You wish to determine the activation energy for the following first-order reaction: AS B + C (b) How would you use these data to determine the activation energy?

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insert step 1> Identify that the problem involves determining the activation energy for a first-order reaction.

insert step 2> Use the Arrhenius equation, which relates the rate constant k to the activation energy (Ea): k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin.

insert step 3> Take the natural logarithm of both sides of the Arrhenius equation to linearize it: ln(k) = ln(A) - Ea/(RT).

insert step 4> Plot ln(k) versus 1/T. The slope of the resulting line will be -Ea/R.

insert step 5> Calculate the activation energy (Ea) by multiplying the slope by -R, where R is the gas constant (8.314 J/mol·K).

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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. It represents the energy barrier that reactants must overcome to transform into products. In the context of a reaction, a higher activation energy indicates that the reaction is slower, as fewer molecules have sufficient energy to react at a given temperature.

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 k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation allows for the determination of activation energy by plotting ln(k) versus 1/T.

First-Order Reaction

A first-order reaction is one where the rate of reaction is directly proportional to the concentration of one reactant. This means that if the concentration of the reactant doubles, the rate of 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.

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