The relationships among the volume, pressure, and temperature of gases were formulated by scientists from the 17th to the 19th centuries. The ideal gas equation that summarizes these relationships is a basic equation in high-school chemistry.
Basic Knowledge
Boyle's law states that PV=constant at constant temperature, while Charles's law states that V/T=constant at constant pressure. Combining the two gives the combined gas law, PV/T=constant. When this is further combined with Avogadro's law (gases of equal volume at the same temperature and pressure contain the same number of molecules), the ideal gas equation PV=nRT is obtained.
The gas constant is R = 8.31 J/(mol·K) = 0.0821 L·atm/(mol·K). At standard conditions (0℃, 1.013×105 Pa), 1 mol of gas occupies 22.4 L.
Boyle's law (PV=k at constant T)
Charles's law (V=V0(1 + t/273) at constant P)
Ideal gas equation (PV=nRT, n=amount in moles)
Gas constant R (8.31 J/(mol·K))
Molar volume (22.4 L/mol at standard conditions)
Law of partial pressures (Dalton) (Ptotal=PA+PB+...)
Average molar mass (can be calculated using M=ρRT/P)
Further Study (Principles and Applications)
An ideal gas is a hypothetical gas in which molecular size and intermolecular forces are ignored. Real gases deviate from this law at high pressure and low temperature, so corrections are made using the van der Waals equation (P + a/V2)(V - b) = RT. a corresponds to intermolecular forces, and b corresponds to molecular volume.
Applications include predicting the amount of gas produced in chemical reactions, the temperature dependence of automobile tire pressure, and calculating the buoyancy of balloons. In a mixture of gases, the relationship partial pressure = mole fraction × total pressure holds.
- PV=nRT is the most important equation
- Remember R=8.31 J/(mol·K) together with its units
- At standard conditions (STP), 1 mol = 22.4 L
- Absolute temperature T(K) = t(℃) + 273
- Partial pressure = mole fraction × total pressure
- Real gases deviate from ideal behavior at high pressure and low temperature
- Van der Waals correction = molecular size (b) and intermolecular forces (a)
Important Notes (Common Confusions and Frequent Mistakes)
① Always convert temperature to absolute temperature K (do not substitute ℃ directly). ② Use consistent pressure units (Pa, atm, or mmHg). ③ Standard conditions are 0℃, 1.013×105 Pa (under the current IUPAC definition, 25℃, 105 Pa); check the textbook version. ④ In partial-pressure calculations, use the mole fraction relative to the total number of moles, not the mass fraction.
Practice
- How many moles are in 24.9 L of gas at 27℃ and 1.0×105 Pa?
- Find the mass of 5.6 L of oxygen O2 at standard conditions (O=16).
- A gas mixture contains 0.8 mol of N2 and 0.2 mol of O2. If its total pressure is 1.0×105 Pa, find the partial pressure of O2.