Interactive Gas Laws Laboratory
Gay-Lussac's Law
**Gay-Lussac\'s Law** (sometimes called Amontons\' Law or the Pressure-Temperature Law) states that the pressure of a given mass of gas is **directly proportional** to its absolute temperature, provided that the volume of the container remains strictly constant.
Gay-Lussac's Law Simulator
1. The Concept of Gay-Lussac's Law
**Gay-Lussac\'s Law** governs the behavior of gases inside rigid, constant-volume containers.
The law states that the absolute pressure of a given mass of gas is **directly proportional** to its absolute temperature, provided the volume of the container remains strictly constant. This means that if you heat a sealed container, the pressure inside will rise linearly. If you cool the container, the pressure will drop.
For Gay-Lussac\'s Law to be valid, the **volume** (\(V\)) and the **amount of gas** (mass or number of moles, \(n\)) must remain strictly constant, and the temperature must be measured in **Kelvin** (absolute scale).
2. Mathematical Expression
The direct proportionality between pressure (\(P\)) and absolute temperature (\(T\)) is expressed mathematically as:
Where:
- P is the absolute pressure of the gas (measured in atm, bar, or Pascals).
- T is the absolute temperature of the gas (measured in Kelvin).
- k is a constant specific to that gas sample at its current volume.
When comparing the same sample of gas at constant volume before and after a temperature change, we use the formula:
This equation is widely used to calculate pressure changes in rigid cylinders, cooking pressure cookers, car tires, and enclosed industrial boilers.
Important warning: Celsius values must always be converted to Kelvin by adding 273.15. Direct proportionality does not apply to Celsius!
3. Microscopic Origin (Kinetic Theory)
From the molecular perspective of **Kinetic Molecular Theory**:
1. Heating the gas increases the thermal energy of the molecules, increasing their average speeds and velocities.
2. Since the volume of the container is rigid and fixed, the molecules cannot move farther apart.
3. The molecules collide with the container walls **more frequently** because they cover the distances between walls faster.
4. Each individual collision also occurs with **greater force** due to the higher momentum of the faster-moving particles.
5. This combination of more frequent collisions and stronger impacts results in a higher net macroscopic wall force, which we record as a pressure spike.
4. Solved Mathematical Problems
- State Gay-Lussac's Law: \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\).
- Convert all temperatures from Celsius to Kelvin: - Initial Temperature \(T_1 = 20.0 + 273.15 = 293.15 \text{ K}\) - Final Temperature \(T_2 = 75.0 + 273.15 = 348.15 \text{ K}\)
- Identify other given values: - Initial Pressure \(P_1 = 3.00 \text{ atm}\)
- Rearrange the equation to solve for the final pressure \(P_2\): \(P_2 = P_1 \times \frac{T_2}{T_1}\).
- Substitute the values into the equation: \(P_2 = 3.00 \text{ atm} \times \frac{348.15 \text{ K}}{293.15 \text{ K}}\).
- Calculate the result: \(P_2 \approx 3.56 \text{ atm}\).
- Conclude: The final pressure of the gas is 3.56 atm, which is safely below the safety warning limit of 5.50 atm (though heating aerosol cans remains highly dangerous and should never be done).
- Recall Gay-Lussac's Law: \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\).
- Convert Celsius temperatures to Kelvin: - \(T_1 = 15.0 + 273.15 = 288.15 \text{ K}\) - \(T_2 = 45.0 + 273.15 = 318.15 \text{ K}\)
- Given initial pressure: - \(P_1 = 2.20 \text{ bar}\)
- Rearrange the formula to solve for the final pressure \(P_2\): \(P_2 = P_1 \times \frac{T_2}{T_1}\).
- Substitute the values: \(P_2 = 2.20 \text{ bar} \times \frac{318.15 \text{ K}}{288.15 \text{ K}}\).
- Calculate the pressure: \(P_2 \approx 2.43 \text{ bar}\).
- Conclude: The tire pressure increases to approximately 2.43 bar as the air warms.
- Use Gay-Lussac's Law: \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\).
- Convert temperatures to Kelvin: - \(T_1 = 25.0 + 273.15 = 298.15 \text{ K}\) - \(T_2 = 100.0 + 273.15 = 373.15 \text{ K}\)
- Identify other values: - \(P_1 = 101.3 \text{ kPa}\)
- Rearrange the formula to solve for the final pressure \(P_2\): \(P_2 = P_1 \times \frac{T_2}{T_1}\).
- Substitute values: \(P_2 = 101.3 \text{ kPa} \times \frac{373.15 \text{ K}}{298.15 \text{ K}}\).
- Calculate the final pressure: \(P_2 \approx 126.8 \text{ kPa}\).
- Conclude: The pressure of the sealed gas inside the flask increases to approximately 126.8 kPa in the boiling water.
5. Practice Questions
6. Frequently Asked Questions (FAQs)
What is Gay-Lussac's Law?
Gay-Lussac's Law is a gas law stating that the pressure of a given mass of gas is directly proportional to its absolute temperature, provided the volume of the container remains strictly constant.
What is the formula for Gay-Lussac's Law?
The formula is P/T = k (constant) or P₁/T₁ = P₂/T₂, where P represents pressure and T represents absolute temperature in Kelvin.
Who discovered Gay-Lussac's Law?
It was published by the French chemist and physicist Joseph Louis Gay-Lussac in 1802, though the French inventor Guillaume Amontons had discovered the general relationship a century earlier in 1702.
What does "isochoric" mean?
An isochoric (or isometric) process is a thermodynamic process in which the volume of the system remains strictly constant. Gay-Lussac's Law describes an isochoric heating or cooling of an ideal gas.
Does Gay-Lussac's Law apply to liquids?
No. Gay-Lussac's Law only applies to gases. Liquids do not behave like ideal gases and do not have proportional pressure-temperature scaling at constant volume.
Why does tire pressure drop in the winter?
In cold winter weather, the air inside vehicle tires cools down. Since the tire volume remains nearly constant, the pressure decreases according to Gay-Lussac's Law, triggering low tire pressure warnings.
Why must temperature be in Kelvin for Gay-Lussac's Law?
Kelvin is an absolute temperature scale starting at absolute zero, where molecular motion theoretically stops. Pressure is directly proportional to the kinetic energy of the molecules, which scales directly with Kelvin, not Celsius.
Can a gas reach zero pressure at absolute zero?
Theoretically, yes. According to Gay-Lussac's Law, an ideal gas would exert zero pressure at 0 K because molecular motion stops. Real gases, however, liquefy and solidify at extremely low temperatures and do not reach zero pressure.
What is a pressure cookers relation to Gay-Lussac's Law?
A pressure cooker is a sealed, constant-volume container. As the water inside is heated, the steam generated cannot escape, causing the internal pressure to rise. According to the law, this pressure spike raises the boiling point of water, cooking food faster.
What is an isochore?
An isochore is a line on a thermodynamic graph representing states of a gas at a constant volume. On a P-T graph, the isochore is a straight line.