Question

Average molar mass of air is $29.0 \,g \,mol ^{-1}$. At the altitude of $x \times 10^{3} m ,$ atmosphere pressure decreases from 1.00 bar to 0.50 bar. What is the value of $x ?$

• A. 1
• B. 6
• C. 2
• D. 4

Answer 1

Answer: (B)

the atmospheric pressure $(p)$ at a height h above see level is related to the atmospheric pressure at level $\left(p_{0}\right)$ by the barometric formula.

$p =p_{0} e^{-m g h / R T} $

$\log _{e} \frac{p}{p_{0}} =\log _{e} e^{m g h / R T}=-\frac{m g h}{R T} $

$\therefore h =\frac{2.303 R T}{m g} \,\log \frac{p_{0}}{p} $

$h =\frac{2.303 \times 8.314 \,J \,mol ^{-1} K ^{-1} \times 298 \,K }{29.0 \times 10^{-3} \,kg \,mol ^{-1} \times 9.81 \times ms ^{-2}}\, \log \frac{1.0}{0.5} $

$6.04 \times 10^{3}= x \times 10^{3}$

Thus, $x = 6$