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Answer :
To determine the number of moles of ibuprofen the patient takes each day, follow these steps:
1. Identify the mass of ibuprofen prescribed per day: The prescription is for 3,200 mg of ibuprofen each day.
2. Convert milligrams to grams: Since 1 gram equals 1,000 milligrams, we convert the prescribed amount from milligrams to grams:
[tex]\[
3,200 \, \text{mg} = \frac{3,200}{1,000} \, \text{g} = 3.2 \, \text{g}
\][/tex]
3. Find the molar mass of ibuprofen: The molar mass of ibuprofen ([tex]\(C_{13}H_{18}O_2\)[/tex]) is approximately 206.29 grams per mole.
4. Calculate the number of moles: To find out how many moles are in 3.2 grams of ibuprofen, use the formula:
[tex]\[
\text{Moles of ibuprofen} = \frac{\text{mass in grams}}{\text{molar mass}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Moles of ibuprofen} = \frac{3.2 \, \text{g}}{206.29 \, \text{g/mol}} \approx 0.0155 \, \text{moles}
\][/tex]
5. Express the result in scientific notation: We can express 0.0155 moles in scientific notation as [tex]\(1.55 \times 10^{-2}\)[/tex].
Therefore, the patient takes approximately [tex]\(1.55 \times 10^{-2}\)[/tex] moles of ibuprofen each day.
1. Identify the mass of ibuprofen prescribed per day: The prescription is for 3,200 mg of ibuprofen each day.
2. Convert milligrams to grams: Since 1 gram equals 1,000 milligrams, we convert the prescribed amount from milligrams to grams:
[tex]\[
3,200 \, \text{mg} = \frac{3,200}{1,000} \, \text{g} = 3.2 \, \text{g}
\][/tex]
3. Find the molar mass of ibuprofen: The molar mass of ibuprofen ([tex]\(C_{13}H_{18}O_2\)[/tex]) is approximately 206.29 grams per mole.
4. Calculate the number of moles: To find out how many moles are in 3.2 grams of ibuprofen, use the formula:
[tex]\[
\text{Moles of ibuprofen} = \frac{\text{mass in grams}}{\text{molar mass}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Moles of ibuprofen} = \frac{3.2 \, \text{g}}{206.29 \, \text{g/mol}} \approx 0.0155 \, \text{moles}
\][/tex]
5. Express the result in scientific notation: We can express 0.0155 moles in scientific notation as [tex]\(1.55 \times 10^{-2}\)[/tex].
Therefore, the patient takes approximately [tex]\(1.55 \times 10^{-2}\)[/tex] moles of ibuprofen each day.
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