Gas laws
Ideal gas equation

In an ideal gas, there are no intermolecular forces and therefore no tendency for the gas to liquefy.

An ideal gas is a theoretical concept representing a gas composed of tiny particles with negligible volume and no intermolecular forces. These particles move randomly, and collisions between them are perfectly elastic, allowing the gas to conform to the ideal gas law under specific conditions.

Real gases do not obey the ideal gas law. However at low pressures, real gases tend to behave like ideal gases. For an ideal gas, \( \frac{PV}{T} \) is constant. The ideal gas equation is given as:

$$ PV = nRT $$ $$\text{where, P = Pressure in atm} $$ $$ \text{V = Volume in dm³} $$ $$ \text{n = Number of moles in mole} $$ $$ \text{R = Molar gas constant} $$ $$\text{T = Temperature in kelvin} $$ $$ \text{At S.T.P; 1 mole = 22.4dm³ } $$ $$ R = \frac{PV}{nT} $$ $$ R = \frac{1atm × 22.4dm³}{1mol × 273K} $$ $$ R = 0.082 \text{ atm dm³ }mol^{-1}K^{-1} $$

Calculations

Example 1: Calculate the number of moles present in a certain mass of gas which occupies 3dm³ at 1.5 atmospheric pressure and 15°C. (R = 0.082 atm dm³ mol-1K-1)

Solution

$$ n = ? $$ $$ V = 3dm³ $$ $$ P = 1.5atm $$ $$ T = 15 + 273 = 288K $$ $$ R = 0.082\text{ atm dm³ }mol^{-1}K^{-1} $$ $$ PV = nRT $$ $$ n = \frac{PV}{RT} $$ $$ n = \frac{1.5 × 3}{0.082 × 288} $$ $$ n = 0.191 mole $$

Example 2: 4 mole of an ideal gas are at a temperature of -15°C and a pressure of 5 atm. What volume in dm³ will the gas occupy at that temperature. (R = 0.082 atm dm³ mol-1K-1)

Solution

$$ n = 4 moles $$ $$ T = -15 + 273 = 258K $$ $$ P = 5 atm $$ $$ V = ? $$ $$ PV = nRT $$ $$ V = \frac{nRT}{P} $$ $$ V = \frac{4 × 0.082 × 258}{5} $$ $$ V = 16.925dm³ $$

Ideal Gas Equation Calculator









Formulas:
  1. For 1: \( n = \frac{PV}{RT} \)

  2. For 2: \( V = \frac{nRT}{P} \)

  3. For 3: \( T = \frac{PV}{nR} \)

Constants: \( R = 0.082 \, \text{atm dm}^3 mol^{-1}K^{-1} \)

Ensure to convert °C to Kelvin before inputting values for temperature

Summary