Question

27. A 500 ml container has 15 x 1012 molecules of an
ideal gas. How many molecules will occupy 100 ml
at same temperature and pressure?
(1) 3 * 1012
(2) 75 x 1012
(3) 7.5 x 1012
(4) 15 x 1012​

Answer 1

Answer:

For the volume, , number of molecules,

Let there are  number of molecules in the volume Since, the gas is given to be ideal gas, therefore it follows the ideal gas law, which is,

PV= NRT =NKT

where,

P = pressure of the gas.

V = volume of the gas.

T = absolute temperature of the gas.

R = Universal gas constant.

k = Boltzmann constant.

n = number of moles of the gas.

N = number of molecules of the gas.

We are given that the temperature and pressure of the gas is same.

Applying ideal gas law for the volume V1 ,

PV1 = N1KT

Applying ideal gas law for the volume V2,

PV2=N2KT

Dividing both these equations, we get,

PV1/PV2 = N1KT/N2KT

V1/V2 = N1/N2

Therefore, N2 = 100/500 * 15*10^12

= 3*10^12 molecules