(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

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(a) The factors determining if a collision between two molecules leads to a chemical reaction are: 1. Energy – the molecules must have enough kinetic energy to overcome the activation energy. 2. Orientation – the molecules must collide in the correct geometry. 3. Steric factors – the molecular structure and size can affect the availability of reactive sites during collision. (b) The rate constant for a reaction, denoted by \(k\), generally increases with an increase in reaction temperature, as described by the Arrhenius equation: \(k = Ae^{(-E_a/RT)}\). (c) Among the three factors, the fraction of molecules with energy greater than the activation energy is the most sensitive to changes in temperature, as higher temperatures significantly increase the number of molecules with sufficient energy to overcome the activation energy barrier.

Step by step solution

01

a) Factors determining collision outcome

There are three main factors that determine if a collision between two molecules will lead to a chemical reaction: 1. Energy: The colliding molecules must have enough kinetic energy to overcome the energy barrier, also known as the activation energy. 2. Orientation: The molecules must collide in the correct geometry or orientation to allow bond formation and breaking. 3. Steric factors: The molecular structure and size can affect the availability of reactive sites during collision, affecting the probability of reaction.
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b) Rate constant and reaction temperature relation

The rate constant for a reaction, usually denoted by \(k\), generally increases with an increase in reaction temperature. This is because as the temperature increases, the kinetic energy of molecules increases, resulting in a higher probability of having enough energy to overcome the activation energy barrier. This relationship is described by the Arrhenius equation: \[k = Ae^{(-E_a/RT)}\] where \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. As \(T\) increases, the exponent becomes less negative, which results in an increase in \(k\).
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c) Temperature-sensitive factor

Among the three factors – frequency of collisions, orientation factor, and the fraction of molecules with energy greater than the activation energy – the most sensitive to changes in temperature would be the fraction of molecules with energy greater than the activation energy. The reason behind this is that as the temperature increases, the distribution of molecular energies becomes broader and shifts toward higher energy values. This change significantly increases the number of molecules with sufficient energy to overcome the activation energy barrier. The frequency of collisions and orientation factors are also influenced by temperature, but their effects are comparatively smaller and more predictable, thus making the energy factor more crucial to consider when evaluating temperature sensitivity.

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