A mixture of ethane and ethene occupied 35.5 L at 1.000 bar and 405 K. This
mixture reacted completely with 110.3 g of O2 to produce CO2 and H2O.
What was the composition of the original mixture? Assume ideal gas
behavior
Write balanced equations for the combustion of ethane and ethene. I have
2C2H6 + 7O2 ==> 4CO2 + 6H2O
C2H4 + 3O2 ==> 2CO2 + 2H2O
Use PV = nRT and solve for mols of the ethane + mols ethene.
Let X = mols ethane
and Y = mols ethene
Then X + Y = mols from above. This is equation 1.
For equation 2, convert mols C2H6(that's X) and mols C2H4(that's Y) to mols O2 needed for combustion.
X*(7/2) + Y*(3/1) = 110.3/32
Solve for two equation simultaneously for X and Y and that will give you mols. Since the problem asks for composition, I would think moles is as good an answer as you want; however, you can convert mols of each to L by using PV = nRT and the conditions of the problem. Post your work if you get stuck.
To determine the composition of the original mixture, we need to use the ideal gas law equation and stoichiometry.
First, let's determine the number of moles of O2 reacted. We can use the molar mass of O2 to convert grams to moles:
Molar mass of O2 = 32.00 g/mol
Number of moles of O2 = 110.3 g / 32.00 g/mol = 3.45 mol
Next, let's determine the number of moles of CO2 and H2O produced. From the balanced chemical equation for the complete combustion of ethane (C2H6) and ethene (C2H4) with O2, we know that:
C2H6 + 7/2 O2 → 2 CO2 + 3 H2O
C2H4 + 3 O2 → 2 CO2 + 2 H2O
Since we don't know the exact ratio of ethane to ethene, let's use the worst-case scenario where the entire moles of O2 reacted in the first equation.
Number of moles of CO2 = 3.45 mol x (2 mol CO2 / 7/2 mol O2) = 0.9857 mol CO2
Number of moles of H2O = 3.45 mol x (3 mol H2O / 7/2 mol O2) = 1.473 mol H2O
Now, let's use the ideal gas law equation to determine the number of moles of the remaining mixture components (ethane and ethene). The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
We have the following information from the given problem:
Pressure (P) = 1.000 bar = 1.000 x 10^5 Pa
Volume (V) = 35.5 L = 35.5 x 0.001 m^3
Temperature (T) = 405 K
Ideal gas constant (R) = 8.314 J/(mol·K)
Let's rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Number of moles of the remaining mixture components = (1.000 x 10^5 Pa) x (35.5 x 0.001 m^3) / (8.314 J/(mol·K) x 405 K)
Calculate this value to find the number of moles.
Finally, knowing the number of moles of ethane and ethene and the initial moles of O2, we can determine their composition by comparing the moles of each component.