What Is Gay-Lussac's Law? Definition, Formula & Real-Life Examples
Gay-Lussac's Law is essential in chemistry and helps students understand various practical and theoretical applications related to this topic. It forms the basis of questions, and is widely used in real-world scenarios like hot gas cylinders and aerosol cans.
What is Gay-Lussac's Law in Chemistry?
A Gay-Lussac's Law refers to the gas law that states: the pressure of a fixed amount of gas is directly proportional to its absolute temperature, provided the volume remains constant.
This concept appears in chapters related to Physical Chemistry, thermodynamics, and the behavior of gases, making it a foundational part of your chemistry syllabus.
Gay-Lussac’s Law Formula
The formula for Gay-Lussac’s Law is:
P₁ / T₁ = P₂ / T₂
Where,
P = Pressure of gas (in atm, Pa, or any consistent unit),
T = Absolute temperature (in Kelvin, K),
(Volume and gas quantity must be constant).
Always use Kelvin for temperature to ensure accuracy in calculations. The law also appears as P ∝ T (if V is constant).
Graphical Representation
The graph of Gay-Lussac's Law shows a straight line when you plot pressure (P) on the y-axis versus absolute temperature (T) on the x-axis, with the slope depending on the volume.
Examples & Real Life Applications
Gay-Lussac's Law applications are seen in our daily life:
- Aerosol Cans: When heated, the pressure inside an aerosol can increases. Too much heat can cause it to burst due to increased pressure.
- Pressure Cookers: As the temperature of the trapped steam rises, its pressure also rises, making food cook faster.
- Vehicle Tires: Tire pressure increases on hot days as air temperature inside the tire rises.
Practice Problems & Worksheets
| Problem | Step-by-Step Solution |
|---|---|
| 1. A gas has a pressure of 2 atm at 300 K. What will the pressure be at 450 K, if volume is constant? |
1. Use the formula: P₁/T₁ = P₂/T₂ 2. Substitute values: 2/300 = P₂/450 3. Cross-multiply: P₂ = (2 × 450)/300 = 3 atm Final Answer: 3 atm |
| 2. If a pressurized can reads 5 atm at 27°C, what will be the pressure at 127°C? |
1. Convert to Kelvin: T₁ = 27 + 273 = 300 K, T₂ = 127 + 273 = 400 K 2. Apply formula: 5/300 = P₂/400 3. P₂ = (5 × 400)/300 = 6.67 atm Final Answer: 6.67 atm |
| 3. State whether doubling the temperature (in Kelvin) doubles the pressure for a fixed volume of gas. |
1. According to formula, P ∝ T (if V is constant) 2. So, doubling T will double P. Final Answer: Yes, pressure will double. |
Comparison with Other Gas Laws
| Law | Relationship | What Stays Constant | Standard Formula |
|---|---|---|---|
| Gay-Lussac's Law | Pressure ∝ Temperature | Volume | P₁/T₁ = P₂/T₂ |
| Charles's Law | Volume ∝ Temperature | Pressure | V₁/T₁ = V₂/T₂ |
| Boyle's Law | Pressure ∝ 1/Volume | Temperature | P₁V₁ = P₂V₂ |
Frequent Related Errors
- Forgetting to convert Celsius to Kelvin when using the formula.
- Swapping the roles of pressure and temperature with volume.
- Mistaking "directly proportional" for "inversely proportional."
- Applying Gay-Lussac’s Law when the volume is not constant (not valid).
Uses of Gay-Lussac's Law in Real Life
Gay-Lussac's Law is widely used in industries and safety engineering. It is critical for the safe storage and transport of compressed gases, design of pressure cookers, and understanding why pressure builds in heated gas cans.
Vedantu educators often highlight such relevance in exam-prep live sessions for practical clarity.
Relation with Other Chemistry Concepts
Gay-Lussac's Law is closely related to the combined gas law (which combines all classic gas laws), ideal gas law, and thermodynamic calculations involving gas pressure. Comparing all gas laws helps in understanding their specific applications in chemistry and physics.
Step-by-Step Reaction Example
- A 1 L rigid cylinder contains a gas at 4 atm and 300 K. What will the pressure be at 600 K?
