Aspirin, C9H8O4, is produced from salicylic acid, C7H6O3, and acetic anhydride, C4H6O3:
C7H6O3 + C4H6O3 --> C9H8O4 + HC2H3O2
a. How much salicylic acid is required to produce 1.5 x 10^2 kg of aspirin, assuming that all of the salicylic acid is converted to aspirin?
b. how much salicylic acid would be required if only 80 percent of the salicylic acid is converted to aspirin?
c. What is the theoretical yield of aspirin if 185kg of salicylic acid is allowed to react with 125kg of acetic anhydride?
d. If the situation described in part c produces 182kg of aspirin, what is the percentage yield?
I'm really confused on this problem, please help? thanks!
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a. To find the amount of salicylic acid required to produce 1.5 x 10^2 kg of aspirin, we need to set up a mole ratio between salicylic acid and aspirin using their stoichiometric coefficients.
The balanced chemical equation is:
C7H6O3 + C4H6O3 -> C9H8O4 + HC2H3O2
From the equation, the stoichiometric coefficient of salicylic acid (C7H6O3) is 1, meaning 1 mole of salicylic acid is needed to produce 1 mole of aspirin (C9H8O4).
To calculate the amount of salicylic acid needed, we can convert the given mass of aspirin to moles using its molar mass and then convert it to the number of moles of salicylic acid.
Molar mass of aspirin (C9H8O4) = (12.01*9) + (1.01*8) + (16.00*4) = 180.16 g/mol
Number of moles of aspirin = mass of aspirin / molar mass of aspirin
= (1.5 x 10^2 kg * 10^3 g/kg) / 180.16 g/mol
Now, we know that the stoichiometric coefficient of salicylic acid is 1, so the number of moles of salicylic acid needed will be the same as the number of moles of aspirin.
Therefore, the amount of salicylic acid required to produce 1.5 x 10^2 kg of aspirin is (1.5 x 10^2 kg * 10^3 g/kg) / 180.16 g/mol.
b. If only 80% of salicylic acid is converted to aspirin, we need to calculate the amount of salicylic acid required based on this conversion efficiency.
Using the same approach as in part (a), we first calculate the number of moles of aspirin required (which would be 100% since the reaction is assumed to go to completion). Then, we divide it by the given conversion efficiency of 80% to find the amount of salicylic acid required.
Number of moles of aspirin required = mass of aspirin / molar mass of aspirin
= (1.5 x 10^2 kg * 10^3 g/kg) / 180.16 g/mol
Amount of salicylic acid required = (Number of moles of aspirin required) / 0.8
c. To find the theoretical yield of aspirin when 185 kg of salicylic acid is allowed to react with 125 kg of acetic anhydride, we need to compare the stoichiometric coefficients of salicylic acid and aspirin in the balanced chemical equation.
From the balanced equation:
1 mole of salicylic acid (C7H6O3) reacts with 1 mole of acetic anhydride (C4H6O3) to produce 1 mole of aspirin (C9H8O4).
First, convert the given masses of salicylic acid and acetic anhydride to moles using their molar masses.
Molar mass of salicylic acid (C7H6O3) = (12.01*7) + (1.01*6) + (16.00*3) = 138.12 g/mol
Molar mass of acetic anhydride (C4H6O3) = (12.01*4) + (1.01*6) + (16.00*3) = 102.09 g/mol
Number of moles of salicylic acid = mass of salicylic acid / molar mass of salicylic acid
= (185 kg * 10^3 g/kg) / 138.12 g/mol
Number of moles of acetic anhydride = mass of acetic anhydride / molar mass of acetic anhydride
= (125 kg * 10^3 g/kg) / 102.09 g/mol
The theoretical yield of aspirin is equal to the lesser of the two quantities obtained above, as it is limited by the reactant in lower quantity (according to the stoichiometry of the balanced chemical equation).
d. To calculate the percentage yield, we divide the actual yield of aspirin (given as 182 kg) by the theoretical yield (calculated in part (c)) and multiply by 100.
Percentage yield = (Actual yield / Theoretical yield) * 100
= (182 kg / Theoretical yield) * 100
To solve this problem, we need to use stoichiometry, which is the calculation of quantities in chemical reactions based on the balanced chemical equation. The balanced chemical equation provided is:
C7H6O3 + C4H6O3 → C9H8O4 + HC2H3O2
a. To determine the amount of salicylic acid required to produce 1.5 x 10^2 kg of aspirin, we need to calculate the molar ratio between salicylic acid and aspirin from the balanced equation.
According to the equation, the ratio of salicylic acid to aspirin is 1:1. This means that for every 1 mole of salicylic acid, we obtain 1 mole of aspirin.
To convert from mass (kg) to moles, we need to use the molar mass of salicylic acid:
Molar mass of C7H6O3 = 138.12 g/mol = 0.13812 kg/mol.
To find the amount of salicylic acid required, we can use the stoichiometry equation:
Number of moles of salicylic acid = (Mass of aspirin / Molar mass of C9H8O4)
Number of moles of salicylic acid = (1.5 x 10^2 kg / 0.13812 kg/mol) = 1085.48 mol
Therefore, 1085.48 moles of salicylic acid are required to produce 1.5 x 10^2 kg of aspirin.
b. If only 80 percent of the salicylic acid is converted to aspirin, we need to modify our molar ratio.
Since the molar ratio in the balanced equation is still 1:1, we can multiply the amount of salicylic acid required by 0.8 to account for the 80 percent conversion:
Amount of salicylic acid required = 1085.48 mol x 0.8 = 868.38 mol
Therefore, 868.38 moles of salicylic acid would be required if only 80 percent of the salicylic acid is converted to aspirin.
c. To determine the theoretical yield of aspirin when 185 kg of salicylic acid reacts with 125 kg of acetic anhydride, you need to calculate the limiting reactant.
To find the limiting reactant, we must compare the number of moles of each reactant using their molar masses:
Molar mass of C7H6O3 = 0.13812 kg/mol
Molar mass of C4H6O3 = 0.10209 kg/mol
Number of moles of salicylic acid = (Mass of salicylic acid / Molar mass of C7H6O3)
Number of moles of salicylic acid = (185 kg / 0.13812 kg/mol) = 1341.22 mol
Number of moles of acetic anhydride = (Mass of acetic anhydride / Molar mass of C4H6O3)
Number of moles of acetic anhydride = (125 kg / 0.10209 kg/mol) = 1223.03 mol
From these calculations, we can see that there is an excess of salicylic acid, indicating that salicylic acid is the limiting reactant. Therefore, the theoretical yield of aspirin will be determined by the amount of salicylic acid.
d. If the reaction described in part c produces 182 kg of aspirin, we can calculate the percentage yield using the following equation:
Percentage yield = (Actual yield / Theoretical yield) x 100
The actual yield is given as 182 kg in the problem, and the theoretical yield of aspirin will be determined by the amount of salicylic acid in this case.
Number of moles of salicylic acid = (Mass of salicylic acid / Molar mass of C7H6O3)
Number of moles of salicylic acid = (185 kg / 0.13812 kg/mol) = 1341.22 mol
Therefore, the theoretical yield of aspirin can be calculated using the stoichiometric ratio:
Theoretical yield = (Number of moles of salicylic acid x Molar mass of C9H8O4)
Theoretical yield = (1341.22 mol x 0.18016 kg/mol) = 241.64 kg
Now, we can calculate the percentage yield:
Percentage yield = (Actual yield / Theoretical yield) x 100
Percentage yield = (182 kg / 241.64 kg) x 100 = 75.37%
Therefore, the percentage yield is 75.37%.