Chemistry/Chapter 7: Chemical Kinetics
7.2.2 Determination of Reaction Order, Rate Law and Rate Constant
Method of Initial Rates:
Explanation level
This topic explains how to determine the reaction order, rate law, and rate constant experimentally using the method of initial rates. It provides a step-by-step approach with worked examples.
Definition
Method of Initial Rates: An experimental method in which the concentration of one reactant is systematically varied while keeping others constant, and the initial reaction rate is measured for each change.
Rate Law: An expression that relates the rate of a reaction to the rate constant and the concentration of reactants raised to appropriate powers.
Rate Constant (k): The proportionality constant in the rate law.
Main Idea
The effect of a change in reactant concentration on reaction rates cannot be derived from a chemical equation. It can only be determined experimentally by determining the order of chemical reactions. For this purpose, the method of initial rates is a simpler way to find the value of the reaction order. In this method, an experiment is designed in which the concentration of one reactant is changed while keeping everything else constant. The concentration of one reactant is systematically varied and the initial reaction rate is determined for each change.
Core Concept
- Compare experiments where the concentration of one reactant changes while others remain constant.
- Determine how the rate changes with concentration.
- The exponent in the rate law is the order with respect to that reactant.
- Once the rate law is determined, the rate constant (k) can be calculated from any experiment.
Detailed Explanation
Method of Initial Rates
- An experiment is designed in which the concentration of one reactant is changed while keeping everything else constant.
- The concentration of one reactant is systematically varied and the initial reaction rate is determined for each change.
Example 7.2: Reaction of NO with Ozone
Problem: Jet engines release Nitrogen (II) oxide in the upper atmosphere. In the ozone layer of upper atmosphere, Nitrogen (II) oxide reacts with ozone to form nitrogen (IV) oxide and oxygen.
Reaction: NO + O3 → NO2 + O2
Data:
| Experiment | Initial [NO] | Initial [O₃] | Initial Rate (mol dm⁻³ s⁻¹) |
|---|---|---|---|
| 1 | 1.00 × 10⁻⁶ | 9.00 × 10⁻⁶ | 1.98 × 10⁻⁴ |
| 2 | 2.00 × 10⁻⁶ | 9.00 × 10⁻⁶ | 3.96 × 10⁻⁴ |
| 3 | 1.00 × 10⁻⁶ | 3.00 × 10⁻⁶ | 6.60 × 10⁻⁵ |
Solution:
To determine the order of reaction with respect to a reactant, examine the relationship between its initial concentration and the rate of reaction while holding the concentration of the other reactant constant.
Determining order with respect to NO:
In experiments 1 and 2, the initial concentration of ozone is kept constant at 9.00 × 10⁻⁶ M while the concentration of NO is doubled from 1.00 × 10⁻⁶ M to 2.00 × 10⁻⁶ M. The initial rate increases from 1.98 × 10⁻⁴ to 3.96 × 10⁻⁴ mol dm⁻³ s⁻¹.
The ratio between these two rates is: 3.96 × 10-41.98 × 10-4 = 2
Thus, the initial rate doubles. This means the rate of reaction is directly proportional to the first power of concentration of NO. Rate ∝ [NO]1
Determining order with respect to O₃:
In experiments 1 and 3, the initial concentration of NO is kept constant at 1.00 × 10⁻⁶ M and the concentration of ozone is decreased to one third, i.e., from 9.00 × 10⁻⁶ to 3.00 × 10⁻⁶ M. The initial rate decreases from 1.98 × 10⁻⁴ to 6.60 × 10⁻⁵ mol dm⁻³ s⁻¹.
The ratio between these rates is: 1.98 × 10-46.60 × 10-5 = 3
Thus, the rate of reaction also decreases to one third. This means the rate of reaction is directly proportional to the first power of concentration of O₃. Rate ∝ [O3]1
Rate Law:
Thus, the rate law for the reaction is: Rate ∝ [NO][O3] Rate = k[NO][O3]
Hence, this reaction is a second order reaction (overall order = 1 + 1 = 2).
Determining Rate Constant (k):
Once the rate law for a reaction is determined experimentally, the rate constant for the reaction can be determined from the same experimental data that has been used to calculate the order of the reaction. For this purpose, substitute the data for any of the above experiments into the rate law expression.
Rate = k[NO][O3]
Let us use data of experiment 1: 1.98 × 10-4 = k[1 × 10-6][9 × 10-6] 1.98 × 10-4 = k[9 × 10-12] k = 1.98 × 10-49 × 10-12 k = 2.2 × 107 mol-1 dm3 s-1
If you use the data of experiment 2 or 3, the same result will be obtained.
