Respuesta :
Answer:
For a: The mass of acetic anhydride needed is 73.91 grams.
For b: The theoretical yield of aspirin is 130.43 grams.
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
- For a:
Given mass of salicylic acid = [tex]1.00\times 10^2g=100g[/tex]
Molar mass of salicylic acid = 138.121 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of salicylic acid}=\frac{100g}{138.121g/mol}=0.724mol[/tex]
For the given chemical reaction:
[tex]C_7H_6O_3+C_4H_6O_3\rightarrow C_9H_8O_4+CH_3COOH[/tex]
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 = [tex]\frac{1}{1}\times 0.724=0.724mol[/tex] 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:
[tex]0.724mol=\frac{\text{Mass of acetic anhydride}}{102.09g/mol}\\\\\text{Mass of acetic anhydride}=73.91g[/tex]
Hence, the mass of acetic anhydride needed is 73.91 grams.
- For b:
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 = [tex]\frac{1}{1}\times 0.724=0.724mol[/tex] 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:
[tex]0.724mol=\frac{\text{Mass of aspirin}}{180.158g/mol}\\\\\text{Mass of aspirin}=130.43g[/tex]
Hence, the theoretical yield of aspirin is 130.43 grams.
(a) The mass of acetic anhydride needed to completely consume the salicylic acid is 73.9 g
(b) The maximum mass of aspirin that could be produced in the reaction is 130.4 g
(a)
From the question,
We are to determine the mass of acetic anhydride that is needed to completely consume 1.00 × 10² g salicylic acid
The given balanced chemical equation for the reaction is
C₇H₆O₃ + C₄H₆O₃ → C₉H₈O₄ + HC₂H₃O₂
This means
1 mole of salicylic acid (C₇H₆O₃) is required to completely react with 1 mole of acetic anhydride (C₄H₆O₃) to produce 1 mole of aspirin (C₉H₈O₄) and 1 mole of HC₂H₃O₂
Now, we will determine the number of moles of salicylic acid present
From the given information,
Mass of salicylic acid = 1.00 × 10² g = 100 g
Using the formula
[tex]Number\ of\ formula = \frac{Mass}{Molar\ mass}[/tex]
Molar mass of salicylic acid = 138.121 g/mol
∴ Number of moles of salicylic acid present = [tex]\frac{100}{138.121}[/tex]
Number of moles of salicylic acid present = 0.724 mole
Since,
1 mole of salicylic acid (C₇H₆O₃) is required to completely react with 1 mole of acetic anhydride (C₄H₆O₃)
Then,
0.724 mole of salicylic acid (C₇H₆O₃) would be required to completely react with 0.724 mole of acetic anhydride (C₄H₆O₃)
∴ The number of moles of acetic anhydride needed is 0.724 mole
Now, for the mass of acetic anhydride needed
From the formula
Mass = Number of moles × Molar mass
Molar mass of acetic anhydride = 102.09 g/mol
∴ Mass of acetic anhydride needed = 0.724 × 102.09
Mass of acetic anhydride needed = 73.91345 g
Mass of acetic anhydride needed ≅ 73.9 g
Hence, the mass of acetic anhydride needed to completely consume the salicylic acid is 73.9 g
(b)
We are to determine the maximum mass of aspirin that could be produced in this reaction,
From the balanced chemical equation
1 mole of salicylic acid (C₇H₆O₃) is required to completely react with 1 mole of acetic anhydride (C₄H₆O₃) to produce 1 mole of aspirin (C₉H₈O₄)
Then,
0.724 mole of salicylic acid (C₇H₆O₃) will react with 0.724 mole of acetic anhydride (C₄H₆O₃) to produce 0.724 mole of aspirin (C₉H₈O₄)
∴ The maximum number of mole of aspirin that could be produced is 0.724 mole
Now,
For the maximum mass of aspirin that could be produced in the reaction,
Using the formula
Mass = Number of moles × Molar mass
Molar mass of aspirin = 180.158 g/mol
∴ The maximum mass of aspirin that could be produced = 0.724 × 180.158
The maximum mass of aspirin that could be produced = 130.4344 g
The maximum mass of aspirin that could be produced ≅ 130.4 g
Hence, The maximum mass of aspirin that could be produced in the reaction is 130.4 g
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