A mixture of ethene (C2H6) and ethene (C2H4) occupies 40 L at 1.00 atm and at 400 K. The mixture reacts completely with 130 g of O2 to produces CO2 and H2O. Assuming ideal gas behaviour, Calculate the mole fractions of C2H4 and C2H6 in the mixture.Correct answer is '0.34'. Can you explain this answer?

Question

Answer

Given:
- Mixture of ethene (C2H6) and ethene (C2H4)
- Volume of mixture: 40 L
- Pressure: 1.00 atm
- Temperature: 400 K
- Reacts completely with 130 g of O2 to produce CO2 and H2O

To Find:
- Mole fractions of C2H4 and C2H6 in the mixture

Solution:

Step 1: Calculate the moles of O2
We know the molar mass of O2 is 32 g/mol. Therefore, the moles of O2 can be calculated using the formula:

Moles of O2 = Mass of O2 / Molar mass of O2
= 130 g / 32 g/mol
= 4.0625 mol

Step 2: Calculate the moles of CO2 and H2O produced
The balanced chemical equation for the reaction is:
C2H6 + 7/2 O2 → 2 CO2 + 3 H2O
From the equation, we can see that 1 mole of C2H6 reacts with 7/2 moles of O2 to produce 2 moles of CO2 and 3 moles of H2O.

Therefore, moles of CO2 produced = 2 * 4.0625 mol = 8.125 mol
And moles of H2O produced = 3 * 4.0625 mol = 12.1875 mol

Step 3: Calculate the moles of C2H4 and C2H6
Since the reaction is complete, all the moles of C2H6 and C2H4 present in the mixture react to produce CO2 and H2O. Therefore, the moles of C2H6 and C2H4 can be calculated by working backwards from the moles of CO2 and H2O produced.

From the balanced chemical equation, we know that 1 mole of C2H6 reacts to produce 2 moles of CO2. Therefore, moles of C2H6 = 8.125 mol / 2 = 4.0625 mol

Similarly, from the balanced chemical equation, we know that 1 mole of C2H4 reacts to produce 2 moles of CO2. Therefore, moles of C2H4 = 8.125 mol / 2 = 4.0625 mol

Step 4: Calculate the mole fractions
The mole fraction of a component in a mixture is given by the formula:

Mole fraction = Moles of component / Total moles of mixture

Mole fraction of C2H6 = 4.0625 mol / (4.0625 mol + 4.0625 mol) = 0.5
Mole fraction of C2H4 = 4.0625 mol / (4.0625 mol + 4.0625 mol) = 0.5

Step 5: Round off the mole fractions
The mole fractions should be rounded off to the nearest hundredth.
Therefore, the mole fraction of C2H6 and C2H4 in the mixture is 0

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