Getting Started
Chemical reactions occur at vastly different speeds, from the slow rusting of iron over years to the instantaneous flash of an explosion. Chemical kinetics is the study of these reaction rates. At the macroscopic level, we can observe how quickly reactants are consumed or products are formed. At the atomic level, this speed is governed by the frequency and effectiveness of collisions between reactant particles, which is directly influenced by their concentrations.
What You Should Be Able to Do
After completing this section, you should be able to:
Write a rate law expression that mathematically describes how reactant concentrations affect the reaction rate, based on experimental data.
Determine the order of a reaction with respect to each reactant and determine the overall reaction order.
Use the method of initial rates to deduce the orders of a reaction.
Calculate the value and units of the rate constant, k, from experimental data.
Key Concepts & Analysis
To understand how reactant concentrations dictate the speed of a reaction, we use an approach that examines how the system changes when we alter its initial conditions. By systematically changing the starting concentration of one reactant at a time, we can isolate its specific effect on the reaction's initial speed.
Baseline Condition: The Initial Rate
When we mix reactants, the reaction begins immediately. The reaction rate is defined as the change in concentration of a substance per unit of time (e.g., in Molarity/second or M·s⁻¹). The rate is fastest at the very beginning of the reaction (time = 0) because the concentrations of the reactants are at their highest. This initial, instantaneous rate is the most useful value for analysis because we know the exact reactant concentrations that are producing it. Our baseline is a single experiment, or "trial," with known initial concentrations and a measured initial rate.
The Process: The Method of Initial Rates
To determine how each reactant influences the rate, we employ the Method of Initial Rates. This experimental process involves running a series of trials. The key is to change the initial concentration of only one reactant between two trials while keeping the concentrations of all other reactants constant.
Consider the generic reaction: A + B → Products
We would set up a series of experiments like this:
| Trial | Initial [A] (M) | Initial [B] (M) | Initial Rate (M·s⁻¹) |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 2.0 x 10⁻³ |
| 2 | 0.20 | 0.10 | 4.0 x 10⁻³ |
| 3 | 0.10 | 0.20 | 8.0 x 10⁻³ |
By comparing trials, we can see the effect of each reactant. This process allows us to build a mathematical model called the rate law.
The Resulting Change: Determining the Rate Law
The rate law is an equation that expresses the reaction rate as a function of reactant concentrations and a proportionality constant. For our generic reaction, the rate law has the form:
Rate = k[A]ᵐ[B]ⁿ
k is the rate constant, a value specific to the reaction at a certain temperature.
[A] and [B] are the molar concentrations of the reactants.
m and n are the reaction orders, which are small, usually whole numbers (0, 1, or 2) that describe how the rate depends on the concentration of that specific reactant.
We determine the orders m and n by analyzing the results of our process:
Find the order for A (m): Compare Trial 1 and Trial 2.
[B] is held constant (0.10 M).
[A] is doubled (from 0.10 M to 0.20 M).
The Initial Rate is also doubled (from 2.0 x 10⁻³ to 4.0 x 10⁻³).
Since doubling the concentration doubled the rate (2¹ = 2), the reaction is first order with respect to A. So, m = 1.
Find the order for B (n): Compare Trial 1 and Trial 3.
[A] is held constant (0.10 M).
[B] is doubled (from 0.10 M to 0.20 M).
The Initial Rate is quadrupled (from 2.0 x 10⁻³ to 8.0 x 10⁻³).
Since doubling the concentration quadrupled the rate (2² = 4), the reaction is second order with respect to B. So, n = 2.
The overall reaction order is the sum of the individual orders: m + n = 1 + 2 = 3. This is a third-order reaction overall.
Our rate law is now: Rate = k[A]¹[B]²
Finally, we calculate the rate constant, k, by substituting data from any trial into the rate law. Using Trial 1:
2.0 x 10⁻³ M·s⁻¹ = k (0.10 M)¹ (0.10 M)²
2.0 x 10⁻³ M·s⁻¹ = k (0.0010 M³)
k = (2.0 x 10⁻³ M·s⁻¹) / (0.0010 M³)
k = 2.0 M⁻²·s⁻¹
The units of k are crucial and depend on the overall reaction order. They ensure that the units of the rate (M·s⁻¹) are correctly produced by the equation.
