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The ideal gas law, also known as the general gas equation, is used to calculate pressure, temperature, volume, and the number of molecules or moles in a given volume of gas. The ideal gas law is often written in an empirical form, with R representing the ideal gas constant. The units used for gas law calculations depend on the specific law being applied, but in SI units, pressure (P) is measured in pascals, volume (V) in cubic metres, temperature (T) in kelvins, and the number of moles (n) in moles. The combined gas law, which combines Charles' Law, Boyle's Law, and Gay-Lussac's Law, can be used to derive relationships between pressure, temperature, and volume.
| Characteristics | Values |
|---|---|
| Gas Constant | R |
| Gas Constant Units | atmospheres, moles, and Kelvin |
| SI Units | p (pressure) in pascals, V (volume) in cubic metres, T (temperature) in kelvins, n (moles) |
| R value | 8.314 J/(mol·K) = 1.989 ≈ 2 cal/(mol·K), or 0.0821 L⋅atm/(mol⋅K) |
| Other R values | 8.31 J/mol · K, 6.02214076 x 10^23/mol |
| Boyle's Law | States that the volume of a given amount of gas held at a constant temperature varies inversely with the applied pressure when temperature and mass are constant |
| Charles' Law | Involves the change in either temperature (T2) or volume (V2) from a known starting amount of each (V1 and T1) |
| Avogadro's Law | Gives the relationship between volume and amount of gas in moles when pressure and temperature are held constant |
| Combined Gas Law | Combines all the changeable pieces in the ideal gas law: pressure, temperature, and volume |
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What You'll Learn
Pressure, volume, and temperature
The ideal gas law, also called the general gas equation, is used to describe the state of a hypothetical ideal gas. It is a combination of simpler gas laws, such as Boyle's, Charles's, and Avogadro's laws. The ideal gas law is expressed as PV = nRT, where P represents pressure, V represents volume, n represents the number of moles of gas, T represents temperature, and R is the gas constant.
Pressure
The SI unit for pressure (P) in the ideal gas law is pascals (Pa). However, pressure can also be measured in other units, such as atmospheres (atm) or Torr. For example, when using the value of R as 62.364 L Torr mol-1K-1, the unit for pressure must be Torr. It is important to use consistent units and convert between them when necessary to ensure accurate calculations.
Volume
The SI unit for volume (V) in the ideal gas law is cubic metres (m^3). However, volume can also be expressed in litres (L). When using certain values of R, such as 62.364 L Torr mol-1K-1, the unit for volume must be litres. Consistency in units is crucial, and conversions may be required to ensure compatibility with the chosen value of R.
Temperature
Temperature (T) in the ideal gas law is always measured in Kelvin (K) rather than Celsius (C) or Fahrenheit. This is because the Kelvin scale is an absolute temperature scale, making it suitable for scientific calculations. It is important to note that 0 Kelvin is equal to -273.15 degrees Celsius, representing the lowest possible temperature.
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SI units
The International System of Units, or SI units, is a modern form of measurement that relates the pressure, volume, and temperature of a gas. SI units are used to calculate changes in a gas' properties, such as pressure change, temperature change, volume change, or the number of molecules or moles in a given volume.
In SI units, pressure is measured in pascals, volume in cubic metres, temperature in kelvins, and kB = 1.38×10−23 J⋅K−1. The gas constant, R, is measured in SI units as 8.31 J/mol · K, though other values of R can be used depending on the units of pressure, volume, and temperature. For example, if pressure is measured in atmospheres, R is 0.082057 L atm/mol-K.
When using SI units, it is important to ensure that the units of pressure, volume, number of moles, and temperature match the units of R. For instance, if the first value of R is used, pressure must be in atmospheres, volume in litres, and temperature in kelvin. If the second value of R is used, pressure must be in Torr, volume in litres, and temperature in kelvin.
The ideal gas law, also called the general gas equation, combines Boyle's Law, Charles' Law, Avogadro's Law, and Gay-Lussac's Law. It is used to calculate the properties of an ideal gas, which is a hypothetical gas that does not interact with other molecules and does not take up space. The ideal gas law can be written in two forms: PV = NkT, which involves N, the number of atoms or molecules, and PV = nRT, which involves n, the number of moles.
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Gas constant
The gas constant, also known as the universal gas constant, ideal gas constant, or molar constant, is denoted by the symbol R or R*. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance. The gas constant is defined as the Avogadro constant (NA) multiplied by the Boltzmann constant (k or kB). The SI value of the gas constant is exact and is given as R = 8.314 J/(mol·K) = 1.989 ≈ 2 cal/(mol·K), or 0.0821 L⋅atm/(mol⋅K). The gas constant is expressed in the same unit as molar heat.
