Gases
The Gas Laws
The Gas Laws
Four variables are usually sufficient to define the state (i.e. condition) of a gas:
- Temperature, T
- Pressure, P
- Volume, V
- Quantity of matter, usually the number of moles, n
The equations that express the relationships among P, T, V and n are known as the gas laws
The Pressure-Volume Relationship: Boyle's Law
Robert Boyle (1627-1691)
Studied the relationship between the pressure exerted on a gas and the resulting volume of the gas. He utilized a simple 'J' shaped tube and used mercury to apply pressure to a gas:
- He found that the volume of a gas decreased as the pressure was increased
- Doubling the pressure caused the gas to decrease to one-half its original volume
Boyle's Law:
The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure
- The value of the constant depends on the temperature and the amount of gas in the sample
- A plot of V vs. 1/P will give a straight line with slope = constant
The Temperature-Volume Relationship: Charles's Law
The relationship between gas volume and temperature was discovered in 1787 by Jacques Charles (1746-1823)
- The volume of a fixed quantity of gas at constant pressure increases linearly with temperature
- The line could be extrapolated to predict that gasses would have zero volume at a temperature of -273.15°C (however, all gases liquefy or solidify before this low temperature is reached
- In 1848 William Thomson (Lord Kelvin) proposed an absolute temperature scale for which 0°K equals -273.15°C
- In terms of the Kelvin scale, Charles's Law can be restated as:
The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature
- Doubling the absolute temperature causes the gas volume to double
- The value of constant depends on the pressure and amount of gas
The Quantity-Volume Relationship: Avogadro's Law
The volume of a gas is affected not only by pressure and temperature, but by the amount of gas as well.
Joseph Louis Gay-Lussac (1778-1823)
Discovered the Law of Combining Volumes:
- At a given temperature and pressure, the volumes of gasses that react with one another are in the ratios of small whole numbers
- For example, two volumes of hydrogen react with one volume of oxygen to form two volumes of water vapor
Amadeo Avogadro interpreted Gay-Lussac's data
Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules
- 1 mole of any gas (i.e. 6.02 x 1023 gas molecules) at 1 atmosphere pressure and 0°C occupies approximately 22.4 liters volume
- Avogadro's Law:
The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas
- Doubling the number of moles of gas will cause the volume to double if T and P remain constant