1. Tardigrade
  2. Question
  3. Chemistry
  4. At the top of a mountain, the thermometer reads 0°C and the barometer reads 710 mm Hg. At the bottom of the mountain the temperature is 30°C and pressure is 760 mm Hg. The ratio of the density of air at the top with that at the bottom is

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Q. 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

States of Matter

Solution:

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)
$\therefore \, \frac{d_1}{d_2} = \frac{710}{273} \times \frac{303}{750} = \frac{1.04}{1}$