Question

Arrange the following in order of increasing density ?
oxygen at ${25}^{\circ }C,$ 1 $atm$; oxygen at $0^{\circ }C,$ 2 $atm$; oxygen at ${273}^{\circ }C,$ 1 $atm$

• A. oxygen at ${25}^{\circ }C,$ 1 $atm$ < oxygen at $0^{\circ }C,$ 2 $atm$ < oxygen at ${273}^{\circ }C,$ 1 $atm$
• B. oxygen at ${25}^{\circ }C,$ 1 $atm$ < oxygen at ${273}^{\circ }C,$ 1 $atm$ < oxygen at $0^{\circ }C,$ 2 $atm$
• C. oxygen at $0^{\circ }C,$ 2 $atm$ < oxygen at ${25}^{\circ }C,$ 1 $atm$ < oxygen at ${273}^{\circ }C,$ 1 $atm$
• D. oxygen at ${273}^{\circ }C,$ 1 $atm$ < oxygen at ${25}^{\circ }C,$ 1 $atm$ < oxygen at $0^{\circ }C,$ 2 $atm$

Answer 1

Answer: (D)

oxygen at ${273}^{\circ }C,$ 1 $atm$ < oxygen at ${25}^{\circ }C,$ 1 $atm$ < oxygen at $0^{\circ }C,$ 2 $atm$

$d=\frac{MP}{RT}$.
As $R$ is constant and M for $O_2$ is constant, density depends upon $\frac{P}{T}$.
The values for $\frac{P}{T}$ will be :
At ${25}^{\circ }C$, 1 $atm$, $\frac{P}{T}=\frac{1}{298}$,
At $0^{\circ }C$, 2 $atm$, $\frac{P}{T}=\frac{2}{273}$,
At ${273}^{\circ }C$, 1 $atm$, $\frac{P}{T}=\frac{1}{546}$
Hence, increasing order of density will be :
$O_2$ at ${273}^{\circ }C$, 1 $atm$ ; $O_2$ at ${25}^{\circ }C$, 1 $atm$ ; $O_2$ at $0^{\circ }C$, 2 $atm$.