Cameron Miranda
The Ideal Gas Law, also known as the Perfect Gas Law, is an equation that relates the pressure, temperature, and volume of an ideal gas. The law is expressed with the individual gas constant, R, which is dependent on the specific gas and its molecular weight. While the Ideal Gas Law is typically used with SI units, where pressure is measured in pascals, volume in cubic meters, and temperature in kelvins, it is important to note that gas pressure and volume can be measured using various units. This raises the question: can the Ideal Gas Law be used with imperial units?
| Characteristics | Values |
|---|---|
| Ideal Gas Law | Also called the general gas equation or Perfect Gas Law |
| Use | Relates pressure, temperature, and volume of an ideal or perfect gas |
| Equation | PV=nRT |
| Gas Constant | R, depends on the particular gas and is related to the molecular weight of the gas |
| SI Units | P is measured in pascals, V in cubic metres, T in kelvins, and n in moles |
| R Value | 8.314 J/(mol·K) = 1.989 ≈ 2 cal/(mol·K), or 0.0821 L⋅atm/(mol⋅K) |
| Other R Values | 0.082057 L atm mol-1K-1, 62.364 L Torr mol-1K-1 |
| STP | Standard condition of temperature and pressure, universal value of 1 atm (pressure) and 0o C |
| Gas Amount | Specified by giving the mass or chemical amount of gas |
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What You'll Learn
The ideal gas law equation
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form: PV = nRT, where n is the number of moles of the gas and R is the universal (or perfect) gas constant, 8.31446261815324 joules per kelvin per mole.
The state of an amount of gas is determined by its pressure, volume, and temperature. The modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature: the appropriate SI unit is the Kelvin. In SI units, p is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in Kelvins.
The Ideal Gas Law is simply the combination of all Simple Gas Laws (Boyle's Law, Charles' Law, and Avogadro's Law), and so learning this one means that you have learned them all. Boyle's Law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed amount of gas. Charles's Law describes the directly proportional relationship between the volume and temperature (in Kelvin) of a fixed amount of gas, when the pressure is held constant.
The Ideal Gas Law can be used to solve for the initial or final value of volume or temperature under the given condition that pressure and the number of moles of the gas stay the same. Volume is directly proportional to the amount of gas at a constant temperature and pressure. Avogadro's Law can apply well to problems using Standard Temperature and Pressure (STP). Given a constant number of moles of gas and an unchanged volume, pressure is directly proportional to temperature.
The ideal gas law assumes that the gas particles have no forces acting among them and that these particles do not take up any space, meaning their atomic volume is completely ignored. An ideal gas is a hypothetical gas because it would be much easier if things like intermolecular forces did not exist to complicate the simple Ideal Gas Law.
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Gas constant R
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. The ideal gas law is often written in an empirical form, where R is the ideal gas constant. The gas constant R is also known as the universal gas constant, or molar constant.
The gas constant R is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The constant is a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance. The Boltzmann constant and the Avogadro constant separately relate energy to temperature and particle count to amount of substance. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB).
The value of the gas constant R is 8.314 J/(mol·K) = 1.989 ≈ 2 cal/(mol·K), or 0.0821 L⋅atm/(mol⋅K). The value of R can be expressed in multiple units, such as 0.082057 L atm mol-1K-1, 62.364 L Torr mol-1K-1, 8.3145 J / mol·K, and 1.987 cal / (mol·K). The value of R to be used depends on the units of pressure, volume, number of moles, and temperature. For example, if the unit of pressure is atm, the value of R to be used is 0.082057 L atm mol-1K-1.
The gas constant R is expressed as energy per temperature increase per mole. It is defined as the product of pressure and volume. The physical significance of R is work per mole per kelvin. The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture.
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Standard temperature and pressure (STP)
The universal value of STP is 1 atm (pressure) and 0°C. This is equivalent to 273.15 Kelvin or 32 degrees Fahrenheit. At STP, 1 mole of gas occupies 22.4 litres (L) of volume. This is also known as the molar volume of a gas at STP.
STP is important in various fields, including physics, chemistry, and engineering, as well as in aeronautics and navigation. It is used in many thermodynamic calculations and tabulations, as it provides a common set of conditions ("state") for tabulating values, making comparisons possible and calculations easier.
The definition of STP has evolved over time. Before 1918, the standard reference conditions for expressing gas volumes in the metric system were 15°C (288.15 K; 59.00°F) and 101.325 kPa (1.00 atm; 760 Torr). During the same period, the standard reference conditions for the imperial or U.S. customary systems were 60°F (15.56°C; 288.71 K) and 14.696 psi (1 atm).
