Answer:
there is 2% of hydrogen and 98% of nitrogen (mass percent)
Explanation:
assuming ideal gas behaviour
P*V=n*R*T
n= P*V/(R*T)
where P= pressure=1.02 atm , V=volume=7.47 L , T=absolute temperature= 296 K and R= ideal gas constant = 0.082 atm*L/(mole*K)
thus
n= P*V/(R*T) = 1.02 atm*7.47 L/( 296 K * 0.082 atm*L/(mole*K)) = 0.314 moles
since the number of moles is related with the mass m through the molecular weight M
n=m/M
thus denoting 1 as hydrogen and 2 as nitrogen
m₁+m₂ = mt (total mass)
m₁/M₁+m₂/M₂ = n
dividing one equation by the other and denoting mass fraction w₁= m₁/mt , w₂= m₂/mt , w₂= 1- w₁
w₁/M₁+w₂/M₂ = n/mt
w₁/M₁+(1-w₁) /M₂ = n/mt
w₁*(1/M₁- 1/M₂) + 1/M₂ = n/mt
w₁= (n/mt- 1/M₂) /(1/M₁- 1/M₂)
replacing values
w₁= (n/mt- 1/M₂) /(1/M₁- 1/M₂) = (0.314 moles/3.48 g - 1/(14 g/mole)) /(1/(1 g/mole)-1/(14 g/mole))= 0.02 (%)
and w₂= 1-w₁= 0.98 (98%)
thus there is 2% of hydrogen and 98% of nitrogen
