Question

The air density of Mount Everest is less than that
at the sea level. It is found by mountaineers that
for one trip lasting a few hours, the extra oxygen
needed by them corresponds to 30000 cc at sea
level (pressure 1 atm, temperature 27°C).
Assuming that the temperature around Mount
Everest is -130°C and that the oxygen cylinder
has capacity of 5.2 litre, the pressure at which
oxygen will be filled in the cylinder is​

Answer 1

The pressure at which oxygen will be filled in the cylinder = 2.75 atm

The number of moles of gas in the container will be equal for both the cases , so we will compare the moles in both cases to find the pressure.

At the sea level -

pressure = P1 = 1 atm

volume = V1 = 30000 cc = 30 l

temperature = T1 = 300 K

n1 = number of moles

Using the ideal gas equation , PV = nRT

=> n1 = P1V1/RT1

At Mount Everest -

pressure = P2

volume = V2 = 5.2 l

temperature = T2 = 143 K

n2 = number of moles

Using the ideal gas equation , PV = nRT

=> n2 = P2V2/RT2

The number of moles will be equal in the two cases , n1 = n2

=> P1V1/RT1 = P2V2/RT2

=> P2 = (P1 × V1 × T2 )/T1 × V2

=> P2 = 1 × 30 × 143/300 × 5.2

=> P2 = 2.75 atm