The Ideal Gas Law
Scientists want to be able to describe the behaviors of an ideal gas, that is, a theoretical gas in which no forces are acting on the gas particles, and the particles do not take up space. Intermolecular forces between the atoms or molecules of a gas are the reason that real gases differ from ideal gases. Real gases are not ideal, but understanding the way an ideal gas would behave gives scientists a way to predict how a real gas might behave under defined conditions.
The ideal gas law is a law that describes the behavior of ideal gases. It can estimate the way many gases will behave under many different conditions. The ideal gas law is represented by the equation $PV=nRT$, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. There are many versions of R. The one used in each calculation depends on the units being used to measure pressure. For Pa, the SI unit, $R=8.314\,\rm{m}^{3}{\rm{Pa/K}}{\cdot}{\rm{mol}}$. The units can all be converted from one to the other: $8.314\;{\rm m^{3}{Pa}}/{\rm K}{\cdot}{\rm{mol}}=8.314\;{\rm{J/K}}{\cdot}{\rm{mol}}$ because ${\rm{m}^{3}{Pa}}={\rm{J}}$.
Useful Values of the Gas Constant, R
8.314 m^{3}Pa/K⋅mol |
8.314 J/K⋅mol |
0.082057 atm⋅L/K⋅mol |
It is important to review converting units so R can be in the unit that is needed. From this equation, it is obvious that pressure is directly proportional to the number of moles of the gas. For example, the more gas there is, the more pressure it exerts. It is also directly proportional to the temperature of the gas: the hotter the gas, the more pressure it exerts. Pressure is indirectly proportional to volume: the greater the volume of a gas, the less pressure it exerts.
Other gas laws are derived from the ideal gas law and are useful for practical applications.
- Boyle's law states that pressure of gas increases as volume decreases at constant temperature and moles of gas, represented by the equation $P_1V_1=P_2V_2$.
- Charles's law states that the volume of gas increases as temperature increases at constant pressure and moles of gas, represented by the equation $\frac{V_1}{T_1}=\frac{V_2}{T_2}$.
- Avogadro's law states that the equal volumes of gases at the same temperature and pressure have equal numbers of atoms or molecules, represented by the equation $\frac{V_1}{n_1}=\frac{V_2}{n_2}$.
- Gay-Lussac's law states that for an ideal gas with constant mass and volume, the pressure exerted on the container is proportional to its absolute temperature, represented by the equation $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ .
Gas Laws
Note that the chosen value for R matched the units given for pressure and temperature. It's important to use dimensional analysis to make sure the desired unit is obtained.
The laws derived from the ideal gas law can be used in simpler cases. For example, if 15 liters of carbon dioxide gas at 25°C is heated to 65°C, calculate the new volume under constant pressure. Using the ideal gas law, under constant pressure conditions, the P is eliminated, and initial and final states may be determined via Charles's law.Kinetic Molecular Theory
The ideal gas law and the laws derived from it are based on the kinetic molecular theory of gases. Kinetic molecular theory is a theory involving the relationship between temperature, pressure, and volume that states that the average kinetic energy of a gas is proportional to its temperature. This theory relies on five assumptions.
- The size of each particle of a gas is negligibly small compared to the distances between particles.
- Gas particles exert no attractive or repulsive forces on one another or the walls of their container.
- Gas particles travel in a continuous, straight-line motion until they collide with other gas particles or the walls of their container.
- When gas particles collide, there is no gain or loss of energy.
- The average kinetic energy of all particles of a gas is proportional to the absolute temperature of the gas.
Absolute temperature, also known as thermodynamic temperature, is the temperature as compared to absolute zero, the cessation of all motion, even subatomic motion, measured in kelvins (K).
The assumption underlying kinetic molecular theory leads to gas effusion and diffusion. Effusion is the process by which gases move through small openings in solids, one particle at a time. Diffusion is the process by which gas moves from an area of higher concentration to an area of lower concentration.