Aspirin can be made in the laboratory by reacting acetic anhydride (C4H6O3) with salicylic acid (C7H6O3) to form aspirin (C9H8O4) and acetic acid (C2H4O2). The balanced equation isC4H6O3+C7H6O3→C9H8O4+C2H4O2
In a laboratory synthesis, a student begins with 2.90 mL of acetic anhydride (density=1.08gml−1) and 1.23 g of salicylic acid. Once the reaction is complete, the student collects 1.24 g of aspirin.
1. Determine the theoretical yield of aspirin for the reaction. Express your answer using three significant figures.
2. Determine the percent yield of aspirin for the reaction. Express your answer using three significant figures.

Answer:

1.- Theoretical yield is 1.64 g of aspirin

2.- %Yield is 75.6%

Explanation:

The theoretical yield of aspirin could be calculated by the molar relation between anhydride acetic and salicylic acid which is 1:1. It means that the reaction of one mole of anhydride acetic with one mole of salicylic acid will produce 1 mole of aspirin and one mole of acetic acid.

It is possible to calculated the number of moles using moles=grams/molar mass. in the attached figure we can see the molar mass of each compound.  

The number of moles of anhydride acetic can be calculated using the density and the volumen.  

g=(1.08 g/mL)*(2.90 mL)=3.13 g of anhydride  

moles= 3.13 g/(102.09 g/mol)= 0.031 moles of anhydride acetic

The same for salicylic acid and we have:  

moles= 1.23g/ (138.12 g/mol)= 0.0090 moles of salicylic acid

There is not 1:1 relation between this two compounds because there is much more anhydride acetic than salicylic acid, so the reaction is limited by the 0.0090 moles of salicylic acid which produce 0.0090 moles of aspirin.  

g= moles*molar mass  

Theoretical yield of aspirin= (0.009 moles)*(182.13 g/mol)= 1.64 g

The percent yield of aspirin for the reaction can be calculated using the nex formula:  

%yield= ((real yield)/(theoretical yield))*100

The real yield was 1.24 g of aspirin  

%Yield=(1.24g/1.64)*100=75.6%

Final answer:

To determine the theoretical yield of aspirin, calculate the moles of acetic anhydride and salicylic acid, use the balanced equation to find the moles of aspirin, and convert to grams. The percent yield is calculated by dividing the actual yield by the theoretical yield and multiplying by 100.

Explanation:

To determine the theoretical yield of aspirin, we need to first calculate the number of moles of acetic anhydride and salicylic acid. Then, we use the balanced equation to find the number of moles of aspirin produced. Finally, we convert the moles of aspirin to grams using its molar mass. The percent yield is calculated by dividing the actual yield by the theoretical yield and multiplying by 100.

Step 1: Calculate the moles of acetic anhydride
2.90 mL × 1.08 g/mL = 3.132 g
Moles of acetic anhydride = mass / molar mass = 3.132 g / 102.09 g/mol = 0.0307 mol

Step 2: Calculate the moles of salicylic acid
Moles of salicylic acid = mass / molar mass = 1.23 g / 138.12 g/mol = 0.0089 mol

Step 3: Use the balanced equation to find the moles of aspirin produced
According to the balanced equation: 1 mol of acetic anhydride reacts with 1 mol of salicylic acid to produce 1 mol of aspirin
Since the moles of acetic anhydride and salicylic acid are the same, the moles of aspirin produced = 0.0089 mol

Step 4: Calculate the theoretical yield of aspirin in grams
The molar mass of aspirin is 180.16 g/mol
Theoretical yield of aspirin = moles of aspirin × molar mass of aspirin = 0.0089 mol × 180.16 g/mol = 1.61 g

Step 5: Calculate the percent yield of aspirin
Percent yield = (actual yield / theoretical yield) × 100
Percent yield = (1.24 g / 1.61 g) × 100 = 77.0%

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