Cecily Zamora
The ideal gas law describes the behaviour of real gases under most conditions, and it can be used to calculate pressure change, temperature change, volume change, or the number of molecules or moles in a given volume. The ideal gas law can be expressed by the equation PV=nRT, where P is pressure, V is volume, n is the number of moles, T is temperature, and R is the universal gas constant. This equation can be used to determine the number of moles of a gas in a given volume by manipulating the equation to make n the subject of the formula.
| Characteristics | Values |
|---|---|
| Molar form of the ideal gas law | Relates pressure, volume, temperature, and number of moles of an ideal gas |
| Equation | PV = nRT, where P is pressure, V is volume, T is temperature, n is the number of moles, and R is the molar gas constant |
| Molar gas constant | Approximately 8.31 J/K⋅mol or m2⋅kg/s2⋅K⋅mol in SI base units |
| Volume expansion | Gases expand and contract rapidly with temperature changes due to large separation of atoms and molecules |
| Pressure and volume relationship | Volume increases in direct proportion to the amount of gas injected, up to a limit; further volume increase is restricted, leading to increased pressure |
| Charles' Law | Volume is directly proportional to temperature at a fixed pressure |
| Avogadro's Law | Relates volume and amount of gas in moles when pressure and temperature are constant |
| Gay Lussac's Law | Pressure of a gas at constant volume is directly proportional to temperature |
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What You'll Learn
Pressure, volume, temperature, and moles
The ideal gas law combines Charles' Law, Avogadro's Law, Boyle's Law, and Gay-Lussac's Law into a single equation that relates gas quantities. It is used to calculate changes in the volume, temperature, pressure, and number of moles of an ideal gas. The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, T is temperature, and R is the gas constant.
The ideal gas law describes the behaviour of real gases under most conditions. It states that the volume occupied by the atoms and molecules of a gas is a negligible fraction of the volume of its container. The properties of a gas depend more on the number of atoms per unit volume and on temperature than on the type of atom. This is because atoms and molecules in a gas are typically widely separated, and the forces between them are quite weak.
Avogadro's Law gives the relationship between volume and the amount of gas in moles when pressure and temperature are held constant. According to Avogadro's Law, if the amount of gas in a container is increased, the volume increases, and if the amount of gas in a container is decreased, the volume decreases.
Charles' Law states that the volume occupied by a gas is proportional to temperature at a fixed pressure. If the Kelvin temperature of a gas is increased, the volume of the gas increases, and if the temperature is decreased, the volume of the gas decreases.
Boyle's Law states that the volume of a given amount of gas held at a constant temperature varies inversely with the applied pressure when the temperature and mass are constant. When the volume of a gas decreases, the molecules strike the walls of its container more often, increasing the pressure. Conversely, when the volume increases, the distance the molecules must travel to strike the walls increases, and they hit the walls less often, decreasing the pressure.
Gay-Lussac's Law states that the pressure of a given amount of gas held at a constant volume is directly proportional to the Kelvin temperature. When a gas is heated, its molecules move faster and strike the walls of the container more frequently, increasing the pressure. Conversely, when the molecules are cooled, they slow down and the pressure decreases.
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Molar form of the ideal gas law
The ideal gas law, also called the general gas equation, is an equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under various conditions, although it has some limitations. The ideal gas law was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law.
The molar form of the ideal gas law relates the pressure, volume, and temperature of an ideal gas to the number of moles of the gas. The equation for the molar form of the ideal gas law is:
PV = nRT
Where:
- P is the pressure exerted by the gas on the container walls
- V is the volume of the container
- N is the number of moles of the gas
- R is the ideal gas constant (approximately 8.31 J/K⋅mol)
- T is the temperature of the gas
This equation can be used to determine the pressure, volume, temperature, or number of moles of a gas, given the other variables. For example, if you know the pressure, volume, and temperature of a gas, you can use the equation to calculate the number of moles present.
The ideal gas law assumes that the volume occupied by the atoms and molecules of the gas is negligible compared to the total volume. It also assumes that there are no intermolecular attractions between the molecules or atoms of the gas, so its potential energy is zero. These assumptions make the ideal gas law most accurate for monatomic gases at high temperatures and low pressures.
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Gay-Lussac's Law
The ideal gas law relates the pressure, volume, temperature, and number of moles of an ideal gas to one another. It can be used to determine the number of moles of a gas. Gay-Lussac's Law is a variant of the ideal gas law where the volume of gas is held constant. It was discovered by the French chemist Joseph Gay-Lussac (1778-1850), who investigated the relationship between the pressure and absolute temperature of a given mass of gas. Gay-Lussac's Law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant.
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Charles' Law
Charles's Law, also known as the law of volumes, is an experimental gas law that describes how gases tend to expand when heated. It was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s. The French natural philosopher Joseph Louis Gay-Lussac confirmed the discovery in a presentation in 1802, although he credited the discovery to Charles's work in the 1780s.
Charles's Law states that the volume of a given mass of gas varies directly with the absolute temperature of the gas when pressure is kept constant. The absolute temperature is the temperature measured with the Kelvin scale. The Kelvin scale is used because zero on the Kelvin scale corresponds to a complete stoppage of molecular motion.
Mathematically, the direct relationship of Charles's Law can be represented by the equation: V1/T1 = V2/T2, where V1 and T1 stand for the initial volume and temperature of a gas, while V2 and T2 stand for the final volume and temperature. This equation can be used to calculate any one of the four quantities if the other three are known. The direct relationship will only hold if the temperatures are expressed in Kelvin.
Charles's Law can be derived from the kinetic theory of gases, which relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules that make up the gas, particularly their mass and speed. The kinetic theory equivalent of the ideal gas law relates PV to the average kinetic energy.
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Avogadro's Law
Mathematically, Avogadro's Law can be expressed as:
\$V = k \times n \: \: \: \text{and} \: \: \: \frac{V_1}{n_1} = \frac{V_2}{n_2}\nonumber$
Where \(n\) is the number of moles of gas and \(k\) is a constant. This law is evident when blowing up a balloon. The volume of the balloon increases as more moles of gas are added by blowing into it. If the container holding the gas is rigid, pressure can be substituted for volume in Avogadro's Law.
\$PV = nRT$
Where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is temperature. This law can be used to calculate the quantity of gas in a container and determine the volume, pressure, or temperature of a gas when the other variables are known.
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Frequently asked questions
The ideal gas law describes the behaviour of real gases under most conditions. It can be derived from basic principles but was originally deduced from experimental measurements of Charles' Law and Boyle's Law.
The ideal gas law relates the pressure, volume, and temperature of an ideal gas to the number of moles of the gas. The equation can be used to calculate the number of moles in a given volume.
The ideal gas law can be expressed by the equation PV = nRT, where P is pressure, V is volume, T is temperature, n is the number of moles, and R is the universal gas constant.
The universal gas constant, R, has units of J/K⋅mol or m2⋅kg/s2⋅K⋅mol in SI base units.
Sure, let's consider the following example: A gas consisting of an unknown number of moles of carbon fills a volume of 0.128 m3 and has a pressure of 135 kPa at a temperature of 273.15 K. Using the ideal gas law equation, we can calculate the number of moles present. First, we need to convert the temperature to Kelvin, so 273.15 K becomes 273.15 + 273.15 = 546.3 K. Now, we can plug the values into the equation: 135,000 Pa x 0.128 m3 = (n) * 8.31 J/K⋅mol * 546.3 K. Solving for n, we find that the number of moles in the gas is approximately 25.6 moles.
