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2 years ago

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Aspirin (C9H8O4) is synthesized by reacting salicylic acid (C7H6O3) with acetic anhydride (C4H6O3). The balanced equation isC7H6

O3 + C4H6O3 → C9H8O4 + HC2H3O2(a) What mass of acetic anhydride is needed to completely consume 1.00 x 10^2 g salicylic acid? (b) What is the maximum mass of aspirin (the theoretical yield) that could be produced in this reaction?

1 answer:

prisoha [69]2 years ago

4 0

<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:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$ .....(1)

<u>For a:</u>

Given mass of salicylic acid = $1.00\times 10^2g=100g$

Molar mass of salicylic acid = 138.121 g/mol

Putting values in equation 1, we get:

$\text{Moles of salicylic acid}=\frac{100g}{138.121g/mol}=0.724mol$

For the given chemical reaction:

$C_7H_6O_3+C_4H_6O_3\rightarrow C_9H_8O_4+CH_3COOH$

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 = $\frac{1}{1}\times 0.724=0.724mol$ 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:

$0.724mol=\frac{\text{Mass of acetic anhydride}}{102.09g/mol}\\\\\text{Mass of acetic anhydride}=73.91g$

Hence, the mass of acetic anhydride needed is 73.91 grams.

<u>For b:</u>

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 = $\frac{1}{1}\times 0.724=0.724mol$ 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:

$0.724mol=\frac{\text{Mass of aspirin}}{180.158g/mol}\\\\\text{Mass of aspirin}=130.43g$

Hence, the theoretical yield of aspirin is 130.43 grams.

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ΔG° = -80.9 KJ

Assuming this reaction takes place at room temperature (25 °C):

K= $1.53x10^{14}$

Explanation:

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First of all one should look up the reduction potentials for the species envolved:

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Knowing their reduction pontentials one can determine a redox pair: one species must oxidate while the other is reducing. <u>Remember: the table gives us the reduction potential, so if we want to know the oxidation potential all that has to be done is reverce the equation and change the potencial signal (multiply to -1).</u>

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(oxidation) $Fe^{2+}$ → $Fe^{3+} + e$ E°oxi=-0.771V

(reduction) $Ce^{4+} + e$ → $Ce^{3+}$ E°red=1.61V

(overall equation) $Fe^{2+}+Ce^{4+}$ → $Ce^{3+}+Fe^{3+}$ E°=Ereduction + Eoxidation= 1.61 v+(-0.771 v) = 0.839v

The cell potential can also be calculated as the cathode potencial minus the anode potential:

E° = E cathode - E anode =1.61 v - 0.771 v=0.839 v

3) Gibbs free energy and Equilibrium constant

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ΔG° = - 80963 J = -80.9 KJ

The Nerst equation gives us the relation of chemical equilibrium and Electric potential.

E=E°- $\frac{RT}{nF} Ln Q$

Where 'R' is the molar gas constant (8.314 J/mol)

It's known that in the equilibrium E=0, so the Nerst equation, at equilibrium, becomes:

E°= $\frac{RT}{nF} Ln K$

Isolating for 'K' gives:

$K=e^{\frac{nFE^{o} }{RT} }$

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K= $1.53x10^{14}$

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$Moles =\frac {Given\ mass}{Molar\ mass}$

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% moles of C = 10.13 / 12.0107 = 0.8434

% of Cl = 89.87

Molar mass of Cl = 35.453 g/mol

% moles of Cl = 89.87 / 35.453 = 2.5349

Taking the simplest ratio for C and Cl as:

0.8434 : 2.5349

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The empirical formula is = $CCl_3$

Molecular formulas is the actual number of atoms of each element in the compound while empirical formulas is the simplest or reduced ratio of the elements in the compound.

Thus,

Molecular mass = n × Empirical mass

Where, n is any positive number from 1, 2, 3...

Mass from the Empirical formula = 12*1 + 3*35.5 = 118.5 g/mol

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So,

Molecular mass = n × Empirical mass

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The molecular formula = $C_2Cl_6$

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