Keith Mack
The ideal gas law, also known as the general gas equation, describes the behaviour of gases under varying conditions of pressure, volume, and temperature. The law is expressed as PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R is the gas constant, and T denotes temperature in Kelvin. While the ideal gas law is a useful approximation, it does not account for molecular size and intermolecular forces, limiting its accuracy to monatomic gases at high temperatures and low pressures. The law can be adapted to different units of pressure and volume by selecting the appropriate value of R, ensuring that the units in the equation align correctly. This article will explore whether the ideal gas law can be applied using imperial units and provide insights into the considerations and calculations involved in using non-SI units.
| Characteristics | Values |
|---|---|
| Ideal Gas Law | Also called the General Gas Equation |
| State of a gas | Determined by its pressure, volume, and temperature |
| SI units | p is measured in pascals, V in cubic metres, n in moles, and T in kelvins |
| Ideal Gas Constant (R) | 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, 8.3145 (J/mol K), 0.08206 (L atm/mol K), 62.37 (L torr /mol K) |
| Standard Temperature and Pressure (STP) | 1 atm (pressure) and 0° C |
| Moles of gas at STP | 1 mole will take up 22.4 L of the volume of the container |
| Ideal gas | A hypothetical gas unaffected by real-world conditions |
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What You'll Learn
The ideal gas law equation: PV = nRT
The ideal gas law, also known as the general gas equation, describes the 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 ideal gas law equation is PV = nRT, where P represents pressure, V represents volume, T represents temperature, n represents the number of moles, and R is the gas constant. This equation applies specifically to an ideal gas or as an approximation to a real gas that behaves similarly to an ideal gas.
The ideal gas law assumes that gases are unaffected by real-world conditions, such as molecular size and intermolecular attractions. Therefore, it is most accurate for monatomic gases at high temperatures and low pressures. At lower densities, the average distance between molecules becomes much larger than their molecular size, reducing the significance of molecular size. Similarly, as temperatures increase, the impact of intermolecular attractions decreases due to higher thermal kinetic energy.
The gas constant, R, is a crucial factor in the ideal gas law equation. Its value depends on the units used in the calculation. For example, when using the first value of R, 0.082057 L atm mol-1K-1, the units for pressure, volume, and temperature must be atm, liter, and Kelvin, respectively. The gas constant R is also known as the universal gas constant, ideal gas constant, or molar gas constant.
The ideal gas law equation, PV = nRT, is a valuable tool for understanding gas behaviour and solving problems in chemistry and engineering. It allows us to determine unknown variables when the others are known, making it a versatile equation in the study of gases.
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The ideal gas law constant, R
The ideal gas law, also known as the general gas equation, is an equation of state for a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under various conditions. 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 modern form of the equation relates pressure, volume, and temperature simply in two main forms. The temperature used in the equation of state is an absolute temperature, with the appropriate SI unit being the Kelvin.
The ideal gas law equation is PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, and T represents temperature. This equation applies only to an ideal gas or as an approximation to a real gas that behaves sufficiently like an ideal gas. The ideal gas law neglects both molecular size and intermolecular attractions, making it most accurate for monatomic gases at high temperatures and low pressures.
The ideal gas constant, R, is a fundamental constant in the physical sciences, appearing in various equations such as the ideal gas law, the Arrhenius equation, and the Nernst equation. It is a constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for the amount of substance. The specific gas constant of a gas or a mixture of gases is given by the molar gas constant divided by the molar mass of the gas or mixture.
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Ideal gas law in SI units
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 various conditions. The ideal gas law is often written in an empirical form, and the state of the gas is determined by its pressure, volume, and temperature. The modern form of the equation relates these variables in two main forms. The temperature used in the equation of state is an absolute temperature, and the appropriate SI unit is the Kelvin.
In SI units, pressure (p) is measured in Pascals, volume (V) in cubic metres, the number of moles (n) in moles, and temperature (T) in Kelvins. The Kelvin scale is a shifted Celsius scale, where 0 K = −273.15 °C, the lowest possible temperature. The Boltzmann constant (kB) is 1.38×10−23 J⋅K−1 in SI units. The ideal gas constant (R) has a value of 8.314 J/(mol·K) = 1.989 ≈ 2 cal/(mol·K), or 0.0821 L⋅atm/(mol⋅K).
