Question

How would you do this?

Hot exhaust gas from a furnace has a composition of 8 mol CO2 and 9 mol H2O with no other components. The exhaust gas is cooled down to 20 oC, and 4 mol of pure water leaves as liquid condensate. The remaining CO2 and water are vented as gas. What mass of input exhaust gas is required to obtain 1.00 kg of water condensate?

choices are:

2.25kg

6.69kg

7.14kg

4.89kg

9.84kg

5.55kg

Answer 1

1 kg water = 1000 g
molar mass of water = 18 g/mol
number of moles of water leaving = mass / molar mass
                                                                       = 1000/18
                                                                       = 55.6 mol

out of 9 mol , 4 mol is condensing

So input mol of water gas for 55.6 mol to condense = 55.6*9/4 = 125 mol

Input CO2 is twice the mol of water that condensate

So input CO2 = 55.6*2 = 111.1 mol

So input has 125 mol of H2O and 111.1 mol of CO2
molar mass of H2O is 18 g/mol
molar mass of CO2 is 44 g/mol

total mass of input = (18*125 + 44*111.1) g = 7138 g = 7.14 Kg
Answer: 7.14 Kg