Core Concept

The Ideal Gas Law is an equation that combines the relationships between pressure, volume, temperature, and the number of moles of a gas. It provides a way to predict and calculate these properties for an ideal gas.

Ideal Gas Law Equation

The Ideal Gas Law is expressed as:

PV=nRT

Where:

• P = Pressure of the gas (in atmospheres, atm)

• V = Volume of the gas (in liters, L)

• n = Number of moles of the gas (in moles, mol)

• R = Ideal gas constant, $0.0821 \, \text{L} \cdot \text{atm} \, \text{K}^{-1} \, \text{mol}^{-1}$

• T = Temperature of the gas (in Kelvin, K)

Key Concepts

1. Universal Gas Constant, R:

   • The ideal gas constant, R, is used to relate all units in the equation and has a value of $0.0821 \, \text{L} \cdot \text{atm} \, \text{K}^{-1} \, \text{mol}^{-1}$ when pressure is in atmospheres.

2. Temperature in Kelvin:

   • Temperature must always be in Kelvin (K) for gas law calculations. To convert from Celsius to Kelvin, use: T (K) = T(°C) + 273.15

3. Units Matter:

   • The units for P, V, and T must match the units in the ideal gas constant R to ensure accurate calculations.

   • Typically: P in atm, V in L, T in K, and nnn in moles.

4. Applicability of the Ideal Gas Law:

   • The Ideal Gas Law applies well to ideal gases, which follow all gas laws perfectly under typical conditions.

   • Real gases approximate ideal behavior at high temperatures and low pressures, where gas molecules are far apart.

Rearranged Forms of the Ideal Gas Law

The Ideal Gas Law can be rearranged to solve for any variable when the others are known:

1. To Find Pressure:

   $P = \frac{nRT}{V}$

2. To Find Volume:

   $V = \frac{nRT}{P}$

3. To Find Moles:

   $n = \frac{PV}{RT}$

4. To Find Temperature:

   $T = \frac{PV}{nR}$