The student is expected to describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyles’s law, Charles' law, Avogadro’s law, Dalton’s law of partial pressure, and the ideal gas law AND describe the postulates of kinetic molecular theory.
Kinetic molecular theory is a model of 5 postulates used to describe the behavior of ideal gases. According to these five postulates, ideal gas particles are of negligible size compared to the space between them, the particles are in continuous, rapid, random motion, their collisions are elastic, and there are no significant interactions among the particles of a gas. When temperature increases for an ideal gas, the kinetic energy of the particles increases proportionally.
Boyle’s law states that the pressure exerted by gas particles is inversely proportional to the volume occupied by the gas. At constant temperature, an increase in pressure will result in a decrease in volume. The equation for Boyle’s law is P1V1 = P2V2, where P1 and V1 represent an initial set of pressure and volume conditions and P2 and V2 represent a new set of conditions.
Charles’ law states that the temperature of a gas is directly proportional to the volume occupied by the gas. When the pressure is held constant, a decrease in temperature results in a decrease in volume. The equation for Charles’ law is V1/T1= V2/T2, where V1 and T1 represent an initial set of volume and temperature conditions and V2 and T2 represent a new set of conditions. For this equation, temperature must be in Kelvin.
Avogadro’s law establishes the relationship between the number of moles (n) of a gas, and the volume occupied by the gas at a constant temperature and pressure, where the volume of a gas is directly proportional to the number of moles of a gas. The equation for Avogadro’s law is V1/n1 = V2/n2, where V1 and n1 represent an initial set of volume and number of moles and V2 and n2 represent a new set of conditions. Avogadro’s principle states that equal volumes of gases contain the same number of atoms or particles.
Dalton’s law of partial pressures states that the total pressure exerted by a mixture of gases is equal to the sum of the individual pressures of all the gases in the mixture. Dalton’s law of partial pressures can be described by the equation Ptotal= P1 + P2 + P3 + … +Pn where Ptotal is the combined pressure of the mixture of gases, P1, P2, P3 and Pn represent the partial pressures of each gas in the mixture and n represents the total number of gases in the mixture.
The ideal gas law describes the relationship between the temperature, pressure, volume, and the number of moles of a gas under specific conditions. This law represents a combination of the relationships described in Boyle’s law, Charles’s law, and Avogadro’s law. The equation for the ideal gas law is PV = nRT, where P = pressure, V = volume, n = number of moles, T = temperature and R = the ideal gas constant. The ideal gas constant R is a physical constant and is specific to the units used for the pressure and volume measurements. For this equation, temperature must be in Kelvin.
Volume of a Gas Varies Inversely with Pressure
Boyle’s law states that the pressure exerted by gas particles is inversely proportional to the volume occupied by the gas. At constant temperature, an increase in pressure will result in a decrease in volume:
(Initial Pressure)(Initial Volume) = (Final Pressure)(Final Volume)
Thus, the equation for Boyle’s law is:
P1V1 = P2V2
In this formula, P1 and V1 represent an initial set of pressure and volume conditions, and P2 and V2represent a new set of conditions.
Volume of a Gas Varied Directly with Temperature
Charles' law states that the temperature of a gas is directly proportional to the volume occupied by the gas. When the pressure is held constant, a decrease in temperature results in a decrease in volume:
(Initial Volume) / (Initial Temperature) = (Final Volume) / (Final Temperature)
The equation for Charles law is:
V1 / T1 = V2 / T2
Here, V1 and T1 represent an initial set of volume and temperature conditions, and V2 and T2represent a new set of conditions. Note: for this equation, temperature must be in Kelvin.
Volume of a Gas Varied Directly with Moles
Avogadro’s law establishes the relationship between the number of moles (n) of a gas and the volume occupied by the gas at a constant temperature and pressure, where the volume of a gas is directly proportional to the number of moles of a gas:
(Initial Volume) / (Initial Moles) = (Final Volume) / (Final Moles)
The following equation for Avogadro’s Law is:
V1 / n1 = V2 / n2
V1 and n1 represent an initial set of volume and number of moles and V2 and n2 represent a new set of conditions. Avogadro’s principle states that equal volumes of gases contain the same number of atoms or particles.
Law of Partial Pressures
Furthermore, Dalton’s law of partial pressures states that the total pressure exerted by a mixture of gases is equal to the sum of the individual pressures of all the gases in the mixture. Dalton’s law of partial pressures can be described by the equation:
PT = P1 + P2 + P3 + …+PN
PT is the total pressure of the mixture of gases. P1, P2, P3, and PN represent the partial pressures of each gas in the mixture, where N represents the total number of gases within the mixture.
Relationship Between Temperature, Pressure, Volume, and Moles
The ideal gas law describes the relationship between the temperature, pressure, volume, and the number of moles of a gas under specific conditions. This law represents a combination of the relationships described in Boyle’s law, Charles' law, and Avogadro’s law. The following is the equation for the ideal gas law:
PV = nRT
In this equation, P = pressure, V = volume, n = number of moles, T = temperature (in Kelvin), and R = the ideal gas constant. The ideal gas constant R is a physical constant and is specific to the units used for the pressure and volume measurements. For this equation, temperature must be in Kelvin. Though it has limitations, the ideal gas law is still considered a relatively precise predictor for gas behaviors.
Kinetic Molecular Theory Describes Ideal Gas Behavior
Kinetic molecular theory is a model of five postulates used to describe the behavior of ideal gases.
1) Ideal gas particles are of negligible size compared to the space between them.
2) The particles are in continuous, rapid, random motion.
3) Their collisions are elastic.
4) There are no significant interactions among the particles of a gas.
5) If temperature increases for an ideal gas, the kinetic energy of the particles increases proportionally.