Use the following initial rate data to determine the activation energy (in kJ/mol) for the reaction A + B ⇌ C.

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1

Step 1: Understand the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea) and temperature (T): k = A * e^(-Ea/(RT)), where A is the pre-exponential factor and R is the gas constant (8.314 J/(mol·K)).

Step 2: Use the initial rate data to determine the rate constants (k) at different temperatures. This typically involves using the rate law for the reaction, which might be given or determined from the data.

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Step 3: Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature value.

Step 4: Plot ln(k) versus 1/T (in Kelvin) to create an Arrhenius plot. The slope of this line will be equal to -Ea/R.

Step 5: Calculate the activation energy (Ea) using the slope from the Arrhenius plot. Multiply the slope by -R to find Ea, and convert the result from J/mol to kJ/mol by dividing by 1000.

Key Concepts

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. This concept is crucial for understanding reaction rates, as higher activation energies typically lead to slower reactions, while lower activation energies facilitate faster reactions.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the reaction orders with respect to reactants A and B. Understanding the rate law is essential for analyzing how changes in concentration affect the reaction rate and for determining the activation energy.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. It is expressed as k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation is fundamental for calculating activation energy from experimental rate data, as it shows how temperature influences reaction rates.

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Related Practice

Textbook Question

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H₃O⁺ by OH^-, which has a second-order rate constant of 1.3⨉10¹¹ M^-1 s^-1 at 25 °C. (b) Under normal laboratory conditions, would you expect the rate of the acid–base neutralization to be limited by the rate of the reaction or by the speed of mixing?

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Textbook Question

The reaction 2 NO1g2 + O21g2S 2 NO21g2 has the thirdorderrate law rate = k3NO423O24, where k = 25 M-2 s-1.Under the condition that 3NO4 = 2 3O24, the integratedrate law is13O242 = 8 kt +113O24022What are the concentrations of NO, O2, and NO2 after100.0 s if the initial concentrations are 3NO4 = 0.0200 Mand 3O24 = 0.0100 M?

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Textbook Question

The following experimental data were obtained in a studyof the reaction 2 HI1g2S H21g2 + I21g2. Predict the concentrationof HI that would give a rate of 1.0 * 10-5 M>sat 650 K.

Verified step by step guidance

1. Step 1: Understand the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea) and temperature (T): k = A * e^(-Ea/(RT)), where A is the pre-exponential factor and R is the gas constant (8.314 J/(mol·K)).
2. Step 2: Use the initial rate data to determine the rate constants (k) at different temperatures. This typically involves using the rate law for the reaction, which might be given or determined from the data.
3. Step 3: Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature value.
4. Step 4: Plot ln(k) versus 1/T (in Kelvin) to create an Arrhenius plot. The slope of this line will be equal to -Ea/R.
5. Step 5: Calculate the activation energy (Ea) using the slope from the Arrhenius plot. Multiply the slope by -R to find Ea, and convert the result from J/mol to kJ/mol by dividing by 1000.

Key Concepts

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. This concept is crucial for understanding reaction rates, as higher activation energies typically lead to slower reactions, while lower activation energies facilitate faster reactions.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the reaction orders with respect to reactants A and B. Understanding the rate law is essential for analyzing how changes in concentration affect the reaction rate and for determining the activation energy.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. It is expressed as k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation is fundamental for calculating activation energy from experimental rate data, as it shows how temperature influences reaction rates.