Question

In a chemical factory, 60.0 L tank of a gas at 27 0C and 125 atm springs a leak. When the leak was discovered, the pressure was reduced to 50 atm. Calculate the number of molecules that escaped during leakage. Engineers discovered that the same type of leakage happened before for another two different temperature values (both are greater than the previous values), can they sketch a graph to show the variation including all three temperature values. Validate which gas law is followed here and Justify that the gas used is an ideal gas?

Answer 1

Given that:

Volume of tank containing gas (V) = 60 L

Pressure reduced due to the leakage of gas to = 50 atm

We also have the data :

Initial temperature of gas = 27 deg C = 300K

Initial pressure (P) = 125 atm

Change in pressure Δ P = 125-50 = 70 atm

Considering, the gas obeys ideal gas law, from ideal gas equation :

P V = n R T

= > n = Δ P / P . V / R T

= > n = (( 70 / 125 ) × 60 ) / ( 0.0821 × 300 ) mol (since R = 0.08206 L.atm/mol.K)

= > n = 33.6 / 24.63 mol

= > n = 1.36419 mol

= > n = 1.36 mol

Therefore , number of moles of gas that escaped will be 1.36 mol considering gas obeying Ideal gas law.