Law of Mass Action Formula, Derivation & Solved Examples
Law of Mass Action is essential in chemistry and helps students understand core ideas about how reactant concentrations influence the speed and outcome of chemical reactions. This topic is also applied in physics, biology, and technology, such as in semiconductors and medicine.
What is Law of Mass Action in Chemistry?
- The law of mass action in chemistry explains how the rate of a chemical reaction depends on the concentrations of the reactants.
- It states that for a reversible reaction, the rate is directly proportional to the product of the active masses (or concentrations) of the reactants, each raised to its respective stoichiometric coefficient.
- This concept appears in chapters related to chemical equilibrium, rate law, and chemical kinetics, making it a foundational part of your chemistry syllabus.
Statement, Equation, and Formula
The law of mass action was proposed by Norwegian scientists Guldberg and Waage. The general formula for a reaction:
aA + bB ⇌ cC + dD
The equilibrium constant (Kc) expression is:
Kc = [C]c [D]d / [A]a [B]b
Here, [ ] indicates the concentration in mol/L. The exponents match the coefficients from the balanced chemical equation.
Derivation & Explanation
The law of mass action can be derived step-by-step as follows:
1. Consider the forward reaction rate for aA + bB → cC + dD:2. Rateforward = kf × [A]a × [B]b
3. The reverse reaction rate is Ratereverse = kr × [C]c × [D]d
4. At equilibrium: Rateforward = Ratereverse
5. kf [A]a [B]b = kr [C]c [D]d
6. Rearranging gives Kc = kf/kr = [C]c [D]d / [A]a [B]b
This is how the law links reaction rates and concentrations at equilibrium.
Step-by-Step Reaction Example
Let’s solve a sample problem using the law of mass action:
1. Consider the reaction: 2NO2 ⇌ N2O42. The equilibrium constant expression is:
3. If [N2O4] = 0.0417 mol/L and [NO2] = 0.0165 mol/L,
4. Substitute the values:
5. Final Answer: Kc = 153
This shows how to apply the law for real calculations.
Applications & Modern Uses
The law of mass action is used in many areas of science and technology:
- Industrial chemistry to optimize chemical manufacturing processes
- Biology, for understanding enzyme reactions and cellular processes
- Semiconductor physics, especially in describing how electrons and holes behave
- Medicine, such as in pharmacokinetics (medicine breakdown in the body) and epidemiology (disease spread)
Law of Mass Action in Semiconductors
In semiconductors, the law of mass action gives the relation between electrons (n) and holes (p):
n × p = ni2
where ni is the intrinsic carrier concentration. This equation helps predict how doping or temperature changes affect the electrical properties of semiconductor materials used in devices like diodes and transistors.
Law of Mass Action vs. Le Chatelier’s Principle
| Law of Mass Action | Le Chatelier’s Principle |
|---|---|
| Gives the mathematical relationship for equilibrium concentrations (Kc or Kp). | Predicts how a system at equilibrium will shift if disturbed (change in concentration, pressure, temperature). |
| Static—explains the final state. | Dynamic—explains the direction of change. |
| Used for calculations and formulas. | Used for qualitative predictions. |
Frequent Related Errors
- Mixing up Kc (equilibrium constant) with rate constants (k).
- Using experimental rate order instead of stoichiometric coefficients in the formula.
- Applying the law to non-elementary or irreversible reactions.
- Confusing Law of Mass Action with Le Chatelier’s Principle in explanations.
Uses of Law of Mass Action in Real Life
The law of mass action is applied in making fertilizers (like ammonia in Haber process), drug formulation, water treatment, and electronics. For example, industries adjust reactant concentrations to maximize product yield, or engineers predict the behavior of light sensors and solar cells using mass action principles.
Relation with Other Chemistry Concepts
The law of mass action connects closely with chemical equilibrium, Le Chatelier's Principle, and rate laws. It is also important for understanding concepts in thermodynamics and reaction types.
Lab or Experimental Tips
To remember the law of mass action: always use the balanced equation and match exponents in your Kc formula to stoichiometric coefficients, not to the speed of the reaction. Vedantu educators often use diagrams and stepwise setups to help students visualize these relationships during live sessions.
