Gas Laws
To study the behavior of gases in relation to volume, temperature, and pressure, the following conditions are investigated:
- Variation of volume with pressure at constant temperature (Boyle’s Law): \( PV = \text{constant} \)
- Variation of volume with temperature at constant pressure (Charles’ Law): \( \frac{V}{T} = \text{constant} \)
- Variation of pressure with temperature at constant volume (Pressure Law): \( \frac{P}{T} = k \)
Boyle’s Law
Boyle’s law states that the pressure of a fixed mass of gas varies inversely with its volume at constant temperature.
\[ P \propto \frac{1}{V} \] \[ P = kV \] \[ P_1 V_1 = P_2 V_2 \]Charles’ Law
Charles' law states that for a fixed mass of gas at constant pressure, the volume is proportional to its absolute temperature.
\[ V \propto T \] \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]Gas Law Example: Applying Charles’s Law
A gas occupies a volume of 20.0 dm³ at 373 K. Its volume at 746 K (with constant pressure) will be determined using Charles’s Law.
Given Data:
- \( V_1 = 20.0 \, \text{dm}^3 \)
- \( T_1 = 373 \, \text{K} \)
- \( T_2 = 746 \, \text{K} \)
- \( V_2 = ? \)
Applying Charles’s Law:
Charles’s Law states:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]Rearranging for \( V_2 \):
\[ V_2 = V_1 \times \frac{T_2}{T_1} \]Calculation:
\[ V_2 = 20.0 \times \frac{746}{373} \] \[ V_2 = 40.0 \, \text{dm}^3 \]Pressure Law
Pressure law states that the pressure of a fixed mass of gas at constant volume is proportional to its absolute temperature.
\[ P \propto T \] \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]Absolute Zero of Temperature
When graphs of volume–temperature or pressure–temperature are extrapolated backward, they cut the temperature axis at -273°C. This temperature is called absolute zero. It is the temperature at which the volume of the gas theoretically becomes zero as it is cooled. At this temperature, gas molecules stop moving completely.
However, this is a theoretical assumption since gases typically liquefy before reaching this temperature.
General Gas Law
The general gas law combines Boyle’s Law, Charles’ Law, and the Pressure Law.
From Boyle’s Law:
\[ PV = k \]From Charles’ Law:
\[ \frac{V}{T} = k \]From Gay-Lussac’s (Pressure) Law:
\[ \frac{P}{T} = k \]Combining these, we get:
\[ \frac{PV}{T} = k \] \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]This equation is known as the general gas law.
It can also be written as:
\[ PV = nRT \]Where:
- \( n \) = number of moles of gas
- \( R \) = universal gas constant = 8.31 J K\(^{-1}\) mol\(^{-1}\)