How to Determine the Rate Law from Experimental Data
Rate law is essential in chemistry and helps students understand various practical and theoretical applications related to this topic. It is the key to predicting how fast reactions happen, what factors affect them, and how to solve calculation-based numericals about reaction speed.
What is Rate Law in Chemistry?
A rate law in chemistry expresses how the rate of a chemical reaction depends on the concentrations of its reactants. This concept appears in chapters related to chemical kinetics, reaction order, and reaction mechanisms, making it a foundational part of your chemistry syllabus.
General Rate Law Formula and Units
The general formula for a rate law is:
Rate is the reaction rate (usually in mol L-1 s-1), [A] and [B] are molar concentrations of reactants, m and n are the orders with respect to A and B, and k is the rate constant.
| Order | Rate Law Example | Units of k |
|---|---|---|
| Zero | Rate = k | mol L-1 s-1 |
| First | Rate = k[A] | s-1 |
| Second | Rate = k[A][B] or k[A]2 | L mol-1 s-1 |
Differential vs Integrated Rate Laws
Differential rate law relates the reaction rate to the instantaneous concentrations of reactants. Integrated rate law relates concentration to time and is used to calculate how much substance remains after a certain period.
| Rate Law Type | Formula Example | When to Use |
|---|---|---|
| Differential | Rate = k[A]n | Finding rate at a specific moment |
| Integrated (First Order) | ln([A]0/[A]) = kt | Finding concentration over time |
How to Determine Rate Law from Experimental Data
To determine the rate law, use the method of initial rates. You observe how changing the initial concentration of reactants affects the rate, keeping other variables constant, and use this data to find the reaction order for each reactant.
- Set up a table with varying concentrations and corresponding initial rates.
- Compare trials where only one reactant’s concentration changes.
- Use the ratio of rates and concentrations:
(Rate2/Rate1) = ([A]2/[A]1)n
- Solve for n (order with respect to A or B).
- Write the complete rate law including all reactants and their orders.
Order of Reaction and Rate Law Examples
The order of a reaction is the sum of the exponents of concentrations in the rate law. It may be zero, first, second, or even fractional. Some rate law examples:
| Reaction | Rate Law | Order |
|---|---|---|
| H₂ + Cl₂ → 2HCl | Rate = k | 0 |
| 2NO + O₂ → 2NO₂ | Rate = k[NO]2[O₂] | 3 |
| Decomposition of H₂O₂ | Rate = k[H₂O₂] | 1 |
Integrated Rate Law Applications
Integrated rate laws let you solve questions like “How much reactant remains after t seconds?” or “What is the half-life of the reaction?” Apply the correct formula depending on the reaction order:
First order: ln([A]0/[A]) = kt
Second order: 1/[A] - 1/[A]0 = kt
For first order reactions, the half-life is t1/2 = 0.693/k, which is independent of concentration.
Step-by-Step Rate Law Example
- Suppose experimentally, doubling [A] doubles the rate, and doubling [B] quadruples the rate.
- This shows rate is first order in A, second order in B.
- So, rate law is: Rate = k[A][B]2
Special Cases: SN1 and SN2 Rate Laws
Some organic reactions have special rate laws:
- SN1 reaction: Rate = k[alkyl halide] (first order, unimolecular, independent of nucleophile)
- SN2 reaction: Rate = k[alkyl halide][nucleophile] (second order, bimolecular)
This is important in organic chemistry and real-life problem-solving.
Frequent Related Errors
- Assuming stoichiometric coefficients in the equation are always the same as rate exponents (they are not).
- Using products or intermediates in the rate law expression.
- Forgetting that temperature affects the rate constant, but not the reaction orders.
- Mixing up differential and integrated forms for the wrong question type.
Lab or Experimental Tips
When analyzing rate data, always pick two experiments where only one reactant concentration changes. Use Vedantu’s interactive chemistry lessons to see worked-out data tables and test your understanding with instant feedback.
Final Wrap-Up
We explored rate law—its definition, formula, interpretation from experimental data, and real-life applications. For further guidance, concept boosters, and practice problems, check out Vedantu's chemistry notes and live doubt-solving sessions.
Relation with Other Chemistry Concepts
The concept of rate law is closely linked to order of reaction, integrated rate law, and reaction mechanism. Understanding these together gives you deep insight into chemical kinetics.
Try This Yourself
- Given: Rate = k[NO]2[O2]. What is the overall order?
- Does the rate constant k depend on concentration changes?
- Suppose doubling [B] quadruples the rate. What is the order with respect to B?
- Is the decomposition of N2O a first-order or second-order reaction?
Suggested Reading and Interlinks
FAQs on Rate Law in Chemistry: Meaning, Formula, and Examples
1. What is the rate law in Chemistry?
The rate law expresses how the speed of a reaction depends on the concentration of reactants. It is usually written as:
Rate = k [A]m [B]n where k is the rate constant and m, n are the reaction orders with respect to each reactant.
2. How do you determine the rate law from experimental data?
To determine the rate law from data, follow these steps:
- Compare initial rates for different concentrations of each reactant.
- Observe how the rate changes when one reactant’s concentration varies.
- Calculate reaction order by identifying the power to which concentration is raised.
3. What is the order of a reaction and how is it found?
The order of a reaction is the sum of exponents of reactant concentrations in the rate law. It is found by:
- Analyzing the rate law equation.
- Adding all powers (orders) of reactants involved.
- Experiments are used to determine actual values.
4. What are differential and integrated rate laws?
Differential rate law shows how rate depends on concentration at a specific instant.
Integrated rate law relates concentration to time.
- Use differential form for instantaneous rate questions.
- Use integrated form for concentration-time calculations (e.g., half-life).
5. What is the rate law for 2NO + O2 → 2NO2?
The experimentally determined rate law for this reaction is:
Rate = k [NO]2 [O2]
This shows the reaction is second order in NO and first order in O2.
6. What are the units of the rate constant (k) for different reaction orders?
The units of k depend on reaction order:
- First order: s-1
- Second order: M-1 s-1
- Zero order: M s-1
7. How is the rate law for an SN1 reaction written?
The rate law for SN1 reactions is:
Rate = k [R–X]
Only the alkyl halide concentration affects rate; it’s first order overall.
8. What is half-life and how is it calculated using integrated rate law?
Half-life (t1/2) is the time taken for reactant concentration to decrease by half.
- First order: t1/2 = 0.693/k
- Second order: t1/2 = 1/(k [A]0)
9. Can intermediates appear in a rate law?
No, only reactant concentrations from the balanced overall equation appear in the experimental rate law. Intermediates are excluded because their concentrations are not measurable during the reaction.
10. Does stoichiometry always match the rate law exponents?
No. The rate law must be found experimentally and is not directly predicted by stoichiometry.
- The exponents (orders) in the rate law may differ from the balanced equation’s coefficients.
11. How does temperature affect the rate law?
Temperature affects the value of the rate constant (k), usually making the reaction faster as temperature rises, but it does not change the exponents (reaction orders) in the rate law.
12. What happens if a concentration is missing from the rate law?
If a reactant’s concentration is not present in the rate law, the reaction is zero order with respect to that reactant; changing its concentration won’t affect the reaction rate.