Try This Yourself
- Write the law of mass action expression for the reaction: N2 + 3H2 ⇌ 2NH3.
- If [N2] = 0.3 M, [H2] = 0.2 M, [NH3] = 0.5 M, calculate Kc.
- Give two examples where the law of mass action is used in real life.
Final Wrap-Up
We explored the Law of Mass Action—its definition, formulas, calculation methods, real applications, and common misunderstandings. For more practice, concept videos, and interactive problem-solving, check the chemistry resources and live classes on Vedantu.
Related pages you may find useful:
FAQs on Law of Mass Action in Chemistry: Meaning, Formula, and Importance
1. What is the law of mass action in chemistry?
The law of mass action states that the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants, each raised to the power of its stoichiometric coefficient.
Key points:
- Applies to reversible reactions.
- Lays the foundation for the concept of equilibrium constant (Kc).
- Formulated by Guldberg and Waage.
2. Who proposed the law of mass action?
The law of mass action was proposed by two Norwegian chemists, Cato Maximilian Guldberg and Peter Waage, in the year 1864. They established the quantitative relationship between reactant concentrations and the reaction rate for chemical equilibrium.
3. How do you write the law of mass action formula?
The general law of mass action formula for the reaction aA + bB ⇌ cC + dD is:
Kc = [C]c[D]d / [A]a[B]b
Here, [ ] denotes molar concentrations, and the exponents are stoichiometric coefficients from the balanced chemical equation.
4. What is an example of law of mass action?
Example:
For the reversible reaction H2(g) + I2(g) ⇌ 2HI(g):
Kc = [HI]2 / ([H2][I2])
This expresses how equilibrium concentrations of HI, H2, and I2 relate according to the law of mass action.
5. What is the application of law of mass action in semiconductors?
The law of mass action in semiconductors relates electron (‘n’) and hole (‘p’) concentrations:
n × p = ni2
Applications include:
- Designing diodes, transistors, and other semiconductor devices.
- Understanding carrier concentrations at equilibrium.
- Predicting behavior under doping or temperature changes.
6. How is law of mass action different from Le Chatelier’s principle?
Law of mass action explains the mathematical relationship between reactant/product concentrations and equilibrium, while Le Chatelier’s principle predicts how a system at equilibrium responds to changes.
Main differences:
- Law of mass action: Focuses on equilibrium constant (Kc), quantitative expression.
- Le Chatelier’s principle: Qualitative prediction of shift in equilibrium when conditions change (concentration, temperature, pressure).
7. Why does the law of mass action sometimes fail in complex reactions?
The law of mass action may not accurately describe complex reactions because:
- Some reactions do not occur via a single step mechanism.
- Rate-determining steps or intermediate formation can influence concentration dependencies.
- Applies best to elementary reactions, not overall multi-step reactions.
8. How does temperature affect the equilibrium constant Kc as per mass action law?
Temperature changes can alter the value of Kc for a reaction:
- For exothermic reactions, increasing temperature lowers Kc.
- For endothermic reactions, increasing temperature raises Kc.
- The relationship follows the van’t Hoff equation.
9. Can the law of mass action be applied to all chemical reactions, including irreversible ones?
The law of mass action is specifically valid for reversible reactions at equilibrium. For irreversible reactions, it helps describe the rate law for elementary steps, but the equilibrium constant concept does not apply.
10. What are the limitations of law of mass action in real industrial processes?
Limitations of the law of mass action in industrial contexts:
- Does not account for non-ideal behavior at high concentrations or pressures.
- Ignores catalyst effects and complex reaction mechanisms.
- Assumes homogeneous systems; not always true in practical scenarios.
11. How is the law of mass action used in biology and physiology?
The law of mass action underlies many biological processes:
- Explains how enzyme-substrate and receptor-ligand binding reach equilibrium.
- Helps model reactions in metabolism and physiological pathways.
- Used in pharmacology to predict drug-receptor interactions.
12. Why are exponents in Kc equal to stoichiometric coefficients and not experimentally determined rate orders?
In the law of mass action, exponents in Kc are taken directly from the balanced chemical equation's stoichiometric coefficients. These reflect the proportions at equilibrium, while experimental rate orders in kinetics depend on the reaction mechanism and may differ from stoichiometry.
