Question

A sample of gas that is a mixture of CO2 and O2 at 300K and 600 hPa has a density of 1 kg m^-3. Determine the proportion of the mixture that is O2.

Answer 1

Solution :-

T= 300 K

Density = 1 kg /m3

1 kg = 1000 g

Volume = 1m3 = 1000 L

Pressure is 600 hectopascal = 0.592154 atm

Lets calculate the total moles of the gases

PV=nRT

PV/RRT= n

0.592154 atm * 1000 L / 0.08206 L: atm per mol K * 300 K = n

24.05 mol = n

So total moles of the gas is 24.05 mol

1000 g = (x*32)+(24.05-x * 44.01)

1000 g = 32x + 1058.4405 – 44.01 x

1000 – 1058.4405 = 32x – 44.01 x

-58.4405 = -12.01 x

X=58.4405/12.01

X= 4.87

So the mole of O2 = 4.87

And moles of CO2 = 24.05 – 4.87 = 19.18 mol