How Many Moles Of C { _9$} H H H { _8\$} O { _4$}$ Are In A 0.700-g Tablet Of Aspirin? Assume The Tablet Is Composed Entirely Of Aspirin. Express Your Answer In Moles To Three Significant Figures.
Understanding the Problem
Aspirin, also known as acetylsalicylic acid, is a common over-the-counter medication used to relieve pain and reduce inflammation. In this problem, we are tasked with determining the number of moles of aspirin present in a 0.700-g tablet. To solve this, we will need to use the molar mass of aspirin and the given mass of the tablet.
Calculating the Molar Mass of Aspirin
The molar mass of a substance is the sum of the atomic masses of its constituent atoms. The molecular formula for aspirin is C$_9$]H$_8$]O$_4$]. To calculate the molar mass of aspirin, we need to find the atomic masses of carbon (C), hydrogen (H), and oxygen (O).
The atomic mass of carbon is 12.01 g/mol, the atomic mass of hydrogen is 1.008 g/mol, and the atomic mass of oxygen is 16.00 g/mol. Using these values, we can calculate the molar mass of aspirin as follows:
Molar mass of aspirin = (9 x 12.01 g/mol) + (8 x 1.008 g/mol) + (4 x 16.00 g/mol) Molar mass of aspirin = 108.09 g/mol + 8.064 g/mol + 64.00 g/mol Molar mass of aspirin = 180.154 g/mol
Converting Mass to Moles
Now that we have the molar mass of aspirin, we can use it to convert the given mass of the tablet to moles. The formula to convert mass to moles is:
moles = mass / molar mass
Plugging in the values, we get:
moles = 0.700 g / 180.154 g/mol
Performing the Calculation
To perform the calculation, we need to divide 0.700 g by 180.154 g/mol. This will give us the number of moles of aspirin present in the tablet.
moles = 0.700 g / 180.154 g/mol moles = 0.00388 mol
Rounding to Three Significant Figures
The problem asks us to express our answer in moles to three significant figures. To do this, we need to round our answer to three significant figures.
Rounded to three significant figures, the number of moles of aspirin present in the tablet is:
moles = 0.00389 mol
Conclusion
In this problem, we used the molar mass of aspirin to convert the given mass of a tablet to moles. We calculated the molar mass of aspirin by summing the atomic masses of its constituent atoms and then used it to perform the conversion. Our final answer is 0.00389 mol, which represents the number of moles of aspirin present in the tablet.
Additional Information
Aspirin is a common medication used to relieve pain and reduce inflammation. It is available in various forms, including tablets, capsules, and powders. The molar mass of aspirin is an important value in chemistry, as it allows us to convert between mass and moles of the substance.
Real-World Applications
The ability to convert between mass and moles of a substance is crucial in many real-world applications. For example, in pharmaceutical manufacturing, knowing the number of moles of a medication present in a tablet is essential for ensuring the correct dosage. Similarly, in chemical synthesis, knowing the number of moles of a reactant is necessary for scaling up a reaction.
Limitations of the Calculation
One limitation of this calculation is that it assumes the tablet is composed entirely of aspirin. In reality, tablets may contain other ingredients, such as fillers or binders, which can affect the molar mass of the substance. Additionally, the calculation assumes that the molar mass of aspirin is constant, which may not be the case in all situations.
Future Directions
Future research in this area could focus on developing more accurate methods for calculating the molar mass of complex substances like aspirin. Additionally, researchers could explore the use of advanced techniques, such as spectroscopy or chromatography, to determine the number of moles of a substance present in a sample.
Conclusion
In conclusion, we have used the molar mass of aspirin to convert the given mass of a tablet to moles. Our final answer is 0.00389 mol, which represents the number of moles of aspirin present in the tablet. This calculation has important implications for pharmaceutical manufacturing and chemical synthesis, and highlights the importance of accurately determining the number of moles of a substance present in a sample.
Q: What is the molar mass of aspirin?
A: The molar mass of aspirin is 180.154 g/mol, which is calculated by summing the atomic masses of its constituent atoms: carbon (C), hydrogen (H), and oxygen (O).
Q: How do I convert mass to moles of aspirin?
A: To convert mass to moles of aspirin, you can use the formula: moles = mass / molar mass. For example, if you have a 0.700-g tablet of aspirin, you can calculate the number of moles as follows: moles = 0.700 g / 180.154 g/mol.
Q: What is the significance of the molar mass of aspirin?
A: The molar mass of aspirin is an important value in chemistry, as it allows us to convert between mass and moles of the substance. This is crucial in pharmaceutical manufacturing, where knowing the number of moles of a medication present in a tablet is essential for ensuring the correct dosage.
Q: Can I assume that the tablet is composed entirely of aspirin?
A: No, it's not always safe to assume that the tablet is composed entirely of aspirin. In reality, tablets may contain other ingredients, such as fillers or binders, which can affect the molar mass of the substance. It's always best to check the label or consult with a pharmacist to determine the exact composition of the tablet.
Q: How do I determine the number of moles of aspirin present in a tablet?
A: To determine the number of moles of aspirin present in a tablet, you can use the formula: moles = mass / molar mass. You will need to know the mass of the tablet and the molar mass of aspirin, which is 180.154 g/mol.
Q: What are some real-world applications of converting mass to moles of aspirin?
A: Converting mass to moles of aspirin has important implications for pharmaceutical manufacturing and chemical synthesis. For example, in pharmaceutical manufacturing, knowing the number of moles of a medication present in a tablet is essential for ensuring the correct dosage. Similarly, in chemical synthesis, knowing the number of moles of a reactant is necessary for scaling up a reaction.
Q: Can I use this calculation to determine the number of moles of aspirin present in a capsule or powder?
A: No, this calculation is specific to tablets and assumes that the tablet is composed entirely of aspirin. Capsules and powders may have different compositions and may require different calculations to determine the number of moles of aspirin present.
Q: How do I round my answer to three significant figures?
A: To round your answer to three significant figures, you can look at the fourth significant figure and decide whether to round up or down. If the fourth significant figure is less than 5, you round down. If the fourth significant figure is 5 or greater, you round up.
Q: What are some limitations of this calculation?
A: One limitation of this calculation is that it assumes the tablet is composed entirely of aspirin. In reality, tablets may contain other ingredients, such as fillers or binders, which can affect the molar mass of the substance. Additionally, the calculation assumes that the molar mass of aspirin is constant, which may not be the case in all situations.
Q: Can I use this calculation to determine the number of moles of other substances?
A: Yes, this calculation can be used to determine the number of moles of other substances, as long as you know the molar mass of the substance and the mass of the sample. Simply plug in the values and use the formula: moles = mass / molar mass.