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

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SUMMARY

The percent yield of C2H5Cl in the reaction between ethane (C2H6) and chlorine (Cl2) is calculated to be 82.9% based on the production of 490 g of C2H5Cl from 300 g of ethane and 650 g of chlorine. The reaction is represented by the simplified equation C2H6 + Cl2 → C2H5Cl + HCl, despite the formation of additional minor products such as C2H4Cl2 and C2H3Cl3. The theoretical yield calculation assumes only one main product, which is why the presence of other products does not affect the yield calculation. Theoretical yield is applicable when focusing on the primary product of interest.

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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?
 
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No, they don't. You can't be certain the other products were produced anyway. The other "products" COULD be unreacted starting material!
 
But, there still may be other products. I don't understand how those cannot have an impact on the reaction balancing.
 
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?
 
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?
 
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.
 

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