### JEE Mains Previous Years Questions with Solutions

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1

### JEE Main 2014 (Offline)

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:
A
Z = 1 + $RT \over Pb$
B
Z = 1 - $a \over VRT$
C
Z = 1 - $Pb \over RT$
D
Z = 1 + $Pb \over RT$

## Explanation

Compressibility factor $\left( Z \right) = {{PV} \over {RT}}$

(For one mole of real gas)

van der Waals equation

$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$

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.$\,\,\,V - b \approx V$

$\left( {P + {a \over {{V^2}}}} \right)V = RT;$

$PV + {a \over V} = RT$

$PV = RT - {a \over V};$

${{PV} \over {RT}} = 1 - {a \over {VRT}}$

Hence, $\,\,\,z = 1 - {a \over {VRT}}$
2

### JEE Main 2013 (Offline)

For gaseous state, if most probable speed is denoted by C*, average speed by $\mathop C\limits^{\_\_}$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:
A
C*: $\mathop C\limits^{\_\_}$ : C = 1.128 : 1.225 : 1
B
C*: $\mathop C\limits^{\_\_}$ : C = 1.225 : 1.128 : 1
C
C*: $\mathop C\limits^{\_\_}$ : C = 1 : 1.225 : 1.128
D
C*: $\mathop C\limits^{\_\_}$ : C = 1 : 1.128 : 1.225

## Explanation

Most probable speed $\left( {{C^ * }} \right) = \sqrt {{{2RT} \over M}}$

Average Speed $\left( {\overline C } \right) = \sqrt {{{8RT} \over {\pi M}}}$

Root mean square velocity $\left( c \right) = \sqrt {{{3RT} \over M}}$

${C^ * }:\overline C :C = \sqrt {{{2RT} \over M}} :\sqrt {{{8RT} \over {\pi M}}} :\sqrt {{{3RT} \over M}}$

$= 1:\sqrt {{4 \over \pi }} :\sqrt {{3 \over 2}}$

$= 1:1.128:1.225$
3

### AIEEE 2012

The compressibility factor for a real gas at high pressure is :
A
1 + RT/pb
B
1
C
1 + pb/RT
D
1–pb/RT

## Explanation

$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT\,\,$

at high pressure ${a \over {{V^2}}}$ can be neglected

$PV - Pb = RT\,\,\,$

and $\,\,\,PV = RT + Pb$

${{PV} \over {RT}} = 1 + {{Pb} \over {RT}}$

$z = 1 + {{Pb} \over {RT}};Z > 1\,\,\,$ at high pressure
4

### AIEEE 2011

'a’ and `b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because
A
a and b for Cl2 < a and b for C2H6
B
a and b for Cl2 > a and b for C2H6
C
a for Cl2 > a for C2H6 and b Cl2 < b for C2H6
D
a for Cl2 < a for C2H6 and b Cl2 > b for C2H6

## Explanation

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 inter-molecular 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 $C{{\rm l}_2}$ $''a'''$ should be greater than for ${C_2}{H_6}$ but for it $b$ should be less than for ${C_2}{H_6}.$