What is gas constant R in PV =n RT: What is R [specific vs R [universal]?

R fundamentally refers to kinetic energy in gas, whether R [specific] or R [universal].

The problem arises when you wonder why there are two gas constants. The answer is that R [specific] is an ideal gas property, whereas R [universal] is a constant for all ideal gases in the universe.

The next point of contention is where to use R [specific] and where to use R [universal].

This post will attempt to clarify some of these issues.

The state equation for a hypothetical ideal gas is PV=n RT. The ideal gas law describes the behavior of an ideal gas sample and how that behavior is related to the gas sample's pressure (P), temperature (T), volume (V), and molarity (n). The term "R" in the equation PV=n RT stands for the universal gas constant.

R = PV/ nT

The universal gas constant is a proportionality constant that relates the kinetic energy of a sample of gas to its temperature and molarity. It is also known as the ideal gas constant or the molar gas constant. The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB):

?R=NA x kB.

Since the 2019 redefinition of SI base units, both NA and k are defined with exact numerical values when expressed in SI units. As a consequence, the SI value of the molar gas constant is exactly 8.314 J?K?1?mol?1.

The joule per mol-kelvin is the unit for the gas constant. This is written as "work per mol per degree." The gas constant, in essence, relates the molar amount of gas and the temperature of the gas to the amount of kinetic energy.

R = PV / n T = Work / (Amount × Temperature)

Universal gas constant vs specific gas constant

When n = moles, R is the universal gas constant. Because n is a number 6.022 × 10^23 atoms (Avogadro number) which is constant for all ideal gases in the universe

When n = mass, R is called the specific gas constant. Each gas has its own specific gas constant.

What is the significance of RT?

RT = work / per unit amount

The amount can be in moles. The amount can also be in mass

When n is in moles, and R is a universal gas constant RT means 1 mole of any ideal gas in the universe will do RT amount of work

When n is mass and R is specific gas constant RT means the amount of work specific to that gas per unit mass. Each gas has a different capacity to produce work on a mass basis

Specific gas constant and universal both signify work.

Where should one use R [specific]

R specific is a property of a gas, Cp-Cv = R

This table has a lot of good data for gases. Refer to column 4 you will notice each gas has its unique gas constant expressed as KJ/kg-k. This is [Cp-Cv], a property of a particular gas. [Cp-Cv] is a property of a gas.?It tells that Cp exceeds Cv by an amount equivalent to R specific which is different for each gas. The reason is specific heat is specific to the atomicity of a gas.

Be careful

If you use molar-specific heat since for an ideal gas 1-mole gas same number of atoms all ideal gases relate to the same kinetic energy which is the universal gas constant.

Look at the table below. You will notice Cp- Cv = R in terms of the universal gas constant in J/mole-k it is by and large the same 8.33 J/mole-k. You cannot probe a gas to find its kinetic energy.?

Derivation of Gas Constant, R

Let us take any gas:?

1 mole?of Argon = 39.948 g Ar =?22.4 l?Ar @ STP

?STP = Standard temperature (0 degc or?273.15 K) & standard pressure = 1 atmosphere

Assume the gas acts ideally.?Then PV = nRT

Solve for R:??R = PV/n T = [1 atm] x [22.4 lit] / [1 mol] x 273.15 k] = 0.0821 atm-liter/ mol-k

Credit: Google