# Value of R in Atm

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The gas constant or ideal gas constant or molar constant is an important physical constant used in most of the fundamental equations of thermodynamics, kinetic theory of gases, etc., and is denoted by the letter “R”. In Physics, the ideal gas constant R is defined as -Work done by the gas (or on the gas) per unit mole per unit temperature change. Though the ideal gas constant R is a constant value it can be expressed in various unit systems.

## Value of Gas Constant

From the ideal gas expression we have,

PV = nRT…….(1)

Where,

P - Pressure of the ideal gas

V - Volume of the ideal gas

n - Number of moles

R - The universal gas constant

T - Temperature

On rearranging the above equation for R we get,

R = PV/nT …….(2)

This is the gas constant formula.

From equation (2) the unit of gas constant R is given by,

⇒ R = (N/m²) x (m³)/(mol) x (K)

⇒ R = N m/mol x K

⇒ R = joule/mol x K (∵ Newton-meter = Joule)

Therefore, the unit of gas constant R is Joule/mol-K or J mol$^{-1}$K$^{-1}$.

The value of R at atm i.e., at STP (standard temperature and pressure) is calculated as follows.

At STP, for 1 mole of gas (n=1mol), the value of temperature is 273K, pressure is 1.01 x 10$^{5}$ N/m$^{2}$ , and volume is 22.4 x 10$^{-3}$m$^{3}$.

Substituting these values in equation (2) and simplifying, we get the value of the gas constant,

R = 8.31 J mol$^{-1}$ K$^{-1}$

Therefore, the value of R is J mol$^{-1}$ K$^{-1}$.

### Value of R:

The value of R can be expressed in various unit systems according to the need for calculation. For example, if you want to use the value of the gas constant in calories then, we know that 4.184 joules are equal to 1 calorie, then the value of R is,

R = 8.31/4.184 Cal mol$^{-1}$ K$^{-1}$ = 1.98 Cal mol$^{-1}$ K$^{-1}$

Similarly, we can express the value of gas constant R, in many units as given in the table below.

 Value of R Units of R in various systems 8.31 J mol⁻¹K⁻¹ 1.98 Cal mol⁻¹ K⁻¹ 8.31 m³(Pa)mol⁻¹K⁻¹ 0.0821 L(atm) mol⁻¹K⁻¹ 62.36 L(torr) mol⁻¹K⁻¹ 1.98 x 10⁻³ k Cal mol⁻¹K⁻¹

### Examples:

1: Calculate the Value of R in ergs mol⁻¹K⁻¹.

Ans: We know that value of R = 8.31 J mol⁻¹K⁻¹,

Now, substituting 1J = 10⁷ergs

R = 8.31 x 10⁷ergs mol⁻¹K⁻¹.

Therefore, the value of R in the CGS system.

2: Calculate the Value of R in L(atm) mol⁻¹K⁻¹.

Ans: From ideal gas equation we know that,

⇒ R = PV/nT

For n=1mol at STP, P=1atm, T=273K, and V=22.4L

Substituting the above values in equation of R,

⇒ R = 1atm x 22.4 L/1mol x 243 K

⇒ R = 0.0821 L(atm) mol⁻¹K⁻¹ is the required answer.

### Did You Know?

• The value of R will be changing as the pressure and volume of the system is varied. Choose the appropriate value of R depending upon which measuring system is being referred to.

• The ideal condition is used to arrive at the value of R at different conditions.