The ideal gas law can be written in terms of the number of molecules of gas: PV = NkT, where P is pressure, V is volume, T is temperature, N is the number of molecules, and k is the Boltzmann constant. This equation relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas. The ideal gas law can be considered another manifestation of the law of conservation of energy, as work done on a gas results in an increase in its energy, increasing pressure and/or temperature, or decreasing volume.
The ideal gas law is closely related to energy, with the units on both sides being joules. The left-hand side of the equation, PV, is pressure multiplied by volume, which is energy. The right-hand side, NkT, is roughly the amount of translational kinetic energy of N atoms or molecules at an absolute temperature T. The ideal gas law is useful because it links pressure, density, and temperature in a unique formula independent of the quantity of the gas considered.
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Limitations of the ideal gas law
The ideal gas law is a mathematical relationship that describes the behaviour of gases under various conditions. It is a good approximation of the behaviour of many gases under many conditions. However, it makes some assumptions about gases that are not necessarily true, and so it has several limitations.
Firstly, the ideal gas law assumes that gas particles have no volume and that there is no intermolecular attraction. In reality, gas particles occupy space, and they are attracted to each other. This means that when a gas is condensed, it turns into a liquid with volume, and the gas law no longer applies because the substance is no longer a gas.
Secondly, the ideal gas law assumes that gas particles move in random motion. While this is true at low pressures, at high pressures or low temperatures, gas particles do not move in random motion, and the ideal gas law may not accurately predict their behaviour.
Thirdly, the ideal gas law does not account for deviations from ideal behaviour, such as the effects of gas mixtures or chemical reactions. For example, in high-altitude environments, the ideal gas law may be more accurate for monitoring gas flow pressure into patients compared to sea-level conditions. Therefore, caution must be exercised when applying the ideal gas law to real-world scenarios, and other factors that may affect gas behaviour must be considered.
Finally, the ideal gas law assumes that the gas particles have no mass. However, in reality, gas particles do have mass, and this can affect their behaviour. For example, lighter gas molecules travel quicker than heavier molecules.
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The ideal gas law vs non-ideal gas law
The ideal gas law is an equation that demonstrates the relationship between temperature, pressure, and volume for gases. It is a combination of simpler gas laws such as Boyle's, Charles's, Avogadro's, and Amonton's laws. The ideal gas law is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is the absolute temperature. This law assumes that gas particles have no intermolecular forces of attraction and exhibit elastic collisions. It is important to note that ideal gases do not exist in reality, as gas particles have volumes and interact with each other, especially at low temperatures.
The ideal gas law is a useful approximation for many gases under certain conditions, typically high temperatures and low pressures. At high temperatures, gas particles move faster, reducing the impact of intermolecular forces. Additionally, at low densities, the average distance between molecules becomes much larger than their size, making molecular size less significant.
Non-ideal gases deviate from the ideal gas law due to factors such as molecular size and intermolecular forces. More detailed equations of state, like the van der Waals equation, account for these deviations. The van der Waals equation includes parameters for intermolecular forces and the volume occupied by gas molecules.
The ideal gas law can be applied to systems containing multiple ideal gases, known as ideal gas mixtures. In such mixtures, gas particles are assumed to have no intermolecular interactions, and the total pressure is partitioned into the partial pressure contributions of each gas particle. However, at high pressures and low temperatures, gas particles interact, limiting the accuracy of the ideal gas law.
In summary, the ideal gas law is a useful approximation for many gases, particularly at high temperatures and low pressures. Non-ideal gases deviate from this law due to molecular size and intermolecular forces, which are accounted for in more complex equations of state like the van der Waals equation. The ideal gas law remains applicable in ideal gas mixtures, assuming no intermolecular interactions, but its accuracy diminishes at high pressures and low temperatures when gas particles interact.
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Frequently asked questions
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.
The equation of state for the ideal gas law is PV = nRT.
The variables in the ideal gas law represent pressure (P), volume (V), the number of moles (n), the gas constant (R), and temperature (T).
Yes, you can use Imperial units with the Ideal Gas Law. The gas constant, R, has different values depending on the units of pressure and volume used. For example, if you use the value of R as 0.082057 L atm mol-1K-1, your unit for pressure must be atm, and for volume must be litres.
In SI units, pressure (P) is measured in pascals, volume (V) in cubic metres, the number of moles (n) in moles, temperature (T) in kelvins, and the gas constant (R) in J/(mol·K).
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