Gas Constant

When written as R, the molar gas constant (also known as the Gas Constant, Universal Gas Constant or Ideal Gas Constant) denotes the amount of gas present in a given volume of space. It is the molar equivalent of the Boltzmann constant, but it is expressed in units of energy per temperature increment per mole, rather than energy per temperature increment per particle, i.e. the pressure-volume product, rather than the Boltzmann constant. It is also made up of the constants from Boyle’s law, Charles law, Avogadro’s law and Gay Lussac’s law. There are many fundamental equations in the physical sciences that contain the physical constant, such as the ideal gas law, the Arrhenius equation and the Nernst equation, which all contain the physical constant.

Gas Constant

The gas constant is a constant of proportionality in physics that connects the energy scale in physics to the temperature scale and the scale used to measure the amount of substance in a given quantity of time. The gas constant’s value is ultimately derived from historical decisions and accidents involving the definition of units of energy, temperature and amount of substance in a given volume of space. The Boltzmann constant and the Avogadro constant, which separately relate energy to temperature and particle count to the amount of substance, were also determined in a similar manner to each other.

Gas Constant R is defined as the product of the Avogadro constant NA and the Boltzmann constant k (also known as the Boltzmann constant).

R = NAk.

The SI base units have been redefined in 2019, and both NA and k are defined with precise numerical values when expressed in SI units. It follows as a natural consequence that the SI value of the molar gas constant is precisely 8.31446261815324 J⋅K−1⋅mol−1.

History

There has been some discussion about whether it would be appropriate to designate the symbol R as the Regnault constant in honour of the French chemist Henri Victor Regnault, whose precise experimental data were used to calculate the initial value of the constant. However, the exact origin of the letter R as a symbol for the constant has remained a mystery

It appears that Clausius’ students, A.F. Horstmann and Dmitri Mendeleev, independently discovered the universal gas constant on September 12, 1874 and published their findings the following day. As a result of his extensive measurements of the properties of gases, Mendeleev was also able to calculate it with high precision, to within 0.3 per cent of the current value.

The ideal gas law contains the following expression for the gas constant:

PV = nRT = mRspecificT

In this equation, P denotes the absolute pressure (in SI unit pascals), V denotes the volume of gas (in SI unit cubic metres), n denotes the amount of gas (in SI unit molecules), m denotes the mass (in SI unit kilogrammes) contained within V and T denotes the thermodynamic pressure (SI unit kelvins). RSpecific is the gas constant that is specific to a given mass. As with molar entropy and molecular heat capacity, the gas constant is expressed in the same units as the other two quantities(molar entropy and molar heat capacity).

Dimensions

From the ideal gas law PV = nRT we get:

R = [PV/nT]

The variables P and V represent pressure and volume, respectively and the variables n and T represent the number of moles of a given substance.

Due to the fact that pressure is defined as force per unit area of measurement, the gas equation can also be expressed as:

R = [ (force/area)*volume / (amount * temperature) ]

Area and volume are represented by the numbers (length)2 and (length)3 respectively. Therefore:

R = [ (force*length) / (amount * temperature) ]

Since force × length = work:

R = [ work / (amount * temperature) ]

Working time per degree per mole is the physical significance of the symbol R. There are many different ways to express it, including using any set of units representing work or energy (such as joules), units representing degrees of temperature on an absolute scale (such as Kelvin or Rankine) and any system of units designating a mole or a similar pure number that allows an equation of macroscopic mass and fundamental particle numbers in a system (such as an ideal gas).

Instead of using the unit of a mole, the constant can be expressed using the unit of a normal cubic metre.

Alternatively, we can say the following:

Force = [ mass * length / ( time )2 ]

As a result, we can write R as follows:

R = [ mass * length2 / amount * temperature * time2 ]

As a result, in SI base units, we have:

R = 8.314462618… kg⋅m2⋅s−2⋅K−1⋅mol−1.

Relationship between the Boltzmann constant and other variables

The Boltzmann constant kB (alternatively k) may be substituted for the molar gas constant by working in pure particle count, N, rather than the amount of substance, n, because the Boltzmann constant is proportional to the amount of substance.

R = NAkB 

The Avogadro constant is denoted by the letter NA. According to the Boltzmann constant, the ideal gas law, for example, has the formula

PV = NkBT 

where N is the number of particles (molecules in this case) or to generalise to an inhomogeneous system, the local form holds: where N is the number of particles (molecules in this case).

Specific gas constant

This value is given by the molar gas constant divided by the molar mass of the gas or mixture of gases (Rspecific), which is the specific gas constant of the gas or mixture.

Rspecific  = R / M 

The specific gas constant can be calculated by dividing the Boltzmann constant by the molecular mass of the gas, just as the ideal gas constant can be calculated by dividing the Boltzmann constant by the ideal gas constant.

Rspecific = kB / m

Thermodynamics also provides an important relationship to consider. According to Mayer’s relation, the specific gas constant is proportional to the specific heat capacities of calorically perfect gas and a thermally perfect gas, respectively.

Rspecific = cP – cv

in which cp denotes the specific heat capacity at constant pressure and cv denotes the specific heat capacity at constant volume.

The specific gas constant is commonly represented by the symbol R, which is especially common in engineering applications. As a result, the universal gas constant is usually denoted by a different symbol, Ř such as the symbol, in order to distinguish it. However, the context and/or units used to express a particular gas constant should be clear enough to indicate whether the universal or specific gas constants are being referenced.

Conclusion

In chemistry and physics equations, the symbol “R” is commonly used to represent the gas constant, also known as the molar gas constant, the ideal gas constant or the universal gas constant. It is a proportionality factor that is used in several equations to connect energy scales and temperature scales together. When it comes to energy per temperature per mole, the gas constant is equivalent to the Boltzmann constant; the only difference is that the gas constant is expressed in units of energy per temperature per mole, whereas the Boltzmann constant is expressed in units of energy per temperature per particle. From a physical standpoint, the gas constant is a proportionality constant that, for a mole of particles at a given temperature, relates the energy scale to the temperature scale.