Rate Law Practice Questions with Answers

A rate law is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentration of its reactants. Mastering this concept is essential for students preparing for chemistry benchmarks, especially when you need to study for exams for the MCAT or advanced placement courses. By quantifying how changes in concentration influence the speed of a reaction, scientists can predict reaction behavior under varying conditions and deduce complex reaction mechanisms.

Concept Explanation

The rate law is an equation that relates the reaction rate to the molar concentrations of reactants, each raised to a specific power known as the reaction order. For a general reaction such as aA + bB → Products, the rate law is expressed as Rate = k[A]^m[B]ⁿ. In this formula, k represents the rate constant, while m and n are the partial orders of the reaction with respect to reactants A and B. It is a common misconception that these exponents are the stoichiometric coefficients from the balanced equation; in reality, they must be determined experimentally through methods like the method of initial rates.

The sum of these exponents (m + n) gives the overall reaction order. The units of the rate constant k vary depending on the overall order to ensure the rate is always expressed in units of concentration per time (e.g., M/s). For instance, a zero-order reaction has a rate independent of concentration, whereas a second-order reaction sees the rate quadruple if the concentration doubles. Understanding these nuances is a key step if you want to study for exams to get straight A’s in your chemistry curriculum.

Solved Examples

Below are fully worked examples to help you visualize how to derive rate laws from experimental data.

Example 1: Determining Reaction Order

Consider the reaction: A + B → C. Experimental data shows that doubling [A] while keeping [B] constant doubles the rate. Doubling [B] while keeping [A] constant quadruples the rate. Find the rate law.

1. Analyze reactant A: Since doubling [A] (2¹) results in doubling the rate (2¹), the reaction is 1st order with respect to A (m = 1).
2. Analyze reactant B: Since doubling [B] (2¹) results in quadrupling the rate (2²), the reaction is 2nd order with respect to B (n = 2).
3. Combine into the rate law: Rate = k[A]¹[B]².

Example 2: Calculating the Rate Constant (k)

For the reaction 2NO + O₂ → 2NO₂, the rate law is Rate = k[NO]²[O₂]. If the rate is 0.050 M/s when [NO] = 0.10 M and [O₂] = 0.20 M, calculate k.

1. Rearrange the rate law to solve for k: k = Rate / ([NO]²[O₂]).
2. Substitute the values: k = 0.050 / (0.10² * 0.20).
3. Calculate the denominator: 0.01 * 0.20 = 0.002.
4. Solve for k: k = 0.050 / 0.002 = 25 M^-2s^-1.

Example 3: Determining Units of k

Determine the units of the rate constant for a third-order reaction where the rate is in M/s.

1. Set up the equation units: (M/s) = k * (M)³.
2. Isolate k: k = (M/s) / M³.
3. Simplify the units: k = M^-2s^-1 or 1/(M²·s).

Practice Questions

Test your knowledge with these Rate Law practice questions. If you find yourself struggling to study for exams when overwhelmed, try breaking these problems down into smaller steps.

1. The reaction 2X + Y → Z is zero order with respect to X and first order with respect to Y. Write the rate law.
2. If the concentration of a reactant in a second-order reaction is tripled, by what factor does the reaction rate increase?
3. A reaction has the rate law: Rate = k[A][B]. What is the overall reaction order?

4. For the reaction A + B → C, the rate triples when [A] is tripled and remains unchanged when [B] is doubled. What is the rate law?
5. Calculate the rate of a reaction if k = 0.25 M^-1s^-1, [A] = 0.40 M, and the reaction is second order with respect to A.
6. Determine the units of k for a first-order reaction.
7. In a certain reaction, doubling the concentration of reactant [A] increases the rate by a factor of 8. What is the order of the reaction with respect to A?
8. If a reaction is Rate = k[A]²[B]⁰, how does the rate change if [B] is halved?
9. A reaction is found to have a rate constant k = 4.5 x 10^-3 s^-1. What is the overall order?
10. Given the data: [A]=0.1M, Rate=0.02; [A]=0.2M, Rate=0.08. Determine the order with respect to A.

Answers & Explanations

1. Rate = k[Y]: Since the reaction is zero order with respect to X, [X]⁰ = 1, so it does not appear in the rate law. It is first order with respect to Y, so [Y] is raised to the power of 1.
2. 9: In a second-order reaction (Rate = k[R]²), tripling the concentration results in a rate change of 3² = 9.
3. 2 (Second Order): The overall order is the sum of the exponents: 1 (for A) + 1 (for B) = 2.
4. Rate = k[A]: The rate is proportional to [A] (3¹ = 3), so it is first order in A. The rate is independent of [B] (2⁰ = 1), so it is zero order in B.
5. 0.04 M/s: Rate = k[A]² = 0.25 * (0.40)² = 0.25 * 0.16 = 0.04.
6. s^-1: For a first-order reaction, Rate (M/s) = k[M]. Dividing both sides by M gives 1/s or s^-1.
7. 3 (Third Order): We solve 2ⁿ = 8. Since 2³ = 8, the order n is 3.
8. No change: Since the reaction is zero order with respect to B, changing the concentration of B has no effect on the rate.
9. First Order: The units of the rate constant (s^-1) are characteristic of a first-order reaction.
10. Second Order: When [A] doubles (0.1 to 0.2), the rate quadruples (0.02 to 0.08). Since 2² = 4, the order is 2.

Quick Quiz

Frequently Asked Questions

What is the difference between the rate constant and the reaction rate?

The reaction rate is the speed at which a reaction occurs (M/s), while the rate constant (k) is a proportionality constant unique to a reaction at a specific temperature. Unlike the rate, the rate constant does not change as the concentrations of reactants decrease during the reaction.

How do you find the overall order of a reaction?

The overall order of a reaction is found by summing the individual exponents of all reactants present in the rate law. For example, if the rate law is Rate = k[A]¹[B]², the overall order is 1 + 2 = 3.

Why are the units of k different for different reaction orders?

Units of k vary to ensure that the final calculation of the reaction rate always results in units of Molarity per second (M/s). As the sum of the concentration exponents changes, the units of k must adjust to cancel out the extra Molarity terms.

Can a reaction order be a fraction or a negative number?

Yes, while many introductory problems use whole numbers, reaction orders can be fractions or negative values. These complex orders often indicate a sophisticated reaction mechanism involving multiple steps or inhibition.

Does temperature affect the rate law?

Temperature does not change the form of the rate law or the reaction orders, but it significantly affects the rate constant k. According to the Arrhenius equation, increasing the temperature typically increases k, thereby speeding up the reaction.

What is a zero-order reaction?

A zero-order reaction is one where the rate is completely independent of the concentration of the reactants. This means that no matter how much reactant you add or remove, the reaction proceeds at a constant speed until the reactant is exhausted.

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