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Q. 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)

    (1) 0.1 kg/m3              (2) 0.02 kg/m3                    (3) 0.5 kg/m3                  (4) 0.2 kg/m3

 

Ans. (4)

Explanation:

From ideal gas equation,

PV space equals space nRT rightwards double arrow PV space equals space straight m over straight M RT space space space space space space space space space space space space space space space space space space space space because straight n space equals straight m over straight M rightwards double arrow PV space equals space fraction numerator open parentheses ρV close parentheses RT over denominator straight M end fraction space space space space space space space space space space space space space space space space because straight m space equals space ρV Where comma space straight M space is space molar space mass space of space hydrogen open parentheses straight H subscript 2 close parentheses space gas space equals space 2 space straight g space mol to the power of negative 1 end exponent space equals space 2 cross times 10 to the power of negative 3 end exponent space Kg space mol to the power of negative 1 end exponent therefore straight rho space equals space PM over RT space equals space fraction numerator 249 cross times 10 cubed cross times 2 cross times 10 to the power of negative 3 end exponent over denominator 8.3 cross times 300 end fraction rightwards double arrow straight rho space equals space 0.2 space Kg divided by straight m cubed