Keith Mack
The ideal gas law combines pressure, volume, and temperature into a single equation. The ideal gas constant, R, is a critical component of this equation and its value depends on the units chosen for pressure, temperature, and volume. While the temperature must be in Kelvin, and the volume in litres, pressure can be measured in kPa, atm, or mm Hg. As a result, R can have three different values.
| Characteristics | Values |
|---|---|
| Ideal Gas Law Equation | PV=nRT |
| Ideal Gas Constant | R |
| Value of R when P is in kPa | 8.315 |
| Unit of R when P is in kPa | J mol-1 K -1 |
| Volume Unit | liters |
| Pressure Units | kPa, atm, mm Hg |
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What You'll Learn
- The ideal gas constant, R, is 8.315 when P is in kPa
- R's value depends on chosen units for pressure, temperature, volume
- Kelvin must be used for temperature, SI unit of litres for volume
- Pressure is measured in kPa, atm, or mm Hg, so R has 3 values
- The combined gas law combines pressure, volume, and temperature
The ideal gas constant, R, is 8.315 when P is in kPa
The ideal gas constant, R, is a fundamental component of the ideal gas law, which combines pressure, volume, and temperature. The ideal gas law is expressed as PV=nRT, where P is the pressure, V is the volume, T is the absolute temperature, n is the number of moles of gas, and R is the universal gas constant. The value of R depends on the units chosen for pressure, temperature, and volume.
The value of R can vary depending on the units used for pressure, volume, and temperature. For example, when pressure is measured in Pascals, and volume is measured in cubic meters (the standard SI units), the universal gas constant is 8.314 J/(mole·K). On the other hand, when pressure is in kilopascals, volume is in liters, the amount of gas is in moles, and temperature is in kelvins, the value for the ideal gas constant (R) is approximately 8.314 kPa·L/(mol·K).
It's important to note that the ideal gas constant, R, is not always equal to 8.315 when P is in kPa. Some sources give the value as 8.314 kPa·L/(mol·K) when working with pressure in kilopascals, volume in liters, amount of gas in moles, and temperature in kelvins. This slight variation in the value of R is due to the different units used for pressure, volume, and temperature.
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R's value depends on chosen units for pressure, temperature, volume
The ideal gas law is given by the equation PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, and T is the temperature of the gas. The variable R in the equation is called the ideal gas constant. The value of R depends on the units chosen for pressure, temperature, and volume in the ideal gas equation.
It is necessary to use Kelvin for the temperature and it is conventional to use the SI unit of liters for the volume. However, pressure is commonly measured in one of three units: kPa, atm, or mm Hg. Therefore, R can have three different values. For example, if the volume is measured in liters, the value of R will be different than if the volume is measured in cubic meters. This is because the conversion factor between the two units needs to be taken into account.
The ideal gas law can be used to calculate the molar volume of gases around STP and at atmospheric pressure. The standard reference conditions for temperature and pressure vary depending on the organization and the industry. For example, the natural gas companies in Europe, Australia, and South America have adopted 15 °C (59 °F) and 101.325 kPa (14.696 psi) as their standard gas volume reference conditions.
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, nRT, is roughly the amount of translational kinetic energy of N atoms or molecules at an absolute temperature T.
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Kelvin must be used for temperature, SI unit of litres for volume
The ideal gas law combines pressure, volume, and temperature into a single equation. The equation is PV=nRT, where P is pressure, V is volume, n is the number of moles, T is temperature, and R is the ideal gas constant. The value of R depends on the units chosen for pressure, temperature, and volume.
Kelvin must be used for temperature when using the ideal gas law. This is because the ideal gas law is based on absolute temperatures, and Kelvin is the SI unit for temperature that uses an absolute scale. The Kelvin scale sets absolute zero (0 K) at the point where molecular motion essentially ceases to exist, which is necessary for the ideal gas law to function accurately.
For volume, it is conventional to use the SI unit of litres. This is because litres are a convenient and standardized unit for measuring volume, especially for gases. Using litres allows for easy comparisons and calculations when dealing with larger volumes of gas, as one litre is equal to 1000 cubic centimetres (1 L = 1000 cm³).
While Kelvin and litres are the standard units for temperature and volume, respectively, the ideal gas law can accommodate different units for pressure. Pressure is commonly measured in one of three units: kilopascals (kPa), atmospheres (atm), or millimetres of mercury (mm Hg). The choice of pressure unit will determine the value of the ideal gas constant (R) used in the equation. For example, if pressure is measured in kPa, then R would be approximately 8.315.
By using Kelvin for temperature, litres for volume, and selecting an appropriate value for R based on the chosen pressure unit, the ideal gas law can be effectively applied to calculate and understand the behaviour of gases under various conditions.
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Pressure is measured in kPa, atm, or mm Hg, so R has 3 values
The ideal gas law combines pressure, volume, and temperature into a single equation. The variable R in the equation is called the ideal gas constant. The value of R depends on the units chosen for pressure, temperature, and volume.
While the Kelvin scale must be used for temperature, and the SI unit of liters for volume, pressure can be measured in one of three units: kPa (kilopascals), atm (atmospheres), or mm Hg (millimeters of mercury). Since R depends on the units chosen for pressure, it can have three different values.
The ideal gas law can be rearranged as follows, with the multiplication signs omitted:
> PV = nRT
Here, P is the pressure, V is the volume, n is the number of moles, T is the temperature, and R is the ideal gas constant.
The conversion factors between the three units of pressure are as follows: 1 atm = 760.0 mm Hg = 101.325 kPa.
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The combined gas law combines pressure, volume, and temperature
\[ \frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}\] at constant n
Where P represents pressure, V represents volume, and T represents temperature. This law is derived from the ideal gas law, which includes a proportionality constant called the Ideal or Universal Gas Constant (R). The value of R depends on the units chosen for pressure, temperature, and volume. While temperature must always be in Kelvin, pressure can be measured in kPa, atm, or mm Hg, and volume is typically measured in liters.
The combined gas law is useful because it allows you to derive any of the relationships needed by combining all the changeable pieces in the ideal gas law: pressure, temperature, and volume. R and the number of moles do not appear in the equation as they are generally constant and therefore cancel out, as they appear in equal amounts on both sides of the equation. This means that the equation can be solved for any of the parameters, and anything that remains constant can be eliminated from the equation. For example, if a question mentions a change in volume but does not specify a change in temperature, you can assume temperature remains constant and will therefore cancel in the calculation.
Charles' Law, for example, gives the relationship between volume and temperature if pressure and the amount of gas are held constant. If the Kelvin temperature of a gas is increased, its volume increases, and vice versa. Gay-Lussac's Law is another example, stating that the pressure of a given amount of gas held at a constant volume is directly proportional to the Kelvin temperature.
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Frequently asked questions
The ideal gas law combines pressure, volume, and temperature into one equation. It can be written as PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
The ideal gas constant, R, depends on the units chosen for pressure, temperature, and volume in the ideal gas equation. If you are using Kelvin for temperature and liters for volume, the pressure is usually measured in kPa, atm, or mm Hg.
If pressure is in kPa, then R = 8.315.
R has units. It is good practice to keep the units with it and not give it as a number without units.
We can use the ideal gas law to find the volume occupied by 3.76 g of oxygen gas at a pressure of 88.4 kPa and a temperature of 19°C.