Key Models & Representations
Flowchart: The Method of Initial Rates
| Step | Action | Example: Rate = k[A]¹[B]² |
|---|---|---|
| 1. Isolate a Reactant | Select two trials where only one reactant's concentration changes. | Compare Trial 1 and 2 to find the order of A. [B] is constant. |
| 2. Analyze the Change | Set up a ratio: (Rate₂ / Rate₁) = ([Reactant]₂ / [Reactant]₁)ᵐ. Solve for the exponent (order, m). | (4.0x10⁻³ / 2.0x10⁻³) = (0.20 / 0.10)ᵐ → 2 = 2ᵐ → m = 1 |
| 3. Repeat for All Reactants | Repeat steps 1 and 2 for each reactant in the equation. | Compare Trial 1 and 3 to find the order of B. [A] is constant. (8.0x10⁻³ / 2.0x10⁻³) = (0.20 / 0.10)ⁿ → 4 = 2ⁿ → n = 2 |
| 4. Assemble the Rate Law | Write the rate law expression using the determined orders. | Rate = k[A]¹[B]² |
| 5. Solve for the Rate Constant (k) | Substitute the concentrations and rate from any single trial into the rate law and solve for k. Determine the units of k. | Using Trial 1: 2.0x10⁻³ = k(0.10)(0.10)² → k = 2.0 M⁻²·s⁻¹ |
Key Terms, Quantities, & Concepts
Reaction Rate: The speed at which a chemical reaction occurs, measured as the change in concentration of a reactant or product over a specific time interval.
Rate Law: An experimentally determined equation that relates the reaction rate to the concentrations of the reactants.
Rate Constant (k): The proportionality constant in the rate law. Its value is specific to a reaction at a given temperature and its units depend on the overall reaction order.
Reaction Order: The exponent to which a reactant's concentration is raised in the rate law. It indicates the degree to which that reactant's concentration affects the reaction rate.
Zero-Order: A reaction order of 0. Changing the concentration of a zero-order reactant has no effect on the reaction rate.
First-Order: A reaction order of 1. The reaction rate is directly proportional to the concentration of a first-order reactant.
Second-Order: A reaction order of 2. The reaction rate is proportional to the square of the concentration of a second-order reactant.
Overall Reaction Order: The sum of the individual reaction orders for all reactants appearing in the rate law.
Method of Initial Rates: An experimental method used to determine the reaction orders and the rate constant by comparing the initial rates of a reaction carried out with different initial concentrations.
Skill Snapshots
Causation
Cause: Doubling the concentration of a first-order reactant. Effect: The initial reaction rate doubles.
Cause: Increasing the temperature of the reaction system. Effect: The value of the rate constant (k) increases, leading to a faster rate.
Cause: A reactant has a reaction order of zero. Effect: Changing the concentration of that reactant does not change the reaction rate.
Comparison
Reaction Order vs. Stoichiometric Coefficient: Reaction order is determined from experimental rate data, whereas a stoichiometric coefficient comes from the balanced chemical equation. The two values are generally not the same.
Rate Constant (k) vs. Reaction Rate: The rate constant (k) is a fixed value for a reaction at a given temperature, while the reaction rate is a variable that changes as reactant concentrations change over time.
First-Order vs. Second-Order: A change in concentration of a first-order reactant has a linear effect on the rate (2x concentration → 2x rate), while a second-order reactant has an exponential effect (2x concentration → 4x rate).
Change and Continuity Over Time (CCOT)
Baseline: A reaction begins with a set of initial reactant concentrations and a corresponding initial rate, governed by the rate law.
Change 1: As the reaction proceeds, reactants are consumed, their concentrations decrease, and therefore the instantaneous reaction rate slows down (for any non-zero order reaction).
Change 2: If the initial concentration of a second-order reactant is tripled in a new experiment, the new initial rate will be nine times faster than the original.
Continuity: For a given reaction at a constant temperature, the rate law expression, the reaction orders (m, n), and the value of the rate constant (k) do not change as the reaction proceeds.
Common Misconceptions & Clarifications
Misconception: The exponents in the rate law are the same as the coefficients in the balanced chemical equation.
- Clarification: Reaction orders can only be determined through experiment. They are not related to the stoichiometry of the reaction because the rate law reflects the underlying reaction mechanism, not the overall net equation.
Misconception: The rate constant, k, is always constant.
- Clarification: The rate constant is only constant at a specific temperature. Its value is highly dependent on temperature; an increase in temperature almost always leads to a significant increase in the value of k.
Misconception: A reactant with a zero order does not participate in the reaction.
- Clarification: A zero-order reactant is still a necessary ingredient and is consumed during the reaction. Its order of zero simply means that its concentration does not influence the rate-determining step of the reaction mechanism. The rate is independent of how much of that reactant is present (as long as some is available).
One-Paragraph Summary
The rate law is a powerful mathematical expression, derived from experimental data, that quantifies the relationship between reactant concentrations and the speed of a chemical reaction. It is defined by reaction orders—exponents that reveal how sensitive the rate is to the concentration of each reactant—and a temperature-dependent rate constant, k. The Method of Initial Rates is the primary experimental technique used to determine these orders by systematically varying initial reactant concentrations and observing the effect on the initial reaction rate. By constructing the rate law, chemists can predict reaction speeds under different conditions and gain insight into the step-by-step molecular pathway, or mechanism, by which reactants are transformed into products.