1. What the Ideal Gas Equation Represents
The ideal gas equation combines all individual gas laws (Boyle’s, Charles’, and Gay-Lussac’s laws) into one simple relation:
PV = nRT
This equation connects pressure, volume, temperature, and amount of gas in a single formula.
2. Variables in the Ideal Gas Equation
Each symbol in the equation has a clear physical meaning:
- P → pressure of the gas
- V → volume of the gas
- n → number of moles
- R → universal gas constant
- T → absolute temperature (in Kelvin)
2.1. Requirement
Temperature must be in Kelvin for the equation to work correctly.
3. Meaning of the Universal Gas Constant (R)
The gas constant R is a fixed value that relates energy scale to temperature and moles. Its value is:
R = 8.314\ \text{J mol}^{-1} \text{K}^{-1}
This constant appears in many areas of physics and chemistry because it links macroscopic gas properties to molecular motion.
3.1. Other Common Units of R
- 0.0821 L·atm mol⁻¹ K⁻¹
- 8.314 J mol⁻¹ K⁻¹
- 62.36 L·torr mol⁻¹ K⁻¹
4. How the Ideal Gas Equation Is Derived
The ideal gas equation is obtained by combining basic gas laws:
PV = nRT
comes from:
- Boyle’s law: \( P \propto 1/V \)
- Charles’ law: \( V \propto T \)
- Avogadro’s law: \( V \propto n \)
Combining these proportionalities gives the full equation.
4.1. Microscopic View
Kinetic theory also gives the same relation:
P = \dfrac{1}{3} \rho \bar{c^2}
This links molecular motion directly to pressure.
5. Using the Ideal Gas Equation
The equation is often used to calculate unknown values when others are known. Common uses:
5.1. 1. Finding Pressure
P = \dfrac{nRT}{V}
5.2. 2. Finding Volume
V = \dfrac{nRT}{P}
5.3. 3. Finding Number of Moles
n = \dfrac{PV}{RT}
6. When the Ideal Gas Equation Works Well
Most gases follow the ideal gas equation closely when:
- pressure is low
- temperature is high
Under these conditions, the molecules are far apart and intermolecular forces become negligible.
6.1. Examples
Air, helium, nitrogen, and oxygen behave nearly ideally at room temperature and atmospheric pressure.
7. When the Ideal Gas Equation Fails
Deviation happens when conditions make molecules come close together:
- high pressure
- low temperature
Here, intermolecular forces become important and real gases no longer perfectly satisfy PV = nRT.
7.1. Real Gas Correction
To fix deviations, modified equations like the Van der Waals equation are used.