Cecily Zamora
The ideal gas law combines the pressure, volume, and temperature of a gas. The variable R in the equation is the ideal gas constant, and its value depends on the units chosen for pressure, temperature, and volume. While the temperature must be in Kelvin, and the volume is usually in litres, pressure can be measured in kPa, atm, or mm Hg. Therefore, R can have three different values, depending on the units used for pressure.
| Characteristics | Values |
|---|---|
| Ideal Gas Law Equation | PV=nRT |
| Variable R | Ideal Gas Constant |
| R Value Dependence | Units chosen for pressure, temperature, and volume |
| Temperature Units | Kelvin |
| Volume Units | SI unit of liters |
| Pressure Units | kPa, atm, or mm Hg |
| R Calculation | Demonstrated with pressure in kPa |
| STP (Standard Temperature and Pressure) | 273.15 K and 1 atm |
| STP Volume | 22.414 L |
| STP Pressure | 101.325 kPa |
| STP Temperature | 273.15 K |
| Combined Gas Law | P1V1/T1 = P2V2/T2 at constant n |
| Gas Law Focus | Volume, pressure, and temperature |
| R Value | 8.315 when P is in kPa |
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What You'll Learn
The ideal gas constant, R, is dependent on chosen units
The ideal gas constant, R, is a fundamental constant in the sciences, appearing in many equations such as the ideal gas law, the Arrhenius equation, and the Nernst equation. It is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for the amount of substance.
The ideal gas constant is dependent on the units chosen for pressure, temperature, and volume in the ideal gas equation. The ideal gas law is typically written as:
$$PV = nRT$$
Where:
- P is the absolute pressure
- V is the volume of gas
- N is the amount of substance
- T is the thermodynamic temperature
The value of $R$ depends on the units chosen for $P$, $V$, and $T. For example, when using SI units, $P$ is measured in pascals (Pa), $V$ in cubic meters (m^3), and $T$ in Kelvin (K). This gives $R$ the value of 8.314 \\(\frac{J}{mol·K}\\).
However, pressure can also be commonly measured in units of kilopascals (kPa), atmospheres (atm), or millimeters of mercury (mm Hg). Using these different units for pressure will result in different values for $R$. For example, when using kPa, $R$ is equal to 8.3145 \frac{L·kPa}{mol·K}.
It is important to note that the ideal gas constant, R, is a universal constant for all gases, and its value is independent of the specific gas being considered. The value of $R$ is typically listed in textbooks and handbooks, and it is essential to use the correct value depending on the chosen units for the ideal gas law equation.
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Kelvin must be used for temperature
The Kelvin scale is an absolute temperature scale that starts at absolute zero, or 0 K, the lowest possible temperature. The Kelvin scale was developed and proposed by the 19th-century British scientist Lord Kelvin, after whom it is named. The Kelvin scale is widely used in science, particularly in the physical sciences.
The Kelvin scale is useful because it is an absolute scale, where zero reflects the complete absence of thermal energy. This is in contrast to relative temperature scales, where objects are described as hotter or colder than something else. The absolute, thermodynamic temperature of an object provides information on the average kinetic energy of its atoms and molecules.
The Kelvin scale is also useful because it has the same magnitude as the Celsius scale, with a rise of 1 K being equal to a rise of 1 °C. This means that any temperature in degrees Celsius can be converted to kelvin by adding 273.15. For example, the triple point of water is 0.01 °C, which is equal to 273.16 K.
The Kelvin scale is used in electronics as an indicator of how noisy a circuit is in relation to an ultimate noise floor, or noise temperature. It is also used as a measure of the colour temperature of light sources.
Therefore, Kelvin must be used for temperature when applying the ideal gas law, as the ideal gas constant, R, depends on the units chosen for pressure, temperature, and volume.
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SI unit of litres is conventional for volume
The ideal gas law combines pressure, volume, and temperature. The ideal gas constant, R, depends on the units chosen for these variables. It is necessary to use Kelvin for the temperature, and it is conventional to use the SI unit of litres for the volume.
The litre (or liter) is a metric unit of volume. It is equal to 1 cubic decimetre (dm^3), 1000 cubic centimetres (cm^3) or 0.001 cubic metres (m^3). The litre is not an SI unit, but it is accepted by the CGPM (the standards body that defines the SI) for use with the SI. The SI unit of volume is the cubic metre (m^3).
The litre was originally defined as the volume of one kilogram of pure water at maximum density (3.98 °C) and standard pressure. This definition was superseded in 1964, and the litre is now defined as equal in volume to the millistere, an obsolete non-SI metric unit formerly used for dry measure.
Litres are commonly used for items (such as fluids and solids that can be poured) that are measured by the capacity or size of their container. Cubic metres, on the other hand, are more commonly used for items measured by their dimensions or displacements. In colloquial contexts, prefixes such as "centi" (10^-2), "deci" (10^-1), "deca" (10^1), and "hecto" (10^2) are often used with litres. For example, decilitres are common in Croatia, Switzerland, and Scandinavia, while hectolitres are often used for beverages in many European countries.
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Pressure can be measured in kPa, atm, or mm Hg
The ideal gas law combines pressure, volume, and temperature. The ideal gas law equation is PV=nRT, where R is the ideal gas constant. The value of R depends on the units chosen for pressure, temperature, and volume. 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 (kilopascal), atm (atmospheres), or mm Hg (millimeters of mercury).
The value of R will change depending on the units used for pressure. For example, if you are using kPa for pressure, R is equal to 8.315. If you are using atm for pressure, R is approximately 0.0821. By selecting the appropriate value of R for the units you are working with, you can solve for any of the variables in the ideal gas law equation.
PV=nRT
1.21 atm) * V = (4.22 mol) * (0.0821) * (307 K)
V = 113.4 L
Therefore, the volume of the gas is 113.4 liters.
In summary, pressure can be measured in kPa, atm, or mm Hg when using the ideal gas law. The choice of units will depend on the specific problem and the information given. By selecting the appropriate value of R for the chosen units, you can solve for any of the variables in the ideal gas law equation.
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R can be calculated when pressure is measured in kPa
The ideal gas law can be rearranged in the following way, omitting the multiplication signs:
> PV = nRT
Here, R is the ideal gas constant, and its value depends on the units chosen for pressure, temperature, and volume in the ideal gas equation. Kelvin is used for temperature, and the SI unit of liters is used for volume. Pressure is commonly measured in one of three units: kPa, atm, or mm Hg. Therefore, R can have three different values.
To calculate R when pressure is measured in kPa, we can substitute the values for pressure, volume, and temperature into the ideal gas equation. For example, we can use 101.325 kPa for pressure, 22.414 L for volume, and 273.15 K for temperature.
It is important to be consistent with the units used when carrying out gas law calculations. For instance, when pressure is measured in kPa, the volume should be in liters (L) or cubic decimeters (dm^3). This ensures that the value of R remains the same.
Additionally, when calculating kPa, it is crucial to calculate the cross-sectional area perpendicular to the axial component. This involves dividing the axial force by the cross-sectional area.
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Frequently asked questions
The ideal gas law combines pressure, volume, and temperature and is written as PV=nRT, where R is the ideal gas constant.
Yes, kPa is one of the three units commonly used to measure pressure in the ideal gas law. The other two units are atm and mm Hg.
The value of R depends on the units chosen for pressure, temperature, and volume. When pressure is measured in kPa, R is equal to 8.315.
