Ideal Gas Equation - Practice Questions & MCQ

• Ideal gas equation-

 The equation which relates the pressure (P), volume (V) and temperature (T) of the given state of an ideal gas is known as an ideal gas equation or equation of state.

From Boyle's law, we get

$V\propto \frac{1}{P}$

and From Charle's Law, we get $V\propto T$.
And from Avogadro's Law, we get $V\propto n$
And from equation (1), (2), (3)
we can write

$\begin{array}{rl}& V\propto \frac{nT}{P}\\ & \text{ or }\frac{PV}{nT}=\text{ constant }\\ & \text{ or }\frac{PV}{nT}=R(\text{ where }R\text{ is proportionality constant })\\ & \text{ or }PV=nRT\end{array}$

So Ideal Gas Equation is given as

$PV=nRT$
 

where 

T= Temperature

P= pressure of ideal gas

V= volume

n= numbers of mole

R = universal gas constant

• Universal gas constant (R)-

           At S.T.P. the value of the universal gas constant is the same for all gases.

          And its value is given as 

$R=8.31\frac{\text{ Joule }}{\text{ mole }\times \text{ Kelvin }}=2\frac{\mathrm{cal}}{\text{ mole }\times \text{ Kelvin }}$

And its Dimension is : $\left[M{L}^2{T}^{-2}{\theta }^{-1}\right]$
- Boltzman's constant (k)-

It is represented by per mole gas constant.

$\text{ i.e }k=\frac{R}{N}=\frac{8.31}{6.023\times {10}^{23}}=1.38\times {10}^{-23}\mathrm{J}/\mathrm{K}$

- Specific gas constant (r)-

It is represented by per gram gas constant.
i.e. $r=\frac{R}{M}$

It's unit is $\frac{\text{ Joule }}{\mathrm{gm}\times \text{ kelvin }}$