A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C.

Its density is : (R = 8.3 J mol⁻¹ K⁻¹)

CONCEPT:

Ideal gas equation - Ideal gas equation is the state of an equation that gives a good approximation of the behavior of many gases under many conditions. It is written as;

PV = nRT ----(1)

where

P is the pressure,  V is the volume

"n" is the amount of gas that is measured in the moles.

R is the universal gas constant, T is the temperature.

CALCULATION:

According to the ideal gas from equation (1) we have;

PV = nRT 

⇒ \(n =\frac {m}{M}\)

where m is the mass of the substance and M is the molar mass of the substance

Now, On putting this value in equation (1) we get;

PV = \(\frac {m}{M}\)RT

⇒ PM = \(\frac {m}{V}\)RT

Here, \(\frac {m}{V}\) =  ρ

PM = ρRT 

⇒ \(\rho = \frac{{PM}}{{RT}}\) ---(2)

Given : P = 249 × 10³ N/m²

M = 2 × 10^-3 kg

T = 300 K

Putting these given values in equation (2) we get;

\(\therefore \rho = \frac{{(249 \times {{10}^3})(2 \times {{10}^{ - 3}})}}{{8.3 \times 300}} \)

\(\rho = \frac{{0.2\,kg}}{{{m^3}}}\)

Hence, option 4) is the correct answer.