(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

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(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.
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(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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Most popular questions from this chapter

(a) Define the following symbols that are encountered in rate equations for the generic reaction \(\mathrm{A} \longrightarrow \mathrm{B}:[\mathrm{A}]_{0}, t_{1 / 2}[\mathrm{~A}]_{t}, k\) (b) What quantity, when graphed versus time, will yield a straight line for a first-order reaction? (c) How can you calculate the rate constant for a first- order reaction from the graph you made in part (b)?

(a) The reaction \(\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\frac{1}{2} \mathrm{O}_{2}(g)\) is first order. Near room temperature, the rate constant equals \(7.0 \times 10^{-4} \mathrm{~s}^{-1} .\) Calculate the half-life at this temperature. (b) At \(415^{\circ} \mathrm{C},\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}\) decomposes in the gas phase, \(\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{CO}(g) .\) If the reaction is first order with a half-life of 56.3 min at this temperature, calculate the rate constant in \(\mathrm{s}^{-1}\).

The following mechanism has been proposed for the gasphase reaction of \(\mathrm{H}_{2}\) with ICl: $$ \begin{array}{l} \mathrm{H}_{2}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{HI}(g)+\mathrm{HCl}(g) \\ \mathrm{HI}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{I}_{2}(g)+\mathrm{HCl}(g) \end{array} $$ (a) Write the balanced equation for the overall reaction. (b) Identify any intermediates in the mechanism. (c) If the first step is slow and the second one is fast, which rate law do you expect to be observed for the overall reaction?

Consider a hypothetical reaction between \(A, B,\) and \(C\) that is first order in \(A,\) zero order in \(B,\) and second order in C. (a) Write the rate law for the reaction. (b) How does the rate change when \([\mathrm{A}]\) is doubled and the other reactant concentrations are held constant? (c) How does the rate change when \([\mathrm{B}]\) is tripled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (e) By what factor does the rate change when the concentrations of all three reactants are tripled? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

(a) If you were going to build a system to check the effectiveness of automobile catalytic converters on cars, what substances would you want to look for in the car exhaust? (b) Automobile catalytic converters have to work at high temperatures, as hot exhaust gases stream through them. In what ways could this be an advantage? In what ways a disadvantage? (c) Why is the rate of flow of exhaust gases over a catalytic converter important?

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