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Problem 134 Hard Difficulty

Aspirin (acetylsalicylic acid, $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} )$ is made by reacting
salicylic acid $\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)$ with acetic anhydride $\left[\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O} ] :$
\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}(s)+\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}(s)+\mathrm{CH}_{3} \mathrm{COOH}(l)
In one preparation, 3.077 g of salicylic acid and 5.50 $\mathrm{mL}$ of acetic anhydride react to form 3.281 $\mathrm{g}$ of aspirin. (a) Which is the limiting reactant $(d \text { of acetic anhydride }=1.080 \mathrm{g} / \mathrm{mL})$ ? (b) What is the percent yield of this reaction? (c) What is the percent atom economy of this reaction?


a) Salicylie acid is the limiting reactant.
b) yield $=82,78$ percent
c) percent atom economy $=75,23$ percent


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Video Transcript

given equation in which you're told the amount of product that forms. Actually, you can calculate what's called the percent yield, which describes sort of how effective the equation waas. So this equation. We have two quantities of reactive Saleh Cilic acid and a seat again hydride, and we know that we produced 3.281 grams of aspirin. This is called the actual yield To figure out that what's called the theoretical yield, or how much we should produce, we have to convert each of our masses two moles. And we do that using the molar mass, which we find from the periodic table by adding up the individual molar masses of each element. Once we have moles of a reacted, we confined moles of product and we do that using the mole ratio from the balanced equation. Once we have moles of product, we confined grams of product and again we use the molar mass. We can complete the same calculation with the acetic anhydride. The only difference is that since we're given volume, we first have to find mass when we do that, using the given density and then we can change it to moles of the reactant and then moles of the product and then finally, grams a product. The calculations will give two different final masses, and so whichever one is the smaller amount, a product is the amount that should form. And again, this is called the Theoretical Yield. But before we start the conversions, the more masses of each of the substances but we look at by a C seven each. Six 03 has a molar mass of seven times 12.11 plus six times 1.8 plus three times 15.999 all found on the periodic table, who are 138.1 to 2 grams per mole. The molar mass of a seat again hydride. It's found similarly to be 100 and two 0.89 grams per mole. And finally, the molar mass of aspirin is 100 80 0.159 grams per mole. Who was used are starting masses, starting with the salads cilic acid, changing two moles by dividing by the molar mass multiplying by the coefficients from the balanced equation, which in this case, it's a 1 to 1 ratio and then multiplying by the molar mass of aspirin. So this mass would produce for 0.26 zero grams a product. If we do the same calculation, given our other quantity of acetic anhydride ch three c e o 20 we start off with the volume. So we have to first multiply by the density and then changed to moles and then using the mole ratio, which again is 1 to 1 and then finally multiplying by the molar mass of aspirin. This gives us 10.5 grams, so you can see that the limiting the agent is Saleh Selic acid on the amount that should be produced. A theoretical yield. Its 4.260 grip. So our percent yield was how much we did produce. We're 3.281 grams, divided by how much we should have produced 4.260 grams times 100 where 75%. Another way to look at the efficiency of a chemical reaction is something called the Adam economy. And this is a percentage that looks that the mass of each Adam in the desire product, which in this case is aspirin divided by the mass of each Adam and all of the reactor's. Or, in this case, a reactant, sir. C seven each, six 03 and ch three c 02 Oh, so to find her Adam economy, we simply look up from atomic mass of each element and multiply it by the coefficient by the subscript in the equation. So the nine times 12.11 plus eight times 1.8 for hydrogen plus four I was 15.999 for oxygen and then divided by on the bottom. We can combine the total numbers of Adams, so there are 11 carbons total 12 hydrogen and six oxygen's, and this gives us an atom economy of 75%.