The gas constant 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 ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. 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 gas constant is derived from the microscopic kinetic theory, which was independently achieved by August Krönig in 1856 and Rudolf Clausius in 1857.
The ideal gas law is often written in an empirical form: PV=nRT, where P is the absolute pressure, V is the volume of gas, n is the amount of substance, and T is the thermodynamic 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, with the SI unit being the Kelvin. In SI units, p is measured in pascals, V in cubic meters, T in Kelvins, and kB = 1.38×10−23 J⋅K−1.
The specific gas constant of a gas or mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture. The specific gas constant can also be related to the Boltzmann constant by dividing the Boltzmann constant by the molecular mass of the gas. The physical significance of R is work per mole per kelvin, and it can be expressed in any set of units representing work or energy.
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Charles' Law, Boyle's Law, and Avogadro's Law
Gas laws have been used since the early 17th century to help scientists find volumes, amounts, pressures, and temperatures of gases. The three primary gas laws are Charles' Law, Boyles' Law, and Avogadro's Law. These laws combine to form the General Gas Equation and the Ideal Gas Law.
Charles' Law
Charles' Law states that the volume of a gas is directly proportional to its temperature (in kelvins) at constant pressure. Calculations using Charles' Law involve the change in either temperature (T2) or volume (V2) from a known starting amount of each (V1 and T1). Charles' Law can be used to determine the current pressure or volume of a gas, as long as the initial states and one of the changes are known.
Boyles' Law
Boyles' Law states that the volume of a given amount of gas is inversely proportional to the applied pressure when the temperature and mass are constant. The law can be used to determine the current pressure or volume of a gas, as long as the initial states and one of the changes are known.
Avogadro's Law
Avogadro's Law gives the relationship between volume and the amount of gas in moles when pressure and temperature are held constant. In 1811, Avogadro postulated that, at the same temperature and pressure, equal volumes of gases contain the same number of gaseous particles.
Units for Gas Law Calculations
The ideal gas law, or general gas equation, is the equation of state of a hypothetical ideal gas. The modern form of the equation relates pressure, volume, and temperature in two main forms. In SI units, p (pressure) is measured in pascals, V (volume) is measured in cubic meters, n (number of moles) is measured in moles, and T (temperature) is measured in kelvins.
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Converting units
When performing calculations involving gas laws, it is essential to use consistent units and convert values to the appropriate units if necessary. Gas law calculations often involve temperature, pressure, volume, and the number of moles or molecules of gas.
Temperature Units
Temperature in the gas law equations is always given in Kelvin (K). If you have a temperature in degrees Celsius (°C), you must convert it to Kelvin using the equation: K = °C + 273.15. For example, if you have a temperature of 25°C, you would add 273.15 to get 298.15 K.
Pressure Units
Pressure can be given in various units, such as atmospheres (atm), pascals (Pa), or Torr. When using the ideal gas law equation, the choice of pressure units will determine the value of the gas constant, R, that you should use. For example, if your pressure is in atm, you would use a value of R of 0.082057 L atm/mol-K, whereas if your pressure is in Torr, you would use a value of R of 62.364 L Torr/mol-K.
Volume Units
Volume can be given in different units, such as litres (L) or cubic metres (m^3). When using the ideal gas law equation, ensure that your volume units are consistent with the chosen pressure units and the value of R. For example, if your pressure is in atm and R is in L atm/mol-K, your volume should be in litres.
Moles and Molecules
The amount of gas can be specified in terms of the number of moles (n) or the number of molecules (N). Avogadro's number, which is approximately 6.022 x 10^23 molecules/mol, can be used to convert between the number of molecules and the number of moles.
In summary, when performing gas law calculations, it is important to identify the units of each quantity involved and ensure they are consistent with the chosen form of the gas law equation and the value of the gas constant, R. Converting units appropriately is crucial to obtaining accurate results.
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Frequently asked questions
The SI unit for temperature in gas law calculations is Kelvin.
Gas law calculations also involve pressure, volume, and the number of molecules or moles in a given volume. Pressure is measured in pascals, volume in cubic metres, and the number of molecules in moles.
The ideal gas law, also known as the general gas equation, is an equation that describes the state of a hypothetical ideal gas. It is a good approximation of how many gases behave under various conditions.
