Gas Constant

Gas Constant Value

The gas constant R also known as universal, molar or ideal gas constant is found in many contexts. 

It relates energy and temperature.

It is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole i.e., the pressure–volume, PV ,where energy is a product of pressure and volume.

In physics, the gas constant is a proportionality constant.

It relates the energy scale  to the temperature scale, where a mole of particles at a given temperature is being considered.

The gas constant R is defined as the product of Avagadro’s number and the Boltzmann’s constant K given by,

                   R = Na x K

The value of R in typical energy units of Joules is calculated by taking exact numerical values of K and Na, expressed in SI units is,

        R = 8.314 J /mol.K      

Gas Constant R Value

The value of gas constant R is calculated by taking P at pascal or  N/m^2, V at m^3, T in K and n in mol.

Where P is the pressure in Pa = 1.01325 x 105 Pa or N/m^2

            V = 22.4 L at STP 

Where V is the Molar volume of a gas at standard temperature and pressure.

                   = 22.4 x 10-3 m3

                T = 273 K

                 n  =1

Using ideal gas law: PV = nRT

(Images to be added soon)

 R = PV/ nT =  1.01325 x 105 N/m2 x  22.4 x 10-3m3/1 mol x 273 K

1.01325 x 105 N.m x  22.4 x 10-3/1 mol x 273 K

Cancelling out common terms we get 1 N-m = 1 Joule

                1.01325 x 105 x  22.4 x 10-3 J/1 mol x 273 K

On solving we get the value of gas constant R in SI unit     

   R = 0.083138 x 102 J/mol.K 〜 8.314 J/mol.K….(1)           

Gas Constant In Calories

Since the value of 1 Calorie = 4.2 Joule

If  4.2 J = 1 calorie

Then, 1 J = 1/ 4.2 calories

Putting it in eq(1), we get,          

 R = 8.314/ 4.2  cal.mol-1 K-1

On solving we get,       

R  =1.975 Cal mol-1 K-1          

Gas constant has various units corresponding to their values that is given below in tabular form:

Gas Constant Units

Universal Gas Constant

The universal constant is an ideal gas constant that we use to quantify the relationship between the properties of a gas.  

The constant is symbolized as ‘R.’

Typically, R relates the pressure in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K).          

In this case, it has the value and units of:         

     R = 0.08206 L. atm / mol.K

R is same for all the gases.     

Unit Of Universal Gas Constant

 Let’s find out the value of R by using the ideal gas law:

              PV = nRT

R  =  PV/nT   

Unit of each quantity

P = Pressure and its unit is atm 

V = Volume, unit =  L

n  = no of moles and unit is mol

T = Temperature in kelvin

 =   L.atm/  mol x K

 Unit of universal gas constant R   = L.atm/ mol.K                    

The dimensional formula for universal gas constant = [ML2T-2K-1]

Universal Gas Constant R Value

Taking n = 1

T = 273 K

P = 1 atm (atmospheric pressure)

V = 22.4 L at STP  

Using ideal gas law equation and putting the values, we get

       R = PV/nT

            = 1 atmx 22.4  L/ 1 mol x 273 K

On solving we get the value of universal gas constant R in SI unit as:

 R = 0.08206 atm L/ mol.K