### Ideal Gas Equation

##
**Ideal Gas
Equation**

The three laws which we have learnt
till now can be combined together in a single equation which is known as ideal
gas equation.

At constant T and n; V ∝ 1/

*p***Boyle’s Law**
At constant p and n; V ∝ T

**Charles’ Law**
At constant p and T; V ∝

*n***Avogadro Law**

Thus,

Where R is proportionality constant.
On rearranging the equation we obtained

R is called gas constant. It is same
for all gases. Therefore it is also called

**Universal Gas Constant**. Equation is called**ideal gas equation**.
Above Equation shows that the value of R
depends upon units in which

*p*, V and T are measured. If three variables in this equation are known, fourth can be calculated. From this equation we can see that at constant temperature and pressure*n*moles of any gas will have the same volume because
and

*n*, R, T and p are constant. This equation will be applicable to any gas, under those conditions when behavior of the gas approaches ideal behavior. Volume of one mole of an ideal gas under STP conditions (273.15 K and 1 bar pressure) is 22.710981 L mol^{-1}.
At
STP conditions used earlier (0 C and 1 atm pressure). Value of R is
8.20578 10

^{-2 }L atm K^{-1}mol^{-1}.
Ideal gas
equation is a relation between four variables and it describes the state of any
gas, therefore, it is also called

**equation of state**.
Let us now
go back to the ideal gas equation. This is the relationship for the
simultaneous variation of the variables. If temperature, volume and pressure of
a fixed amount of gas vary from T

_{1}, V_{1}and*p*_{1 }to T_{2}, V_{2}and*p*_{2}then we can write
The above
said equation is a very useful equation. If out of six, values of five
variables are known, the value of unknown variable can be calculated from the
above equation. This equation is also known as

**Combined gas law**.
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