Ethyl chloride vapor decomposes by the first-order reaction: C 2 H 5 Cl → C 2 H 4 + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉10 14 s -1 . Find the value of the rate constant at 710 K.

Hello everyone. So in this question we're being told to consider the following first order action. That's given right over here if the reaction has an activation energy of kg joules per mole and are erogenous constant of 2.1 times 10 to the 13th power as two negative one, calculate the rate constant of the reaction at 650 kelvin's. So let's recall what the Arrhenius equation is. So this is equal to K. equaling two capital a. E. Race apart of negative E. A over R. T. What this case stands for here is the rate constant with this E. Of a value is the activation energy usually in the units of joules per mole. Then we have this capital R. This is the ideal gas constant and that's 8.314 joules per mole times Calvin's. We'll just write this in later. T here, right next to the R. Is going to be temperatures and it's in the units of kelvin's. And then of course are a here is the Arrhenius constant or the frequency factor In our case we're given the Arrhenius constant. Let's go ahead and solve for E. Of A. So the E. Of a. Is to go to 100 and three killer jewels per mole. We want to go ahead and convert this killer jewel unit into jewels. So do a direct conversion here for every jewels. We have one killer jewel, this gives me a of a value to be 103000 units being jewels per mole. Now for my cake constant here is equal to 2. times 10 to the 13 seconds. Raised to negative 101 over seconds times E raised the power of negative 30 00. You forgot the units here. This is jules per month divided by Our our value. That's 8.314 joules per mole times kelvin multiplied by T. And that is our temperature and that is 650 Calvin's. Alright, so here we're just solving for K. The rate constant of the reaction. So we're simplifying this values here. So we'll just keep 2.1 times 10 to the 13 S. Race to power negative one as constant. Then we have e raised to power now of negative 19.5960 to 89. Alright, so we find this further. We get that K. Is equal to 2.1 times 10 to the 13 as raising power of negative one, multiplied by 5.27861 times to the negative nine. Alright, let's put this all into our calculators. We finally get the rate constant of this reaction is equal to 1.6 times 10 to the fifth. Power. S per seconds raised to a negative one. Or just one over seconds. So this race constant Here is going to be my final answer for this problem

Ch.15 - Chemical Kinetics

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Tro 6th Edition

Ch.15 - Chemical Kinetics

Problem 118a

Chapter 15, Problem 118a

Ethyl chloride vapor decomposes by the first-order reaction: C₂H₅Cl → C₂H₄ + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉10¹⁴ s^-1. Find the value of the rate constant at 710 K.

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Identify the Arrhenius equation: k = A \cdot e^{-\frac{E_a}{RT}}.

Substitute the given values into the Arrhenius equation: A = 1.6 \times 10^{14} \text{s}^{-1}, E_a = 249 \text{kJ/mol}, T = 710 \text{K}.

Convert the activation energy from kJ/mol to J/mol: E_a = 249 \times 10^3 \text{J/mol}.

Use the gas constant R = 8.314 \text{J/mol} \cdot \text{K} in the equation.

Calculate the exponent: -\frac{E_a}{RT} and then find the rate constant k by evaluating the Arrhenius equation.

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Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that if the concentration of the reactant doubles, the rate of the reaction also doubles. The rate law for a first-order reaction can be expressed as rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation shows how temperature influences reaction rates, with higher temperatures generally leading to increased rates.

Activation Energy

Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. A higher activation energy indicates that fewer molecules have sufficient energy to react at a given temperature, thus affecting the rate of the reaction. In the context of the Arrhenius equation, a higher Ea results in a smaller rate constant at lower temperatures.