The Ideal Gas Equation
Gaseous State | States of Matter | Class 11 Chemistry
1. Derivation of the Equation
The Ideal Gas Equation is derived by combining the empirical gas laws. It describes the state of a hypothetical ideal gas.
- Boyle's Law: $V \propto \frac{1}{P}$ (at constant $n, T$)
- Charles's Law: $V \propto T$ (at constant $n, P$)
- Avogadro's Law: $V \propto n$ (at constant $P, T$)
Combining these:
$$ V \propto \frac{nT}{P} \implies V = R \frac{nT}{P} $$
$$ PV = nRT $$
2. Universal Gas Constant ($R$)
$R$ represents the work done per degree per mole. Its value depends on the units of Pressure, Volume, and Temperature.
| Unit System | Value of R |
|---|---|
| SI Units (Joules) | $8.314 \, J \cdot K^{-1} \cdot mol^{-1}$ |
| Litre-Atmosphere | $0.0821 \, L \cdot atm \cdot K^{-1} \cdot mol^{-1}$ |
| Litre-Bar | $0.0831 \, L \cdot bar \cdot K^{-1} \cdot mol^{-1}$ |
| CGS (Calories) | $\approx 2 \, cal \cdot K^{-1} \cdot mol^{-1}$ |
3. Relation with Density and Molar Mass
Substituting moles $n = \frac{\text{Mass } (m)}{\text{Molar Mass } (M)}$:
$$ PV = \frac{m}{M} RT $$ $$ P = \frac{m}{V} \frac{RT}{M} $$Since Density $d = m/V$:
$$ P = \frac{dRT}{M} \quad \text{or} \quad M = \frac{dRT}{P} $$
This shows that for an ideal gas, density is directly proportional to Pressure and inversely proportional to Temperature.
4. Combined Gas Law
For a fixed amount of gas (constant $n$), if conditions change from $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$:
$$ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $$Practice Quiz
Test your knowledge on the Ideal Gas Law.
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