Question

The air density at Mount Everest is less than that at the sea level. Mountaineers find that for one trip lasting a few hours, the extra oxygen needed by them corresponds to $30,000\text{cc}$ at sea level (pressure 1 atmosphere, temperature ${27}^{\circ }\text{C}$). Assuming that the temperature around Mount Everest is $–{73}^{\circ }\text{C}$ and that the oxygen cylinder has a capacity of $5.2\text{litre}$, the pressure at which $O_2$ be filled (at site) in the cylinder is

• A. $3.86\text{atm}$
• B. $5.00\text{atm}$
• C. $5.77\text{atm}$
• D. $1\text{atm}$

Answer 1

The correct option is A $3.86\text{atm}$

At sea level, $PV=\mu RT$
Putting datas from the question
$\Rightarrow 1\times \left(30\text{litre}\right)=\mu \times \left(0.0821\right)\times 300$
Number of moles $\Rightarrow \mu =1.22$
(remember $R=0.0821\frac{\text{atm-litre}}{\text{mole-K}})$
Similarly at everest, $P\times 5.2=1.22\times 0.0821\times 200$
$\Rightarrow P=3.86\text{atm}$