Test: JEE Main 35 Year PYQs- States of Matter - JEE MCQ

PV = nRT (number of moles = n/V) ∴ n/V = P/RT..

Value of gas constant ( R ) = 0.0821L atm K^–1 mol^–1          
= 8.314 × 10⁷ ergs K^–1mol^–1          
= 8.314JK^–1mol^–1  = 1.987 cal K^–1 mol^–1

Kinetic theory of gases proves all the given gas laws.

ln between two successive collisions, no force is acting on the gas molecules. Resultantly they travel with uniform velocity during this interval and hence, moves along a straight line.

In van der waals  equation ‘b’ is for volume correction

Distribution of molecular velocities at two different temperature is given shown below.

NOTE : At higher temperature more molecules have higher velocities and less molecules have lower velocities.
As  evident from fig. thus it is clear that With the increase in temperature the most probable velocity increase butthe fraction of such molecules decreases.

From the ideal gas equation :

PV = nRT or n =  = 1.27 × 10^–3

The value of a is a measure of the magnitude of the attractive forces between the molecules of the gas.
Greater the  value of ‘a’, larger is the attractive intermolecular force between the gas molecules.
The value of b related to the effective size of the gas molecules. It is also termed as excluded volume.
The gases with higher value of a and lower value of b are more liquefiable, hence for Cl₂ “a” should be greater than for C₂H₆ but for it b should be less than for C₂H₆.

 = RT at high pressure  can be

neglected

PV – Pb = RT    and  PV = RT + Pb

Z > 1 at high pressure

Most probable speed  

Average Speed 

Root mean square velocity (c)

 = 1 :1.128 : 1.225

Compressibility factor (Z) = 

(For one mole of real gas) van der Waals equation

At low pressure, volume is very large and hence correction term b can be neglected in comparison to very large volume of V.

i.e. 

Hence, 

Number of moles of O₂

Number of moles of  

∴ Ratio =  = 7 : 32

Hydrogen bond is a type of strong electrostatic dipole-dipole interaction and dependent on the inverse cube of distance between the molecular ion-dipole interaction

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant. i.e V ∝ n Hence in the given case.
Initial  moles  and  final  moles  are  equal (n_T)_i = (n_T)_f