Percentage yield in a reaction problem

[jackthehat]

Summary:: We are given a description of a reaction and the masses of two reactants and are initially asked to calculate which of two is the excess reagent and how much of the excess reagent would be left over if we have 100% completion. Then we are given a final mass (after purification) of the main product and asked to calculate the percentage yield.

I have this problem which is in three parts, I have correctly solved the first part but not the subsequent parts b) or c). The problem is -

Problem
A chemist heats a mixture of 125.0 grams of salicylic acid (C7 H6 O3) and 100.0 grams of acetic anhydride (C4 H6 O3), to produce Aspirin (acetylsalicylic acid- C9 H6 O3) and C2 H4 O2.

a) Which reagent is in excess?

b) How much will be left over after the reaction has gone to completion?

c) After the reaction described in parts a & b, the chemist purifies her aspirin product and finds that she has made 151.2 g of aspirin. What is the percent yield for this reaction?

Now for part a) .. I first of all wrote out the full balanced equation
C7 H6 O3 + C4 H6 O3 ---> C9 H8 O4 + C2 H4 O2
and so we see that the molar ratios of Salicylic Acid to Aspirin and Acetic Anhydride to Aspirin are both 1:1.
Next by using the molar masses of the two reactants and the main product (Aspirin) we can work out what molar mass of Aspirin 1 mole of each reactant would produce. Then taking ratios of actual mass and molar mass we can calculate what actual mass of aspirin would be produced by each actual mass of reactant (reagent) we have. the greater is produced by the excess reagent. from my calculations I calculated that ...
125g of salicylic acid would produce 163.00g of aspirin whereas
100.0g of acetic anhydride would produce 176.47g of aspirin ..
so acetic anhydride is the excess reagent.
For part b) .. I assumed that the 100% completion of reaction could be taken from our balanced equation previously as 180.0g of aspirin would be produced if 1 mole of reagents were reacted to 100% completion. So we have 100.0g of the excess reagent present which would produce ..
(100.0g/it's molar mass) x 180.0g (molar mass of aspirin) that is ..
(100.0/102.0) x 180.0 = 176.47g and so what would be left over is ..
180.0g - 176.47g = 3.530g (to 4 sig. figures)
I was marked wrong for this answer
For part c) .. I took the % yield to be 151.20g (of aspirin produced) divided by the 176.47 that theoretically would be produced by 100% completion taking into account the amount of reagent we had. then converting this fraction to percentage.
ie. .. (151.5/176.47) x 100 % .. which gave me .. 85.68%
I was marked wrong for this part.
I am at a loss to know where i went wrong in parts b) and c) ..
can anyone help point me in the right direction ?
Regards,
Jack

[Moderator's note: Moved from a technical forum and thus no template.]

 

[BvU]

So we have 100.0g of the excess reagent present which would produce ..

The excess reagent isn't the limiting one. You already calculated that with 100% completion 163 g of C₉H₈O₄ is produced. How much of the excess is needed for that ?

 

[jackthehat]

Hi BvU,
Thank you for taking the time to look at my problem and give some input.
Do you mean that the limiting reagent produces the maximum mass of product we are able to produce in this reaction and so we have to calculate how much excess reagent mass it would take to produce 163g of product .. finally subtracting that mass of excess reagent from the original amount we started with to get how much is left over so solving part b) ?
Finally for part c) .. do we then take the ratio of this product mass (163g) to the mass that the excess reagent could potentially produce (176.47g) to get the correct percentage yield to solve part c) ?
Regards.
Jackthehat

 

[Borek]

Do you mean that the limiting reagent produces the maximum mass of product we are able to produce in this reaction and so we have to calculate how much excess reagent mass it would take to produce 163g of product .. finally subtracting that mass of excess reagent from the original amount we started with to get how much is left over so solving part b) ?

Yes.

Finally for part c) .. do we then take the ratio of this product mass (163g) to the mass that the excess reagent could potentially produce (176.47g) to get the correct percentage yield to solve part c) ?

No. Percentage yield is the real over theoretical. Theoretical yield is the one given by the limiting reagent. You can't ever get a yield higher than the one calculated from the limiting reagent, that's why it is called "limiting".

 

[jackthehat]

Hi Borek,
Thank you for taking the time and effort to answer my problem. I was really confused as to what ratio I had to use to find the percentage yield, and I think that was because I hadn't really understood what percentage yield really meant. That it was, as you state, " the real over theoretical " . To tell the truth I think I was confused as to what exactly the theoretical 100% reaction completion value was ... whether it was the theoretical value that the excess reagent could produce or the one that the limiting reagent could produce and so following on from that confusion I was then unsure what the yield value should be. Thanks to you my confusion has now been cleared up. Thank you again.
Regards,
Jackthehat