chemical reactions

Introduction

Chemical kinetics is the study of Reaction Rates. A rate law expresses the relationship between the rate of a reaction and the concentrations of reactants. The rate law provides crucial information about the mechanism of a reaction.

units of reaction constant

General Form of a Rate Law

For a generic reaction:

$$ aA + bB → cC + dD $$

The rate law is expressed as:

$$ Rate = k[A]]^m[B]]^n \dots $$

Where:

• k is the rate constant (Temperature dependent).
• [A]] and [B]] are the molar concentrations of reactants A and B.
• m and [n]] are the reaction orders with respect to A and B, respectively. These are not necessarily the same as the stoichiometric coefficients (a and b). They must be determined experimentally.

Reaction Order

The overall reaction order is the sum of the individual orders (m + n). The reaction order indicates how the rate changes with changes in reactant concentration:

• Zero Order: The rate is independent of the reactant’s concentration. If [A]] doubles, the rate stays the same.
• First Order: The rate is directly proportional to the reactant’s concentration. If [A]] doubles, the rate doubles.
• Second Order: The rate is proportional to the square of the reactant’s concentration. If [A]] doubles, the rate quadruples. !1(https://i.ytimg.com/vi/7I0Xg92_eA4/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD&rs=AOn4CLCQ4AEMO0Ml8RjsNs9lov04Ob_SBQ) !1(https://www.chadsprep.com/wp-content/uploads/2020/02/2nd-Order-Integrated-Rate-Law-Plots.png)

Determining Rate Laws

There are several methods to determine rate laws experimentally:

• Method of Initial Rates: Method of Initial Rates This method uses initial Reaction Rates measured under different initial reactant concentrations. By comparing the changes in rate with changes in concentration, the reaction orders can be determined.

• Integrated Rate Laws: Integrated Rate Laws These laws relate concentration to time. By plotting experimental data according to the integrated rate laws for different orders, the correct order can be identified by the linear plot.

• Graphical Methods: Analyzing plots of concentration versus time can help determine the reaction order. For example, a plot of ln[A]] vs. time yields a straight line for a first-order reaction.

Rate Constant (k)

The rate constant, k, is a proportionality constant that relates the rate to the reactant concentrations. Its value depends on:

• Temperature: Generally, k increases with temperature. Arrhenius Equation
• Activation Energy: Activation Energy A higher Activation Energy results in a smaller k.
• Presence of a Catalyst: Catalysts increase k by providing an alternative reaction pathway with lower Activation Energy. Catalysis

Units of k

The units of k depend on the overall reaction order:

• Zero Order: M/s or mol L⁻¹ s⁻¹
• First Order: s⁻¹
• Second Order: M⁻¹s⁻¹ or L mol⁻¹ s⁻¹

Example Rate Law Problem

Problem:

The following data were collected for the reaction: A + B → C

Determine the rate law for this reaction, including the value of the rate constant, k.

Solution:

1. Determine the order with respect to A:

Compare experiments 1 and 2, where [B]] is constant but [A]] doubles:

• The rate increases by a factor of 4 (4.0 x 10⁻⁴ / 1.0 x 10⁻⁴ = 4).
• Since the rate quadruples when [A]] doubles, the reaction is second order with respect to A (2² = 4).

2. Determine the order with respect to B:

Compare experiments 1 and 3, where [A]] is constant but [B]] doubles:

• The rate increases by a factor of 2 (2.0 x 10⁻⁴ / 1.0 x 10⁻⁴ = 2).
• Since the rate doubles when [B]] doubles, the reaction is first order with respect to B.

3. Write the rate law:

The rate law is: Rate = k[A]]²[B]]¹ or simply Rate = k[A]]²[B]]

4. Determine the value of the rate constant, k:

Use the data from any experiment to solve for k. Let’s use experiment 1:

1.0 x 10⁻⁴ M/s = k (0.10 M)² (0.10 M)

k = (1.0 x 10⁻⁴ M/s) / (0.001 M³) = 0.1 M⁻²s⁻¹

5. Final Answer:

The rate law for the reaction is: Rate = 0.1 M⁻²s⁻¹ [A]]²[B]]

Elementary Reactions

An elementary reaction is a single step in a reaction mechanism. For elementary reactions, the reaction orders are equal to the stoichiometric coefficients. Complex reactions involve multiple elementary steps. The slowest elementary step, called the rate-determining step, determines the overall rate law. Rate-Determining Step