Textbook Question
(b) What is the difference between a unimolecular and a bimolecular elementary reaction?
Ch.14 - Chemical Kinetics
Chapter 14, Problem 64
The temperature dependence of the rate constant for a reaction is tabulated as follows: Temperature (K) k 1M 1 s1 2 600 0.028 650 0.22 700 1.3 750 6.0 800 23 Calculate Ea and A.
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Identify the Arrhenius equation: $k = A e^{-\frac{E_a}{RT}}$, where $k$ is the rate constant, $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant (8.314 J/mol·K), and $T$ is the temperature in Kelvin.
Take the natural logarithm of both sides of the Arrhenius equation to linearize it: $\ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T}$.
Plot $\ln k$ versus $\frac{1}{T}$ using the given data points. The slope of the line will be $-\frac{E_a}{R}$, and the y-intercept will be $\ln A$.
Calculate the slope of the line from the plot, which is $-\frac{E_a}{R}$. Use this slope to solve for $E_a$ by rearranging the equation: $E_a = -\text{slope} \times R$.
Determine the y-intercept from the plot, which is $\ln A$. Solve for $A$ by taking the exponential of the y-intercept: $A = e^{\text{y-intercept}}$.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Arrhenius Equation
The Arrhenius equation relates the rate constant (k) of a chemical reaction to the temperature (T) and activation energy (Ea). It is expressed as k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, R is the universal gas constant, and T is the temperature in Kelvin. This equation highlights how temperature influences reaction rates and is fundamental for calculating Ea and A.
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Activation Energy (Ea)
Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. A higher Ea indicates a slower reaction rate at a given temperature, while a lower Ea suggests a faster reaction. Understanding Ea is crucial for predicting how temperature changes affect reaction rates.
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Pre-exponential Factor (A)
The pre-exponential factor (A) in the Arrhenius equation is a constant that represents the frequency of collisions and the orientation of reactants during a reaction. It reflects the likelihood that collisions will lead to a successful reaction. A is temperature-dependent and can be determined alongside Ea when analyzing the temperature dependence of rate constants.
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