At 300 K, the density of a certain gaseous molecule at 2 bar is double

1.	At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen at 4 bar. The molar mass of gaseous molecule is ……………. (A) 28 g mol-1(B) 56 g mol-1 (C) 112 g mol-1(D) 224 g mol-1
Answer» Correct option is: (C) 112 g mol^-1 PV = nRT = PV = \(\frac WM RT\) = PM = \(\frac WV RT\) = PM = \(\rho\)RT ....(i) Let say density of \(N_2\) at 4 bat = \(\rho\) then the density of unknown gas at 2 atm = 2\(\rho\) Using equation (i) For \(N_2\) gas 4 \(\times\) 28 = \(\rho\) \(\times\) R \(\times\) 300 ...(ii) for unknown gas 2 \(\times\) M = 2e \(\times\) R \(\times\) 300 ....(iii) iii ÷ ii, we got \(\frac {2M}{4\times28} = \frac {2\rho\times R\times300}{\rho\times r\times 300}\) M = \(\frac {2 \times 4\times 28}{2}\) M = 112 g/mol (C) 112 g mol^-1

At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen at 4 bar. The molar mass of gaseous molecule is ……………. (A) 28 g mol-1(B) 56 g mol-1 (C) 112 g mol-1(D) 224 g mol-1

Answer»

Correct option is: (C) 112 g mol^-1

PV = nRT = PV = \(\frac WM RT\)

= PM = \(\frac WV RT\)

= PM = \(\rho\)RT ....(i)

Let say density of \(N_2\) at 4 bat = \(\rho\)

then the density of unknown gas at 2 atm = 2\(\rho\)

Using equation (i)

For \(N_2\) gas

4 \(\times\) 28 = \(\rho\) \(\times\) R \(\times\) 300 ...(ii)

for unknown gas

2 \(\times\) M = 2e \(\times\) R \(\times\) 300 ....(iii)

iii ÷ ii, we got

\(\frac {2M}{4\times28} = \frac {2\rho\times R\times300}{\rho\times r\times 300}\)

M = \(\frac {2 \times 4\times 28}{2}\)

M = 112 g/mol