Question

At the top of a mountain, the thermometer reads 0${}^{\circ }$C and the barometer reads 710 mm Hg. At the bottom of the mountain the temperature is 30${}^{\circ }$C and pressure is 760 mm Hg. The ratio of the density of air at the top with that at the bottom is

• A. 1 : 1.04
• B. 1.04 : 1
• C. 1.5 : 1
• D. 1 : 1

Answer 1

Answer: (B)

PV = nRT $\Rightarrow$ PV = $\frac{w}{M}$ RT
w = mass of the gas, M = molar mass of the gas
PM = $\frac{w}{V}$ RT $\Rightarrow$ PM = dRT
d = density of the gas
$d=\frac{PM}{RT}$
$\frac{d_1}{d_2}=\frac{P_1}{T_1}\times \frac{T_2}{T}{P}_2$
(M and R are constants)
$\therefore \frac{d_1}{d_2}=\frac{710}{273}\times \frac{303}{750}=\frac{1.04}{1}$