Since 1982, the International Union of Pure and Applied Chemistry (IUPAC) has defined STP as a temperature of 0°C (273.15 K or 32°F) and an absolute pressure of 1 bar (100 kPa or 105 Pa). This definition is different from the one provided by the National Institute of Standards and Technology (NIST), which uses a temperature of 20°C (293.15 K or 68°F) and an absolute pressure of 1 atm (14.696 psi or 101.325 kPa).
It is important to note that the ideal gas law can be used with different units of pressure and volume. The choice of the gas constant, R, depends on the units used. For example, if the pressure is in atm and the volume is in litres, the gas constant would be 0.082057 L atm mol-1K-1.
The ideal gas law is a valuable tool for estimating gas properties at both standard and non-standard conditions. It is a famous equation that relates all the factors needed to solve a gas problem.
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Converting units
The ideal gas law can be used with different units for pressure, volume, and temperature. The choice of units will depend on the value of the gas constant, R, chosen. For example, if the value of R is 0.082057 L atm mol-1K-1, then the unit for pressure must be atm, the unit for volume must be litres, and the temperature must be in Kelvin.
Converting between different units is an important skill when dealing with the ideal gas law. The International System of Units (SI) is the standard metric system that is currently used and consists of seven SI base units: length, mass, time, temperature, electric current, luminous intensity, and amount of substance. The SI system is used almost universally in science, including in the US. However, some countries, like the US, still use their own system of units.
The imperial system, also known as the British Imperial system, is used in Britain and some other Commonwealth countries. Unlike the metric system, the imperial system is not based on the number 10. Common imperial units include inches, pounds, and yards. To convert from imperial units to metric units, you can use the following examples as a guide:
- 1 foot = 12 inches
- 1 inch = 2.54 centimetres
- To convert feet to inches, multiply the number of feet by 12
- To convert inches to feet, divide by 12
- 1 mile = 1760 yards
- 1 mile = 1.6093 kilometres
- To convert miles to yards, multiply by 1760
- To convert yards to miles, divide by 1760
There are also online conversion calculators that can be used to convert between different units.
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Ideal vs non-ideal gas
The ideal gas law, also called the general gas equation, is a hypothetical gas equation that is used to model real thermodynamic processes. It is a combination of Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form and is a good approximation of the behaviour of many gases under many conditions. The state of an amount of gas is determined by its pressure, volume, and temperature, and the ideal gas law relates these factors in two main forms. The ideal gas law assumes that gas particles have no forces acting among them and do not take up any space, meaning their atomic volume is ignored.
In contrast, non-ideal gas behaviour is more realistic and is required when performing more rigorous analyses of actual systems. Non-ideal gas behaviour accounts for how gases behave in reality and is often favoured in real-world applications. To model non-ideal gas behaviour, one must capture the irreversible energy losses and work them into each process, taking into account equipment efficiency and other losses in the cycle.
The ideal gas law can be used with different units of pressure and volume, such as atmospheres (atm), litres (L), and Kelvin (K). The gas constant, R, will change depending on the units used. For example, if using atmospheres for pressure and litres for volume, the gas constant R is 0.082057 L atm mol-1K-1. On the other hand, if using Torrs for pressure and litres for volume, R is 62.364 L Torr mol-1K-1. The temperature is always measured in Kelvin, and the amount of gas is measured in moles.
The ideal gas law is a useful tool for relating the factors that determine the state of a gas, such as pressure, volume, and temperature. It simplifies the math when dealing with thermodynamic processes and is a good approximation for many gases. However, non-ideal gas behaviour is more realistic and is necessary for more accurate and rigorous analyses of actual systems. The ideal gas law can be used with different units of pressure and volume, but it is important to use the appropriate gas constant, R, that matches the chosen units.
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Frequently asked questions
The Ideal Gas Law, also called the Perfect Gas Law or the general gas equation, is an equation of state of a hypothetical ideal gas. It relates the pressure, temperature, and volume of an ideal or perfect gas.
The Ideal Gas Law in the Imperial system would use pounds per square inch (psi) for pressure, cubic feet (ft^3) for volume, and degrees Rankine (°R) for temperature.
In the SI system, the Ideal Gas Law uses pascals (Pa) for pressure, cubic meters (m^3) for volume, moles (mol) for the amount of gas, and Kelvin (K) for temperature.
Yes, the Ideal Gas Law can be used in both the Imperial and SI systems, but the gas constant, R, will change depending on the units of pressure and volume used. It is important to ensure that the units of pressure, volume, number of moles, and temperature match the units of R.
