3.7 g of a gas at 25°C occupies the same volume as 0.184 g H2 at 17°C at same pressure. Molecular weight of the gas is

Question

3.7 g of a gas at 25°C occupies the same volume as 0.184 g H2 at 17°C at same pressure. Molecular weight of the gas is (A) 59.1 (B) 41.3 (C) 144.6 (D) 40.2

Tardigrade Admin · Accepted Answer

Since pressure and volume of H2 and given gas are same (PV) textgas = (PV)H2 (m textgas/M textgas) RT(gas) = (mH2/MH2)RT(H2) (3.7/M textgas) × R × 298 = (0.184/2) × R × 290 M textgas = 41.3

Q. $3.7 g$ of a gas at $2 5^{\circ} C$ occupies the same volume as $0.184 g H_{2}$ at $1 7^{\circ} C$ at same pressure. Molecular weight of the gas is

$59.1$

$41.3$

$144.6$

$40.2$

Since pressure and volume of $H_{2}$ and given gas are same
$(P V)_{gas} = (P V)_{H_{2}}$
$\frac{m _{gas}}{M _{gas}} R T_{(g a s)} = \frac{m _{H_{2}}}{M _{H_{2}}} R T_{(H_{2})}$
$\frac{3.7}{M _{gas}} \times R \times 298 = \frac{0.184}{2} \times R \times 290$
$M_{gas} = 41.3$

Q. 3.7g of a gas at 25∘C occupies the same volume as 0.184gH2​ at 17∘C at same pressure. Molecular weight of the gas is

59.1

41.3

144.6

40.2