This reaction has an activation energy of zero in the gas phase: CH 3 + CH 3 → C 2 H 6 a. Would you expect the rate of this reaction to change very much with temperature?

hey everyone in this example, we need to identify the relationship between the reaction rate and temperature. So we want to recall our formula where our rate constant K. Is equal to our frequency factor represented by a here, which is then multiplied by Euler number which is raised to our activation energy divided by r gas constant times the temperature. We can also interpret this equation by saying that we can take the L. N. Of the rate constant for a single reaction At different absolute temperatures. So we would therefore have to rate constants K. one And then that is going to be placed over K two. So just to be clear, these are the rate constants for a single reaction at two absolute, We can say two different absolute temperatures and now we can set this equal to our activation energy divided by r gas constant. R. Where now we're going to multiply by the inverse values of our initial temperature. T one Subtracted from the inverse value of our final temperature T. two. And so here it's clear that our rate constant K. Is directly related to temperature. And so we can say that therefore if we increase our rate constant or we can say if we increase our temperature, we would also increase our rate constant. So the answer here is that they have a direct relationship. So this would be our final answer. To complete this example. If you have any questions please leave them down below and I will see everyone in the next practice video

Ch.15 - Chemical Kinetics

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Tro 6th Edition

Ch.15 - Chemical Kinetics

Problem 107a

Chapter 15, Problem 107a

This reaction has an activation energy of zero in the gas phase: CH₃ + CH₃ → C₂H₆
a. Would you expect the rate of this reaction to change very much with temperature?

Verified step by step guidance

Understand the concept of activation energy: Activation energy is the minimum energy required for a chemical reaction to occur. It acts as a barrier that reactants must overcome to transform into products.

Recognize the significance of zero activation energy: When a reaction has an activation energy of zero, it means that there is no energy barrier for the reaction to proceed. The reactants can convert to products without needing additional energy input.

Consider the effect of temperature on reaction rate: Generally, increasing the temperature increases the kinetic energy of molecules, leading to more frequent and energetic collisions, which typically increases the reaction rate.

Analyze the specific case of zero activation energy: Since the reaction has no energy barrier, the rate of reaction is not dependent on the energy distribution of molecules. Therefore, changes in temperature will have minimal effect on the rate of reaction.

Conclude the analysis: For this reaction with zero activation energy, the rate is expected to remain relatively constant with changes in temperature, as there is no energy barrier to influence the rate.

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Key Concepts

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

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. In reactions with zero activation energy, the reactants can convert to products without needing to overcome an energy barrier, suggesting that the reaction can proceed readily under a variety of conditions.

Temperature and Reaction Rate

The rate of a chemical reaction typically increases with temperature due to the increased kinetic energy of the molecules, which leads to more frequent and effective collisions. However, in reactions with zero activation energy, the rate is less sensitive to temperature changes since the energy barrier is already negligible.

Collision Theory

Collision theory states that for a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation. In the case of the given reaction, the lack of activation energy implies that even at lower temperatures, collisions can lead to product formation, resulting in a relatively constant reaction rate regardless of temperature fluctuations.

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Collision Theory

Related Practice

Textbook Question

The evaporation of a 120-nm film of n-pentane from a single crystal of aluminum oxide is zero order with a rate constant of 1.92⨉1013 molecules/cm²•s at 120 K. a. If the initial surface coverage is 8.9⨉1016 molecules/cm², how long will it take for one-half of the film to evaporate?

The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)

C₂H₅Br(aq) + OH^- (aq) → C₂H₅OH(l) + Br^- (aq)

Temperature (°C) k (L,mol •s)

25 8.81⨉10^-5

35 0.000285

45 0.000854

55 0.00239

65 0.00633

b. Determine the rate constant at 15 °C.

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Textbook Question

The reaction 2 N₂O₅ → 2 N₂O₄ + O₂ takes place at around room temperature in solvents such as CCl₄. The rate constant at 293 K is found to be 2.35⨉10^-4 s^-1, and at 303 K the rate constant is found to be 9.15⨉10^-4 s^-1.Calculate the frequency factor for the reaction.

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Textbook Question

Consider the two reactions:

O + N₂ → NO + N E_a = 315 kJ/mol

Cl + H₂ → HCl + H E_a = 23 kJ/mol

a. Why is the activation barrier for the first reaction so much higher than that for the second?

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Textbook Question

Consider the two reactions:

O + N₂ → NO + N E_a = 315 kJ/mol

Cl + H₂ → HCl + H E_a = 23 kJ/mol

b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.

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Textbook Question

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon- 14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 19.5% of the C-14 found in living organisms. How old is the bone?

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This reaction has an activation energy of zero in the gas phase: CH3 + CH3 → C2H6a. Would you expect the rate of this reaction to change very much with temperature?

Verified Solution

Key Concepts

Activation Energy

Temperature and Reaction Rate

Collision Theory

This reaction has an activation energy of zero in the gas phase: CH₃ + CH₃ → C₂H₆
a. Would you expect the rate of this reaction to change very much with temperature?