Example 7.3: Writing Rate Law from Given Orders
Problem: The following reaction is first order in H₂ and half order in Br₂. Write the rate law for the reaction. H2 + Br2 → 2HBr
Solution:
Given information indicates that: Rate ∝ [H2]1 (i) Rate ∝ [Br2]12 (ii)
Combining (i) and (ii), we get the rate law for the reaction: Rate ∝ [H2][Br2]12 Rate = k[H2][Br2]12
Concept Assessment Exercise 7.1
1. Phosgene is a toxic gas. It has been used in World War II. This gas is prepared by the reaction of carbon monoxide with chlorine. CO(g) + Cl2(g) → COCl2(g)
The following data were obtained for kinetic study of this reaction.
| Experiment | Initial [CO] | Initial [Cl₂] | Initial Rate (mol dm⁻³ s⁻¹) |
|---|---|---|---|
| 1 | 1.000 | 0.100 | 1.29 × 10⁻²⁹ |
| 2 | 0.100 | 0.100 | 1.30 × 10⁻³⁰ |
| 3 | 0.100 | 1.000 | 1.30 × 10⁻³⁰ |
Write rate law for this reaction.
2. The following reaction is second order in NO₂ and is independent of the concentration of CO. Write rate law for the reaction. What is the overall order of the reaction? NO2 + CO → NO + CO2
Intermediate Level
Method of Initial Rates
| Step | Action |
|---|---|
| 1 | Compare experiments where one concentration changes |
| 2 | Determine how rate changes with concentration |
| 3 | The exponent is the order |
| 4 | Write rate law |
| 5 | Calculate k from any experiment |
Example 7.2
Data:
| Exp | [NO] | [O₃] | Rate |
|---|---|---|---|
| 1 | 1.00 × 10⁻⁶ | 9.00 × 10⁻⁶ | 1.98 × 10⁻⁴ |
| 2 | 2.00 × 10⁻⁶ | 9.00 × 10⁻⁶ | 3.96 × 10⁻⁴ |
| 3 | 1.00 × 10⁻⁶ | 3.00 × 10⁻⁶ | 6.60 × 10⁻⁵ |
Order with respect to NO: - Compare Exp 1 and 2: [NO] doubles, rate doubles → order = 1.
Order with respect to O₃: - Compare Exp 1 and 3: [O₃] decreases to 13, rate decreases to 13 → order = 1.
Rate Law: Rate = k[NO][O3]
Rate Constant (k): k = 1.98 × 10-4(1 × 10-6)(9 × 10-6) = 2.2 × 107 mol-1 dm3 s-1
Example 7.3
- First order in H₂
- Half order in Br₂
Rate Law: Rate = k[H2][Br2]12
Important Points
- 1. Method of initial rates: Vary one concentration, keep others constant.
- 2. Compare rates to determine order.
- 3. Rate law: Rate = k[A]x[B]y.
- 4. Rate constant (k): Calculated from experimental data.
- 5. Example 7.2: Rate = k[NO][O₃], k = 2.2 × 10⁷ mol⁻¹ dm³ s⁻¹.
- 6. Example 7.3: Rate = k[H₂][Br₂]12.
- 7. Concept Assessment: Phosgene and NO₂ + CO reactions.
Remember
- - Method of initial rates: Vary one concentration at a time
- - Order: Determined from rate change
- - **Rate law:** Rate = k[A]x[B]y
- - Rate constant: Calculated from data
- - **Example 7.2:** Rate = k[NO][O₃]
- - **Example 7.3:** Rate = k[H₂][Br₂]12
Common Mistakes
- 1. Thinking order is from stoichiometry: It is determined experimentally.
- 2. Not keeping other concentrations constant: Must vary one at a time.
- 3. Forgetting to calculate k: Use data from any experiment.
- 4. Mixing up the rate law: Use correct exponents.
Quick Revision
- Method of initial rates: Vary one concentration, keep others constant.
- Compare rates to determine order.
- Rate law: Rate = k[A]x[B]y.
- Rate constant (k): Calculated from experimental data.
- Example 7.2: Rate = k[NO][O₃], k = 2.2 × 10⁷ mol⁻¹ dm³ s⁻¹.
- Example 7.3: Rate = k[H₂][Br₂]12.
- Concept Assessment: Phosgene and NO₂ + CO reactions.
60-Second Revision
- Method of initial rates: Vary one concentration at a time
- Order: Determined from rate change
- **Rate law:** Rate = k[A]x[B]y
- Rate constant: Calculated from data
- **Example 7.2:** Rate = k[NO][O₃]
- **Example 7.3:** Rate = k[H₂][Br₂]12
QUALITY VALIDATION
- Topic: 7.2.2 Determination of Reaction Order, Rate Law and Rate Constant
- Chapter: 7 (Chemical Kinetics)
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- Derivations checked: N/A
- Examples checked: PASS
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- Unnecessary repetition: NO
- Notes format maintained: PASS
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7.2.2 Determination of Reaction Order, Rate Law and Rate Constant
Sticky Notes · Quick Revision
Key Point 1
- Method of initial rates: Vary one concentration at a time
Key Point 2
- Order: Determined from rate change
Key Point 3
- **Rate law:** Rate = k[A]x[B]y
Key Point 4
- Rate constant: Calculated from data
Key Point 5
- **Example 7.2:** Rate = k[NO][O₃]
Key Point 6
- **Example 7.3:** Rate = k[H₂][Br₂]12
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