General Gas Equation

by • 10/09/2013 • GeneralComments (0)518

General Gas Equation

An equation formed by the combination of Boyle’s Charles law and Avogadro’s law is called “General Gas Equation”. It is also called Equation of state.

An equation which represents the properties of gases like pressure, Temperature, volume and moles collectively present is called “General Gas Equation”.

 

Derivation:

According to Boyle’s Law:

V ∞

1

                ——- (1) at constant temp

P

 

According to Charle’s Law:

V  ∞  T

                ——- (2) at constant pressure

 

According to Avogadro’s Law:

V  ∞  n

                ——- (2) at constant pressure and temp

 

By comparing eq (1), (2) and (3)

V ∞

nT

                ——- (1) at constant temp

P

V  =

Constant nT  
P  

PV =

RnT

PV =

nRT

 

Here R is constant of proportionality and called “General Gas Constant”

 

Value of General Gas Constant

i.             When Pressure is in atom and volume is in dm3 at STP DATA, AS STP

P = 1 atm

T = 273 K

N = 1 mol

V = 1 mol

V = 22.41 dm3

R = ?

Since according to general gas equation

Formula                               PV = NRT                              or            nRT = PV

  =

(1 atm) x (22.41 dm3)

 

(1 mol) x (273 K)

 

 

  =

22.41 atm.dm3

 

273 mol.K

 

 

  = 0.821

atm.dm3

mol.K

 

ii.            In MKS System and at STP

DATA

P = 101300 N/m2

T = 273

n = 1 mol

V = 22.4 dm3 + 1000

V = 0.0224 m3

R = ?

 

FORMULA:

PV =

nRT

nRT =

PV

R =

PV

nT

=

(101300 N/m2) x (0.0224 m3)

(1 mol) x (273 K)

=

22.69.12

N/m2.m3

273

=

8.314 N.m/mole.K

R =

8.314J/mol.K

 

 

General Form of General Gas Equation:

Consider a gas with initial volume V1,  present P1 and temperature T1, while the final volume of gas is v2, pressure is P2 and the temperature T2.

Initial State:

 

 

This is called general form of general gas equation.

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