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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]\[2 C _6 H _4\left( CO _2 H \right)( OH )+\left( CH _3 CO \right)_2 O \rightarrow C _6 H _4\left( CO _2 H \right)\left( CO _2 CH _3\right)+ H _2 O\][/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 determine the volume of acetic anhydride needed to produce 1.00 kg (1000 g) of aspirin with a 100% yield, we can follow these steps:

1. Calculate the moles of aspirin to be produced:

The molar mass of aspirin ([tex]\(C_9H_8O_4\)[/tex]) is 180.16 g/mol.

[tex]\[ \text{moles of aspirin} = \frac{\text{mass of aspirin}}{\text{molar mass of aspirin}} = \frac{1000 \text{ g}}{180.16 \text{ g/mol}} \approx 5.5506 \text{ mol} \][/tex]

2. Determine the moles of acetic anhydride required:

The reaction shows that 1 mole of acetic anhydride ([tex]\((CH_3CO)_2O\)[/tex]) produces 2 moles of aspirin. Therefore, the moles of acetic anhydride needed is the same as the moles of aspirin because each acetic anhydride molecule is responsible for producing one aspirant molecule, simplifying the stoichiometry to a 1:1 molar ratio.

[tex]\[ \text{moles of acetic anhydride} = \text{moles of aspirin} = 5.5506 \text{ mol} \][/tex]

3. Calculate the mass of acetic anhydride required:

The molar mass of acetic anhydride is 102.09 g/mol.

[tex]\[ \text{mass of acetic anhydride} = \text{moles of acetic anhydride} \times \text{molar mass of acetic anhydride} = 5.5506 \text{ mol} \times 102.09 \text{ g/mol} = 566.663 \text{ g} \][/tex]

4. Calculate the volume of acetic anhydride needed:

The density of acetic anhydride is 1.0820 g/cm³.

[tex]\[ \text{volume of acetic anhydride} = \frac{\text{mass of acetic anhydride}}{\text{density of acetic anhydride}} = \frac{566.663 \text{ g}}{1.0820 \text{ g/cm}^3} \approx 523.718 \text{ cm}^3 \][/tex]

Since 1 cm³ is equivalent to 1 mL, we can express the volume as:

[tex]\[ \text{volume of acetic anhydride} \approx 523.718 \text{ mL} \][/tex]

Thus, the volume of acetic anhydride required to produce 1.00 kg of aspirin, assuming a 100% yield, is approximately 523.718 mL.

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