<u>Answer:</u>
<u>For a:</u> The mass of acetic anhydride needed is 73.91 grams.
<u>For b:</u> The theoretical yield of aspirin is 130.43 grams.
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
Given mass of salicylic acid = ![1.00\times 10^2g=100g](https://tex.z-dn.net/?f=1.00%5Ctimes%2010%5E2g%3D100g)
Molar mass of salicylic acid = 138.121 g/mol
Putting values in equation 1, we get:
![\text{Moles of salicylic acid}=\frac{100g}{138.121g/mol}=0.724mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20salicylic%20acid%7D%3D%5Cfrac%7B100g%7D%7B138.121g%2Fmol%7D%3D0.724mol)
For the given chemical reaction:
![C_7H_6O_3+C_4H_6O_3\rightarrow C_9H_8O_4+CH_3COOH](https://tex.z-dn.net/?f=C_7H_6O_3%2BC_4H_6O_3%5Crightarrow%20C_9H_8O_4%2BCH_3COOH)
By stoichiometry of the reaction:
1 mole of salicylic acid reacts with 1 mole of acetic anhydride.
So, 0.724 moles of salicylic acid will react with =
of acetic anhydride.
Now, to calculate the mass of acetic anhydride, we use equation 1:
Moles of acetic anhydride = 0.724 moles
Molar mass of acetic anhydride = 102.09 g/mol
Putting values in equation 1, we get:
![0.724mol=\frac{\text{Mass of acetic anhydride}}{102.09g/mol}\\\\\text{Mass of acetic anhydride}=73.91g](https://tex.z-dn.net/?f=0.724mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20acetic%20anhydride%7D%7D%7B102.09g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20acetic%20anhydride%7D%3D73.91g)
Hence, the mass of acetic anhydride needed is 73.91 grams.
By stoichiometry of the reaction:
1 mole of salicylic acid is producing 1 mole of aspirin.
So, 0.724 moles of salicylic acid will produce =
of aspirin.
Now, to calculate the mass of aspirin, we use equation 1:
Moles of aspirin = 0.724 moles
Molar mass of aspirin = 180.158 g/mol
Putting values in equation 1, we get:
![0.724mol=\frac{\text{Mass of aspirin}}{180.158g/mol}\\\\\text{Mass of aspirin}=130.43g](https://tex.z-dn.net/?f=0.724mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20aspirin%7D%7D%7B180.158g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20aspirin%7D%3D130.43g)
Hence, the theoretical yield of aspirin is 130.43 grams.