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3 years ago

Nitrogen-13 has a half-life of about 10 minutes. How much of a 320g sample of N-13 would remain after 40 minutes?

Chemistry

1 answer:

lubasha [3.4K]3 years ago

5 0

Answer:

The half-life of a radioisotope describes the amount of time it takes for said isotope to decay to one-half the original amount present in the sample.

Nitrogen-13, because it has a half-life of ten minutes, will experience two half-lives over the course of the twenty minute period. This means that 25% of the isotope will remain after this.

0.25 x 128mg = 32mg

32mg of Nitrogen-13 will remain after 20 minutes.

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

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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:

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

For a:

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.

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