How Do You Calculate Percent Yield of C2H5Cl in a Complex Reaction?

[alingy1]

Homework Statement

"The reaction of ethane gas (C2H6) with chlorine gas produces C2H5Cl as its main product (along with HCl). In addition, the reaction invariably produces a variety of other minor products, including C2H4Cl2, C2H3Cl3, and others. Naturally, the pro- duction of these minor products reduces the yield of the main product. Calculate the percent yield of C2H5Cl if the reaction of 300. g of ethane with 650. g of chlorine produced 490. g of C2H5Cl." (Zumdahl, Chemistry, 2013)

Homework Equations

Balancing and math principles.

The Attempt at a Solution

Ok, I have the answer in the solution manual. It gives out 82.9%.
But, the thing I do not understand about the way they do the problem is this:
They use the formula C2H6+ Cl2-> C2H5Cl+ HCl
However, that's not what is really happening. There are other products formed.
I thought of this formula (which is missing ''the other'' products):
C2H6+ Cl2-> C2H5Cl+ HCl +C2H4Cl2+C2H3Cl3 + others
I found different ways of balancing this last formula if I ignore the others.

Why does the first equation give the right answer? Won't the other molecules intervene in the calculations?

 

[chemisttree]

No, they don't. You can't be certain the other products were produced anyway. The other "products" COULD be unreacted starting material!

 

[alingy1]

But, there still may be other products. I don't understand how those cannot have an impact on the reaction balancing.

 

[Borek]

Theoretical yield assumes only one product.

Note that in this particular case you can't uniquely balance reaction with several products. Each of these:

2C₂H₆ + 3Cl₂ -> C₂H₅Cl + C₂H₄Cl₂ + 3HCl

50C₂H₆ + 67Cl₂ -> 33C₂H₅Cl + 17C₂H₄Cl₂ + 67HCl

1028C₂H₆ + 1119Cl₂ -> 937C₂H₅Cl + 91C₂H₄Cl₂ + 1119HCl

is balanced OK. Which one of these is the correct one?

 

[alingy1]

All of them could be correct i guess. Hmm, you are intriguing me here. Theoretical yield applies only when there is one product? What about the HCl?

 

[Borek]

Sorry, lousy wording, one main product. HCl doesn't matter, as its amount is related to the main product - you don't need more ethane to produce HCl.