energy
Activation energy is like a barrier or hill that molecules must overcome to react.
It's the minimum energy needed for the molecules to successfully convert into products. Think of a chemical reaction as a hurdle race:
  • Molecules must acquire enough kinetic energy to leap over the hurdle, which is the activation energy.
  • This energy allows them to break old bonds in the molecules and form new bonds, turning reactants into products.
Not all molecules have enough energy to overcome the hurdle. Only those colliding molecules with energy greater than or equal to the activation energy can successfully react. This concept explains why some reactions require heat; the added energy helps molecules bypass the activation energy barrier.
Temperature and Rate Constant
Temperature significantly affects how fast a reaction occurs, as it influences the rate constant (k).
With higher temperature, the molecules in a substance move more quickly. This increased movement results in:
  • More frequent collisions between molecules.
  • Collisions occurring with greater energy, increasing the chance they exceed the activation energy.
The relationship between temperature and rate constant is given by the Arrhenius equation:\[ k = Ae^{-\frac{Ea}{RT}} \]Where:
  • \( k \) is the rate constant,
  • \( A \) is a pre-exponential factor,
  • \( Ea \) is the activation energy,
  • R is the gas constant,
  • T is the temperature in Kelvin.
As T increases, the exponential factor becomes larger, making \( k \) larger too. So, with higher temperatures, reactions tend to happen quicker because the increased temperature boosts the rate constant.

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Most popular questions from this chapter

(a) Two reactions have identical values for \(E_{a} .\) Does this ensure that they will have the same rate constant if run at the same temperature? Explain. (b) Two similar reactions have the same rate constant at \(25^{\circ} \mathrm{C}\), but at \(35^{\circ} \mathrm{C}\) one of the reactions has a larger rate constant than the other. Account for these observations.

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: $$ \begin{aligned} \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q) \\ \mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)+\mathrm{I}^{-}(a q) \end{aligned} $$ (a) Write the chemical equation for the overall process. (b) Identify the intermediate, if any, in the mechanism. (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: \(\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}\). This rapid reaction gives the following rate data: $$ \begin{array}{lll} \hline\left[\mathrm{OCl}^{-}\right](M) & {\left[I^{-}\right](M)} & \text { Initial Rate }(M / s) \\ \hline 1.5 \times 10^{-3} & 1.5 \times 10^{-3} & 1.36 \times 10^{-4} \\ 3.0 \times 10^{-3} & 1.5 \times 10^{-3} & 2.72 \times 10^{-4} \\ 1.5 \times 10^{-3} & 3.0 \times 10^{-3} & 2.72 \times 10^{-4} \\ \hline \end{array} $$ (a) Write the rate law for this reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when \(\left[\mathrm{OCl}^{-}\right]=2.0 \times 10^{-3} \mathrm{M}\) and \(\left[\mathrm{I}^{-}\right]=5.0 \times 10^{-4} \mathrm{M}\)

Consider the following hypothetical aqueous reaction: \(\mathrm{A}(a q) \longrightarrow \mathrm{B}(a q)\). A flask is charged with \(0.065 \mathrm{~mol}\) of \(\mathrm{A}\) in a total volume of \(100.0 \mathrm{~mL}\). The following data are collected: $$ \begin{array}{lccccc} \hline \text { Time (min) } & 0 & 10 & 20 & 30 & 40 \\ \hline \text { Moles of A } & 0.065 & 0.051 & 0.042 & 0.036 & 0.031 \\ \hline \end{array} $$ (a) Calculate the number of moles of \(\mathrm{B}\) at each time in the table, assuming that there are no molecules of \(\mathrm{B}\) at time zero, and that \(A\) cleanly converts to \(B\) with no intermediates. (b) Calculate the average rate of disappearance of \(\mathrm{A}\) for each 10 -min interval in units of \(M / \mathrm{s}\). (c) Between \(t=10 \mathrm{~min}\) and \(t=30 \mathrm{~min},\) what is the average rate of appearance of \(\mathrm{B}\) in units of \(M / s\) ? Assume that the volume of the solution is constant.

The temperature dependence of the rate constant for a reaction is tabulated as follows: $$ \begin{array}{lc} \hline \text { Temperature (K) } & k\left(M^{-1} \mathrm{~s}^{-1}\right) \\ \hline 600 & 0.028 \\ 650 & 0.22 \\ 700 & 1.3 \\ 750 & 6.0 \\ 800 & 23 \\ \hline \end{array} $$ Calculate \(E_{a}\) and \(A\).
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