2. Use formula: P₁ / T₁ = P₂ / T₂
3. 4 / 300 = P₂ / 600
4. Cross-multiply: P₂ = (4 × 600) / 300 = 8 atm
Final Answer: Pressure will be 8 atm at 600 K
Lab or Experimental Tips
Remember: Use Kelvin for temperature! An easy way is to add 273 to the Celsius value. Vedantu educators advise always checking if the gas container is rigid (volume constant), as this determines if Gay-Lussac’s Law applies.
Try This Yourself
- If a pressure cooker shows 2 atm at 373 K, what will be the pressure at 423 K?
- List two devices that work based on Gay-Lussac's Law.
- Why is it dangerous to heat a closed aerosol can?
- Convert 50°C to Kelvin and state its effect if used directly in calculations.
Final Wrap-Up
We explored Gay-Lussac's Law—its definition, formula, key differences with other gas laws, graphical and real-life applications, and common errors.
Charles's Law | Boyle's Law
FAQs on Gay-Lussac's Law Explained: Formula, Graph, and Uses
1. What is Gay-Lussac's Law?
Gay-Lussac's Law states that the pressure of a fixed amount of gas is directly proportional to its absolute temperature, provided the volume is constant. This means that as the temperature increases, the gas pressure increases, assuming the gas does not escape and the container does not expand.
2. What is the formula for Gay-Lussac's Law?
The formula for Gay-Lussac's Law is:
P₁/T₁ = P₂/T₂
Where:
• P₁ = Initial Pressure
• T₁ = Initial Absolute Temperature (in Kelvin)
• P₂ = Final Pressure
• T₂ = Final Absolute Temperature (in Kelvin)
3. What is a real-life example of Gay-Lussac's Law?
Gay-Lussac's Law applies to many everyday situations, such as:
• Aerosol cans: Pressure inside increases on heating and can be hazardous if overheated.
• Pressure cookers: The pressure rises with temperature, cooking food faster.
• Car tires: Tire pressure increases on a hot day due to rising air temperature.
4. How is Gay-Lussac's Law different from Charles's Law?
Gay-Lussac's Law relates pressure and temperature at constant volume, while Charles's Law relates volume and temperature at constant pressure. In summary:
• Gay-Lussac: Pressure ∝ Temperature (Volume constant)
• Charles's: Volume ∝ Temperature (Pressure constant)
5. What units are used for temperature and pressure in Gay-Lussac's Law?
In Gay-Lussac's Law:
• Temperature must always be measured in Kelvin (K).
• Pressure can be any consistent unit (atm, Pa, mmHg), as long as the same unit is used for both initial and final conditions.
6. Why must temperature be in Kelvin for Gay-Lussac's Law calculations?
Temperature must be in Kelvin because the law is based on absolute temperature. Celsius or Fahrenheit scales can result in incorrect ratios or negative pressures, which are not possible in physical chemistry calculations.
7. Can Gay-Lussac's Law be used for all gases?
Gay-Lussac's Law best describes the behavior of ideal gases at moderate temperatures and pressures. Real gases may slightly deviate at high pressures or low temperatures, but the law is a close approximation under standard laboratory conditions.
8. What would happen if the volume is not kept constant in Gay-Lussac's Law?
If volume is not constant, Gay-Lussac's Law does not strictly apply. Instead, you must use the Combined Gas Law or Ideal Gas Law, which account for changes in pressure, volume, and temperature together.
9. What is the graphical representation of Gay-Lussac's Law?
A graph of pressure (P) versus absolute temperature (T in Kelvin) at constant volume is a straight line, showing a direct proportional relationship. This means as temperature increases, pressure increases at a constant rate.
10. How can I solve numerical problems using Gay-Lussac's Law?
To solve problems:
1. Write down known values for pressure and temperature (convert temperature to Kelvin).
2. Use the formula: P₁/T₁ = P₂/T₂.
3. Rearrange for the unknown value and solve using correct units.
11. What is the Combined Gas Law and how does it relate to Gay-Lussac's Law?
The Combined Gas Law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into one formula: (P₁V₁)/T₁ = (P₂V₂)/T₂. When volume is constant, it simplifies to Gay-Lussac's Law (P₁/T₁ = P₂/T₂).
12. What are some safety hazards related to the use of Gay-Lussac's Law in daily life?
Ignoring Gay-Lussac's Law can cause:
• Aerosol can explosions if overheated
• Pressure vessel ruptures due to uncontrolled temperature rise
Always handle pressurized containers according to recommended temperature guidelines.
