The tabulated data were collected for the second-order reaction: Cl(g) + H2(g) → HCl(g) + H(g). Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction. Temperature (K) and Rate Constant (L/mol # s) are as follows: 90 K, 0.00357; 100 K, 0.0773; 110 K, 0.956; 120 K, 7.781.

Verified step by step guidance

Convert the given temperatures from Kelvin to the reciprocal of temperature in Kelvin (1/T) for each data point.

Take the natural logarithm of the rate constant (k) for each temperature to obtain ln(k).

Plot ln(k) on the y-axis against 1/T on the x-axis to create the Arrhenius plot.

Determine the slope of the line from the Arrhenius plot, which is equal to -Ea/R, where Ea is the activation energy and R is the universal gas constant (8.314 J/mol K).

Calculate the activation energy (Ea) using the slope, and determine the frequency factor (A) by finding the y-intercept of the line, which is equal to ln(A).

Key Concepts

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

Second-Order Reactions

Second-order reactions are chemical reactions where the rate is proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants. In this case, the reaction between Cl(g) and H2(g) is second-order, meaning that the rate constant (k) will depend on the concentrations of both reactants. Understanding this concept is crucial for analyzing the rate data provided.

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 is fundamental for determining the activation barrier and frequency factor from the provided rate constants at different temperatures.

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 form products. In the context of the Arrhenius plot, a linear relationship between ln(k) and 1/T allows for the determination of Ea from the slope of the line, which is essential for understanding the kinetics of the given reaction.

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Textbook Question

The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1/T (in K) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.

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Textbook Question

The data shown here were collected for the first-order reaction: N₂O(g) → N₂(g) + O(g) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.

Temperature (K) Rate Constant (1 , s)

800 3.24⨉10^{- 5}

900 0.00214

1000 0.0614

1100 0.955

Textbook Question

The tabulated data show the rate constant of a reaction measured at several different temperatures. Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.

Temperature (K) Rate Constant (1 , s)

300 0.0134

310 0.0407

320 0.114

330 0.303

340 0.757

Textbook Question

A reaction has a rate constant of 0.0117/s at 400.0 K and 0.689/s at 450.0 K. a. Determine the activation barrier for the reaction.

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Textbook Question

A reaction has a rate constant of 0.000122/s at 27 °C and 0.228/s at 77 °C. b. What is the value of the rate constant at 17 °C?