15 Gas Laws
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Boyle’s Law: Volume and Pressure
Boyle’s law describes the inverse relationship between the pressure and volume of a fixed amount of gas at a constant temperature.
LEARNING OBJECTIVES
Apply Boyle’s law using mathematical calculations.
KEY TAKEAWAYS
Key Points
- According to Boyle’s law, an inverse relationship exists between pressure and volume.
- Boyle’s law holds true only if the number of molecules (n) and the temperature (T) are both constant.
- Boyle’s law is used to predict the result of introducing a change in volume and pressure only and only to the initial state of a fixed quantity of gas.
- The relationship for Boyle’s law can be expressed as follows: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume values, and P2 and V2 are the values of the pressure and volume of the gas after change.
Key Terms
- isotherm: In thermodynamics, a curve on a p-V diagram for an isothermal process.
- Boyle’s law: The absolute pressure and volume of a given mass of confined gas are inversely proportional while the temperature remains unchanged within a closed system.
- ideal gas: A theoretical gas composed of a set of randomly moving, noninteracting point particles.
Boyle’s Law
Boyle’s law (sometimes referred to as the Boyle-Mariotte law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains unchanged within a closed system. This can be stated mathematically as follows:
[latex]P_1V_1 = P_2V_2[/latex]
History and Derivation of Boyle’s Law
The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. Boyle showed that the volume of air trapped by a liquid in the closed short limb of a J-shaped tube decreased in exact proportion to the pressure produced by the liquid in the long part of the tube.
The trapped air acted much like a spring, exerting a force opposing its compression. Boyle called this effect “the spring of the air” and published his results in a pamphlet with that title. The difference between the heights of the two mercury columns gives the pressure (76 cm = 1 atm), and the volume of the air is calculated from the length of the air column and the tubing diameter.
The law itself can be stated as follows: for a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional—that is, when one doubles, the other is reduced by half.
Remember that these relations hold true only if the number of molecules (n) and the temperature (T) are both constant.
Interactive: The Volume-Pressure Relationship: Gases can be compressed into smaller volumes. How does compressing a gas affect its pressure? Run the model, then change the volume of the containers and observe the change in pressure. The moving wall converts the effect of molecular collisions into pressure and acts as a pressure gauge. What happens to the pressure when the volume changes?
EXAMPLE
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