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1

### JEE Main 2021 (Online) 27th August Morning Shift

The unit of the van der Waals gas equation parameter 'a' in $$\left( {P + {{a{n^2}} \over {{V^2}}}} \right)(V - nb) = nRT$$ is :
A
kg m s$$-$$2
B
dm3 mol$$-$$1
C
kg m s$$-$$1
D
atm dm6 mol$$-$$2

## Explanation

$${{a{n^2}} \over {{V^2}}} = atm \Rightarrow a = atm \times {{d{m^6}} \over {mo{l^2}}}$$
2

### JEE Main 2021 (Online) 26th August Evening Shift

The interaction energy of London forces between two particles is proportional to rx, where r is the distance between the particles. The value of x is :
A
3
B
$$-$$3
C
$$-$$6
D
6

## Explanation

For London dispersion forces.

$$E \propto {1 \over {{r^6}}}$$

Hence, x = $$-$$6
3

### JEE Main 2020 (Online) 3rd September Evening Slot

A mixture of one mole each of H2 , He and O2 each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of H2 is 2 atm, the total pressure of the gases in the cylinder is :
A
14 atm
B
38 atm
C
6 atm
D
22 atm

## Explanation

According to Dalton’s law of partial pressure, pi = xi × PT

pi = partial pressure of the ith component

xi = mole fraction of the ith component

pT = total pressure of mixture

$$\Rightarrow$$ 2 atm = $$\left( {{{{n_{{H_2}}}} \over {{n_{{H_2}}} + {n_{He}} + {n_{{O_2}}}}}} \right)$$ $$\times$$ pT

$$\Rightarrow$$ pT = $$\left( {{{1 + 1 + 1} \over 1}} \right)$$ $$\times$$ 2 = 6 atm
4

### JEE Main 2020 (Online) 2nd September Morning Slot

Which one of the following graphs is not correct for ideal gas? d = Density, P = Pressure, T = Temperature
A
II
B
III
C
I
D
IV

## Explanation

For ideal gas,

PM = dRT [As V = $${M \over d}$$ ]

$$\Rightarrow$$ d = $${{PM} \over {RT}}$$

$$\therefore$$ d $$\propto$$ $${1 \over T}$$ $$\Rightarrow$$ d v/s $${1 \over T}$$ graph is Straight line.

d v/s T $$\Rightarrow$$ graph is Hyperbolic.

As d $$\propto$$ p

$$\therefore$$ d v/s p graph is Straight line.

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