the volume carbon dioxide and water vapor produced at the end of combustion of 20 cm^3 of ethane in air.

Question

20 cm3 of ethane (C2H6) burns completely in air to form carbon dioxide and water vapour. Determine the volume of each gas formed at the end of the reaction.

Answer 1

Step 1. Write the raw chemical reaction equation:

C₂H₆ + O₂ → CO₂ + H₂O

Step 2. Balance the equation:

2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O

Step 3: Convert the volume of Ethane (20cm³) into moles (because the chemical reaction equation represents moles of reactants and products).

To do so, requires use of the ideal gas law PV = nRT or n = (PV)/(RT). No pressure or temperature is given so this is a problem. At this point, you could do a couple of things to guess at what is wanted but I'll assume the volume of Ethane given is at STANDARD temperature and pressure, aka STP (273.15 K and 1 atm). In reality, it doesn't matter as long as you assume the Ethane and the CO2 and H2O are at the same temperature and pressure. Anyway for the sake of calculations, I'll pick STP (commonly used in Chemistry problems). Also, it is common to use the measure of liters for volume, so I'll convert 20cm³ to liters by dividing by 1000 to get 0.020 L. I'll also use as the value of the ideal gas constant R the number 0.082057 L atm mol^-1K^-1.

So n = [(1atm)(0.020L)]/[(0.082057 L atm mol^-1K^-1)(273.15K)] = 8.92305 x 10^-4 moles Ethane

Step 4 Determine the number of moles of CO₂ and H₂O from the chemical reaction equation.

For every 2 moles of ethane there are 4 moles of CO₂ produced (so twice the quantity of Ethane) and 6 moles of H₂O produced (so 3 times the quantity of Ethane). So there is (2)(8.92305 x 10^-4) = 0.001785 moles of CO₂ produced and (3)(8.92305 x 10^-4) = 0.002677 moles of H₂O produced.

Step 5: Convert the moles of CO₂ and H₂O back into volume.

Use the ideal gas law again PV = nRT but this time solve for V to get V = (nRT)/(P).

So for CO₂: V = [(0.001785 moles)(0.082057 L atm mol^-1K^-1)(273.15K)]/(1 atm) = 0.04L. Multiplying by 1000 to get back to cubic centimeters gives 40 cm³.

For H₂O, V = [(0.002677 moles)(0.082057 L atm mol^-1K^-1)(273.15K)]/(1 atm) = 0.06L. Multiplying by 1000 to get back to cubic centimeters gives 60 cm³.

There are some shortcuts that can be done but this the the Full Monty sort of calculation.