Answered

Aspirin, [tex]C _6 H _4\left( CO _2 H \right)\left( CO _2 CH _3\right)[/tex], can be prepared in the chemistry laboratory by the reaction of salicylic acid, [tex]C _6 H _4\left( CO _2 H \right)( OH )[/tex], with acetic anhydride, [tex]\left( CH _3 CO \right)_2 O[/tex]:

[tex]\[
C _6 H _4\left( CO _2 H \right)( OH )+\left( CH _3 CO \right)_2 O \rightarrow C _6 H _4\left( CO _2 H \right)\left( CO _2 CH _3\right)+ H _2 O
\][/tex]

What volume of acetic anhydride (density, [tex]1.0820 \, \text{g/cm}^3[/tex]) is required to produce 1.00 kg of aspirin, assuming a [tex]100 \%[/tex] yield?

[Ans: 262 ml]



Answer :

GinnyAnswer
To solve this problem, we need to determine the volume of acetic anhydride required to produce 1.00 kg (or 1000 grams) of aspirin. We'll walk through the process with the necessary steps and given constants.

### Step-by-Step Solution:

1. Determine the molar masses:
- Molar mass of aspirin ([tex]$C_9H_8O_4$[/tex]): The molar mass of aspirin is [tex]\( 180.158 \)[/tex] g/mol.
- Molar mass of acetic anhydride ([tex]$C_4H_6O_3$[/tex]): The molar mass of acetic anhydride is [tex]\( 102.09 \)[/tex] g/mol.

2. Calculate the moles of aspirin produced:
Given the mass of aspirin produced is 1000 grams:
[tex]\[ \text{Moles of aspirin} = \frac{\text{mass of aspirin produced}}{\text{molar mass of aspirin}} = \frac{1000 \text{ g}}{180.158 \text{ g/mol}} \approx 5.55068 \text{ mol} \][/tex]

3. Use stoichiometry to find moles of acetic anhydride required:
From the chemical equation, the reaction between salicylic acid and acetic anhydride to form aspirin is a 1:1 molar ratio. Therefore:
[tex]\[ \text{Moles of acetic anhydride required} = \text{Moles of aspirin} = 5.55068 \text{ mol} \][/tex]

4. Calculate the mass of acetic anhydride required:
Using the molar mass of acetic anhydride:
[tex]\[ \text{Mass of acetic anhydride required} = \text{moles of acetic anhydride} \times \text{molar mass of acetic anhydride} = 5.55068 \text{ mol} \times 102.09 \text{ g/mol} \approx 566.669 \text{ g} \][/tex]

5. Convert mass to volume using the density of acetic anhydride:
Given that the density of acetic anhydride is 1.0820 g/cm³:
[tex]\[ \text{Volume of acetic anhydride} = \frac{\text{mass of acetic anhydride}}{\text{density of acetic anhydride}} = \frac{566.669 \text{ g}}{1.0820 \text{ g/cm}^3} \approx 523.724 \text{ cm}^3 \][/tex]

6. Convert cm³ to mL:
Since [tex]\(1 \text{ cm}^3 = 1 \text{ mL}\)[/tex]:
[tex]\[ \text{Volume of acetic anhydride} = 523.724 \text{ cm}^3 = 523.724 \text{ mL} \][/tex]

### Conclusion:
The volume of acetic anhydride required to produce 1.00 kg of aspirin, assuming a 100% yield, is approximately [tex]\( 523.724 \)[/tex] mL.