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The gas constant, represented by the symbol “R”, is the constant of proportionality of the ideal gas law . The latter is a mathematical equation that relates the four variables that completely define the state of an ideal gas, that is, pressure , volume , temperature, and number of moles . Furthermore, this law is a combination of all the gas laws, including Boyle’s law, both forms of Charles and Gay-Lussac’s law , and Avogadro’s law.
Among its many uses, the gas constant allows one to calculate the particular value of P, V, not T for a gas for any combination of the other three variables, without needing to know what the state of the gas was before, or how the gas came to be. gas to its current state.
R, in addition to receiving the name “gas constant”, is also known as the universal gas constant, ideal gas constant and molar gas constant, the latter due to its units.
Despite being called the “gas” constant, stemming from the experiments that led to its original discovery, the constant R is, in fact, one of the fundamental constants of nature, and is of great importance both in chemistry like in physics. For this reason, it constantly appears in multiple laws and equations that, in principle, have nothing to do with gases.
Units and value of R
Like any constant of proportionality that is dimensional, the value of the gas constant depends on the units in which it is expressed. The same is true of almost all other constants in science, since any physical quantity can always be expressed in different units, as convenient.
Generally speaking, the dimensions of the constant R are expressed in two different ways in most of its applications:
That is, units of energy divided by number of moles and units of absolute temperature, or:
That is, units of pressure multiplied by units of volume, divided by moles and absolute temperature units.
That being said, the following table presents the values of R in the units most frequently used by chemists, as well as the context in which each value is used:
| R value in different units | Common use |
| R= 0.08206 atm.L.mol -1 K -1 | Calculations with the ideal gas equation and osmotic pressure calculations. |
| R= 0.08314 bar.L. mole -1 K -1 | Calculations with the ideal gas equation using the pressure in bar. |
| R=62.3637 Torr.L. mole -1 K -1 | Calculations with the ideal gas equation using the pressure in Torr or mmHg. |
| R= 8,314 J. mol -1 K -1 | Thermodynamic calculations, including the use of the Nernst equation. |
| R= 1,987 cal.mol -1 K -1 | Thermodynamic calculations, not including the use of the Nernst equation. |
| R= 8,314 kg.m 2 .s -2 .mol -1 K -1 | Root mean square velocity calculations and ideal gas law calculations using the MKS system. |
There are other values when using imperial units of measurement or technical units, but these apply more to engineering than to chemistry.
The ideal gas law
As mentioned above, the gas constant first appears as the constant of proportionality in the ideal gas law . This law is given by the following mathematical expression:
In this equation, P represents the pressure, V the volume, n the number of moles, and T the absolute temperature. Depending on the units used for P, V, T and n, the correct value of R must be used. Otherwise, it will be necessary to perform a unit transformation prior to the calculation being performed.
The gas constant and the average kinetic energy of an ideal gas
Using the kinetic model of gases, a very interesting relationship can be obtained between the gas constant and the root mean square velocity, or the mean kinetic energy of the particles of a gas. This model considers a gas as a series of hard spheres with a well-defined mass, but of negligible size and that only interact with each other and with the walls of the container through elastic collisions (like billiard balls). Using these conditions, a bit of physics and a bit of statistics, the following relationship can be arrived at:
where M is the molar mass of the gas, T is the temperature, and <v 2 > is the root mean square velocity. As the molar mass M=m/n and (1/2).m. <v 2 > equals the average kinetic energy of the gas particles, R could be viewed as the ratio of the average kinetic energy of a mole of particles to temperature. In other words, R is the constant of proportionality that allows defining the absolute temperature in terms of the thermal agitation of the atoms and molecules.
The Nernst equation and the gas constant
The Nernst equation is a thermodynamic equation that allows the determination of the electromotive force (E) of an electrochemical cell under non-standard conditions from the cell potential under standard conditions (Eº), the temperature and the concentrations of the chemical species involved in an electrochemical cell. Redox reaction. The equation is the following:
In this equation, E and Eº are the cell potentials under non-standard and standard conditions, respectively, T is the absolute temperature, n the number of moles of electrons exchanged per mole of reaction, F is Faraday’s constant, and Q is the reaction quotient. The latter corresponds to the product of the concentrations of the reaction products raised to their respective stoichiometric coefficients divided by the product of the concentrations of the reaction reactants raised to their respective stoichiometric coefficients.
When using this equation, R must be given in Jouls.K -1 mol -1 so that the result of the second term on the right hand side of is in volts, and thus can be subtracted with the standard potential of the cell.
Gas constant and Boltzmann constant
The Boltzmann constant is a universal constant that appears in the formula for the Boltzmann distribution, as well as in the well-known Boltzmann formula. The first allows us to determine the number of molecules that can have a given energy level at a given temperature. The second provides the interpretation of entropy as a measure of disorder in a system.
Both equations have profound implications in both chemistry and physics. Well, it turns out that Boltzmann’s constant is nothing more than the same universal gas constant, only divided by Avogadro’s number, which changes its units from energy.K -1 .mol -1 to energy.K -1 . particle -1 .
In essence, the Boltzmann constant and the gas constant represent exactly the same thing, just on different scales.
References
The Ideal Gas Law. (2020, August 15). Retrieved from https://chem.libretexts.org/@go/page/1522
Engineering ToolBox, (2004). Universal and Individual Gas Constants . Retrieved from https://www.engineeringtoolbox.com/individual-universal-gas-constant-d_588.html
The fundamental physical constants. (2021, March 30). Retrieved from https://espanol.libretexts.org/@go/page/1989
Pressure, volume, quantity, and temperature related: the ideal gas law. (2020, October 30). Retrieved from https://espanol.libretexts.org/@go/page/1869
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