1

### AIPMT 2010 Mains

The pressure exerted by 6.0 g of methane gas in a 0.03 m3 vessel at 129oC is (Atomic masses : C = 12.01, H = 1.01 and R = 8.314 J K$-$1 mol$-$1 )
A
215216 Pa
B
13409 Pa
C
41648 Pa
D
31684 Pa

## Explanation

PV = nRT

$\Rightarrow$ $P = {{nRT} \over V}$ = ${w \over m}{{RT} \over V}$

= ${6 \over {16.05}} \times {{8.314 \times 402} \over {0.03}}$

= 41648 Pa
2

### AIPMT 2009

The energy absorbed by each molecule (A2) of a substance is 4.4 $\times$ 10$-$19 J and bond energy per molecule is 4.0 $\times$ 10$-$19 J. The kinetic energy of the molecule per atom will be
A
2.2 $\times$ 10$-$19 J
B
2.0 $\times$ 10$-$19 J
C
4.0 $\times$ 10$-$20 J
D
2.0 $\times$ 10$-$20 J

## Explanation

Energy absorbed by each molecule = Bond energy per molecule + Kinetic energy per molecule

$\Rightarrow$ 4.4 × 10–19 J = 4.0 × 10–19 J + Kinetic energy per molecule

$\Rightarrow$ 0.4 × 10–19 = Kinetic energy per molecule

Kinetic energy per atom =
Kinetic energy per molecule
2

=
0.4 × 10–19
2
= 0.2 × 10–19 J

= 2 × 10–20 J
3

### AIPMT 2008

Volume occupied by one molecule of water (density = 1 g cm$-$3) is
A
3.0 $\times$ 10$-$23 cm3
B
5.5 $\times$ 10$-$23 cm3
C
9.0 $\times$ 10$-$23 cm3
D
6.023 $\times$ 10$-$23 cm3

## Explanation

1 mole of water contains 6.023 × 1023 molecules of water

6.023 × 1023 molecules of water weigh = 18 g

So, 1 molecule of water weighs = ${{18} \over {6.023 \times {{10}^{23}}}}$

Now, volume of 1 molecule of water

=
Mass of 1 molecule of water
Density of water
.

= ${{18} \over {6.023 \times {{10}^{23}}}} \times {1 \over {1\,g\,c{m^{ - 3}}}}$

= 3 $\times$ 10-23 cm3
4

### AIPMT 2008

If a gas expands at constant temperature, it indicates that
A
kinetic energy of molecules remains the same
B
number of the molecules of gas increases
C
kinetic energy of molecules decreases
D
pressure of the gas increases.

## Explanation

Kinetic energy of a gas is expressed as

K.E = ${3 \over 2}nRT$

Thus, on expansion of fixed amount of gas at constant temperature the kinetic energy remains constant.