Key Ideas
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- Kinetic energy: the energy of all motion
- Elastic collision: the conservation of kinetic energy during collisions
Kinetic Molecular Theory
Gases are in continuous, chaotic motion and, except during elastic collisions, are widely separated from each other
- Gases are widely separated with no intermolecular bonding between molecules
- Rapid, chaotic, random movement in straight lines until they collide with another particle or the wall of the container
- When gases collide, kinetic energy can be transferred from one particle to another, but no energy is lost
Pressure
Pressure is the measure of the force exerted by the particles on the walls of the container during collisions.
Pressure \(=\frac{Force}{Area}\) (The force per unit area of the container)
| Unit |
Symbol |
Conversion to kPa |
| Kilopascal |
kPa |
1 |
| Pascal |
Pa |
1000 Pa |
| Atmosphere |
atm |
0.987 atm |
| Bar |
bar |
1 bar |
| Millimeters of Mercury |
mmHg |
750 mmHg |
The Universal Gas Equation
For all gas equations, units must be kept constant
- P: Pressure is in kPa
- V: Volume is in L
- n: mol is in mol
- T: Temperature is in Kelvin (\(0K\approx -273^oC\))
- R: The gas constant is \(=8.31\,J\,K^{-1}\,mol^{-1}\)
Volume and Pressure
- Given an amount of gas at a constant temperature, the volume will be inversely proportional to the pressure
- \(P\propto \frac{1}{V}\)
- \(P_1V_1=P_2V_2\)
Volume and Temperature
- Given an amount of gas at a constant pressure, the volume of the gas will be directly proportional to the temperature
- \(V\propto T\)
- \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)
Combined Gas Law
- \(\frac{P_1\times V_1}{n_1\times T_1}=\frac{P_2\times V_2}{n_2\times T_2}\)
Universal Gas Equation
- \(P\times V=n\times R\times T\)
Molar Volume of Gas
- If an amount of gas has a constant pressure and a constant temperature, the volume of the gas will be the same. If the gas is at SLC - Standard Laboratory Conditions (\(100kPa,\,25^oC\)) then \(1\,\text{mol}\) of gas occupies \(24.8L\)
Dalton's Law of Partial Pressure
The total pressure exerted by a mixture of gases is equal to the sun of all the partial pressures of the constituent gases
- \(P_{TOTAL}=P_1+P_2+P_3+P_{...}\)
