Pressure and volume are related, particularly when dealing with gases. The relationship depends on the context, but the most common method involves using the Ideal Gas Law.
Using the Ideal Gas Law
The Ideal Gas Law provides a fundamental equation for calculating pressure and volume (along with other variables) of an ideal gas.
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The Equation: The Ideal Gas Law is expressed as:
PV = nRT
Where:
- P = Pressure
- V = Volume
- n = Number of moles of gas
- R = Ideal gas constant (the value depends on the units used for pressure, volume, and temperature - a common value is 0.0821 L atm / (mol K))
- T = Temperature (in Kelvin)
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How to Use It: To calculate either pressure (P) or volume (V), you need to know the values of the other variables (n, R, and T).
- To solve for Pressure (P): P = nRT / V
- To solve for Volume (V): V = nRT / P
Example:
Let's say you have 2 moles of an ideal gas at a temperature of 300 K in a container with a volume of 10 liters. What is the pressure? (Assume R = 0.0821 L atm / (mol K))
P = (nRT) / V
P = (2 mol 0.0821 L atm / (mol K) 300 K) / 10 L
P = 4.926 atm
Other Relationships: Boyle's Law
If the amount of gas (n) and temperature (T) are held constant, then the relationship between pressure and volume is described by Boyle's Law:
- Boyle's Law: P₁V₁ = P₂V₂
This means the initial pressure (P₁) times the initial volume (V₁) is equal to the final pressure (P₂) times the final volume (V₂). You can use this to calculate a new volume if the pressure changes, or vice versa, as long as the amount of gas and the temperature remain constant.
Summary
Calculating pressure volume involves applying the Ideal Gas Law (PV=nRT) when you know the number of moles, ideal gas constant, and temperature, or Boyle's Law (P₁V₁ = P₂V₂) when the amount of gas and temperature are constant. Make sure to use consistent units for all variables and constants!
