Gavin Howe
The ideal gas law, also known as the general gas equation, is a fundamental equation that describes the relationship between pressure, volume, temperature, and the amount of gas in moles. It is a combination of Boyle's, Charles', Avogadro's, and Gay-Lussac's laws. The ideal gas law is often used to calculate volume, density, and pressure. When calculating the ideal gas law, the volume must be in liters (L) in the SI unit system. The law is expressed as PV = nRT, where P is pressure, V is volume, T is temperature, n is the number of moles, and R is the ideal gas constant. The value of R depends on the units used for the gas properties. In this equation, it is crucial to ensure that all quantities are in the correct units to obtain accurate results.
| Characteristics | Values |
|---|---|
| Ideal Gas Law | PV = nRT |
| P = Pressure, V = Volume, n = Number of moles, T = Temperature, R = Gas Constant | |
| Volume Unit | Liters (L) |
| Temperature Unit | Kelvin (K) |
| Pressure Unit | Atmospheres (atm) |
| Molar Volume at STP | 22.4 L |
| Gas Constant R | 0.082057 L atm mol-1K-1 or 0.08206 atm L mol-1 K-1 |
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What You'll Learn
Volume must be in litres (L)
When calculating the ideal gas law, the volume must be in litres (L). This is because the ideal gas law is generally expressed with volume in litres when working in the International System of Units (SI). The ideal gas law equation relates the pressure (P), volume (V), temperature (T), and the amount of substance in moles (n) of a gas.
The equation is PV = nRT, where R is the ideal gas constant. The value of R depends on the units used for the properties of the gas. When the ideal gas constant relates pressure in atmospheres, volume in litres, and temperature in Kelvin, the value of R is 0.082057 L atm mol-1K-1.
To convert from other units of volume such as millilitres (mL) or cubic centimetres (cc), you can use the conversion factor that 1 litre is equal to 1000 millilitres or 1000 cubic centimetres. For example, if you have a volume of 250 mL, you would convert it to litres by calculating 250 mL / 1000 = 0.25 L and then use this value in your calculations.
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Pressure and temperature
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 many conditions. The ideal gas law is closely related to energy, with the units on both sides being joules. The equation of state given here (PV = nRT) applies only to an ideal gas or as an approximation to a real gas that behaves like an ideal gas. The ideal gas law is a fundamental equation that describes the relationship between pressure (P), volume (V), temperature (T), and the amount of gas in moles (n). The volume of a gas is directly proportional to its Kelvin temperature.
The ideal gas law can be derived from the kinetic-molecular theory of gases, which assumes that gases are essentially point masses moving in constant, random, straight-line motion. The law is also based on the assumptions of the kinetic theory of ideal gases, which considers that there are no intermolecular attractions between the molecules or atoms of an ideal gas. This means that its potential energy is zero, and all the energy possessed by the gas is kinetic energy.
The ideal gas law can be used to calculate the initial or final value of pressure or volume of a certain gas when one of the two factors is missing. Charles's Law, for instance, describes the directly proportional relationship between the volume and temperature (in Kelvin) of a fixed amount of gas, when the pressure is held constant. Avogadro's Law also applies to problems using standard temperature and pressure, given a constant number of moles of gas and an unchanged volume. In this case, pressure is directly proportional to temperature.
When using the ideal gas law to calculate any property of a gas, it is important to ensure that all quantities are in the correct units to get accurate results. The volume must be measured in litres (L), as this is standard in the International System of Units (SI). The temperature used in the equation of state is an absolute temperature, with the appropriate SI unit being the Kelvin. The pressure and volume of a gas are related to its energy. Work done on a gas results in an increase in its energy, increasing pressure and/or temperature, or decreasing volume.
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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 means that the volume of a gas is directly proportional to the number of moles of gas, when the temperature and pressure are held constant. For example, if you increase the number of moles of gas in a balloon, the volume of the balloon will also increase.
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The gas constant, R
The ideal gas law, also called the general gas equation, is a fundamental equation that describes the relationship between pressure (P), volume (V), temperature (T), and the amount of gas in moles (n). The equation is expressed as PV = nRT, where R is the ideal gas constant.
The gas constant is defined as the product of pressure and volume and is expressed as energy per temperature increase per mole. It is also known as the universal gas constant or molar constant. The value of R at standard atmospheric pressure is R = 8.3144598 J.mol-1.K-1. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB). The SI value of the molar gas constant is exact and can be expressed in multiple units.
The ideal gas law is a good approximation of the behavior 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 Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The modern form of the equation relates pressure, volume, and temperature simply in two main forms. The temperature used in the equation is an absolute temperature, with the SI unit being Kelvin.
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Ideal gas law equation
The ideal gas law, also called the general gas equation, is a hypothetical ideal gas equation of state. 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 ideal gas law is often written in an empirical form, with the ideal gas constant denoted as 'R'. The modern form of the equation relates pressure, volume, and temperature in two main forms. The temperature used in the equation of state is an absolute temperature, with the appropriate SI unit being Kelvin. The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, T is the temperature, and n is the number of moles. The gas constant R is a constant of units of energy per temperature increment per mole, also known as the universal gas constant, ideal gas constant, and molar gas constant.
The ideal gas law can be used to calculate volume, density, and pressure. It is a fundamental equation that describes the relationship between pressure, volume, temperature, and the amount of gas in moles. The volume must be measured in litres (L) when using the SI unit system. To convert from other units of volume, such as millilitres (ml), you can use the conversion factor that 1 litre is equal to 1000 millilitres.
The ideal gas law is particularly useful because it links pressure, density, and temperature in a unique formula, independent of the quantity of the gas being considered. It can be used to solve for the initial or final value of volume or temperature when pressure and the number of moles of gas remain constant. The law can also be written in terms of specific volume, the reciprocal of density.
The ideal gas law is most accurate for monatomic gases at high temperatures and low pressures. This is because the law neglects molecular size and intermolecular attractions, which become less important at lower densities and higher temperatures. More detailed equations of state, such as the van der Waals equation, account for deviations caused by molecular size and intermolecular forces.
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Frequently asked questions
The ideal gas law, also called the general gas equation, is an equation that describes the relationship between pressure (P), volume (V), temperature (T), and the amount of gas in moles (n).
The volume must be in liters (L) when using the SI unit system. Milliliters (mL) can be converted to liters by dividing by 1000.
The ideal gas constant, denoted as R, is a universal constant that quantifies the relationship between the properties of a gas. The value of R depends on the units used for the gas properties.
The ideal gas equation is PV = nRT, where P is pressure, V is volume, T is temperature, n is the number of moles, and R is the ideal gas constant.
Temperature is always given in Kelvin when using the ideal gas equation. The ideal gas law is most accurate for monatomic gases at high temperatures and low pressures since it neglects molecular size and intermolecular attractions.
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