1

### JEE Main 2016 (Online) 10th April Morning Slot

Initially, the root mean square (rms) velocity of N2 molecules at certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :
A
u/2
B
2u
C
4u
D
14u
2

### JEE Main 2017 (Online) 8th April Morning Slot

Among the following, the incorrect statement is :
A
At low pressure, real gases show ideal behaviour.
B
At very low temperature, real gases show ideal behaviour.
C
At very large volume, real gases show ideal behaviour.
D
At Boyle’s temperature, real gases show ideal behaviour.

## Explanation

A real gas do not show ideal behaviour at low temperature, high pressure and low volume.

So according to the question, at low temperature real gas show ideal behaviour. This statement is wrong.
3

### JEE Main 2017 (Online) 9th April Morning Slot

At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen (N2 ) at 4 bar. The molar mass of gaseous molecule is :
A
28 g mol$-$1
B
56 g mol$-$1
C
112 g mol$-$1
D
224 g mol$-$1

## Explanation

Density = ${{Mass} \over {Volume}}$

PV = RT $\Rightarrow$ V = ${{RT} \over P}$

So, Density(d) = ${{MP} \over {RT}}$

Now, d1 = x, P1 = 4, M1 = 28, d2 = 2x, P2 = 2, M2 = ?

$\therefore$ ${{{d_1}} \over {{d_2}}} = {{{M_1}{P_1}} \over {R{T_1}}} \times {{R{T_2}} \over {{M_2}{P_2}}} = {{{M_1}{P_1}} \over {{M_2}{P_2}}}$ [As T1 = T2 ]

$\Rightarrow$ M2 = ${{{M_1}{P_1}{d_2}} \over {{d_1}{P_2}}}$

= ${{2x \times 28 \times 4} \over {2 \times x}}$ = 112 g mol-1
4

### JEE Main 2018 (Online) 16th April Morning Slot

Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl = 35.5 u)
A
1.46
B
0.46
C
1.64
D
0.64

## Explanation

We know, PV = nRT

n = no. of moles = ${m \over M}$

So,   PV = ${m \over M}RT$

$\Rightarrow $$\,\,\,\, P = {m \over V} \times {{RT} \over M} \Rightarrow$$\,\,\,\,$ P = d $\times$ ${{RT} \over M}$ [ d = density = ${m \over V}$ ]

at constant temperature and pressure d $\propto$ M

Now let d1 and d2 are the density of ammonia and HCl.

$\therefore\,\,\,\,$ ${{{d_1}} \over {{d_2}}} = {{{M_{N{H_3}}}} \over {{M_{HCl}}}}$

$\Rightarrow$ $\,\,\,\,$ ${{{d_1}} \over {{d_2}}}$ = ${{17} \over {36.5}}$ = 0.46