Definitions [4]
A temperature scale with absolute zero (zero kelvin) as the starting point is called the absolute scale or the kelvin scale.
The volume of a given mass of a dry gas varies inversely as the pressure and directly as the absolute temperature.
V ∝ \[\frac {1}{P}\] × T or \[\frac {PV}{T}\] = k (constant)
If volume changes from V1 to V2, pressure from P1 to P2, and temperature from T1 to T2, then:
\[\frac {P_1V_1}{T_1}\] = \[\frac {P_2V_2}{T_2}\] = k (constant)
“The relation between three properties of a gas, i.e., pressure, volume and temperature, is called the ideal gas equation.”
OR
The relation between the three properties of a gas - pressure (P), volume (V), and temperature (T) - expressed as PV = nRT, is called the ideal gas equation.
The process of converting a gas into a liquid by applying pressure and/or reducing temperature is called liquefaction. The essential conditions are low temperature and high pressure.
Formulae [1]
\[\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\]
Theorems and Laws [2]
The total pressure of a gaseous mixture equals the sum of the partial pressures of all individual gases.
Partial pressure of a gas: Pi = xi × PTotal, where xi = mole fraction of gas i
Pressure of pure dry gas: Pdry gas = PTotal − Paq, where Paq = aqueous tension (vapour pressure of water)
Rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
\[\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}\]
\[\text{Rate of diffusion}=\frac{\text{Volume of gas diffused}}{\text{Time required for diffusion}}\]
Key Points
- An ideal gas has point-mass molecules, no intermolecular forces, and perfectly elastic collisions.
- The Ideal Gas Equation, PV = nRT, combines all three laws into a single universal relationship.
- The Universal Gas Constant R = 8.314 J mol⁻¹ K⁻¹ is the same for all ideal gases.
- Real gases approximate ideal behaviour at low pressure and high temperature.
- Always use absolute temperature (Kelvin) in gas law calculations. T(K) = T(°C) + 273.15
Critical Constants:
| Constant | Meaning |
|---|---|
| Critical Temperature (Tc) | The temperature below which a gas can be liquefied by increasing pressure alone; above Tc, liquefaction is not possible regardless of pressure |
| Critical Pressure (Pc) | The minimum pressure required to liquefy 1 mole of gas placed at its critical temperature |
| Critical Volume (Vc) | The volume occupied by 1 mole of gas at its critical temperature |
A gas below its critical temperature is called vapour; above it is called a gas.
