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Chapter 3: Problem 118

The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{3} \mathrm{O}_{4}\). a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains \(500 . \mathrm{mg} \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .\) What amount (moles) of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) molecules and what number of molecules of acetylsalicylic acid are in a \(500 .-\mathrm{mg}\) tablet?

Short Answer

Expert verified
a. The molar mass of aspirin can be calculated as: \(Molar~mass~of~aspirin = 9*(12.01~g/mol) + 8*(1.01~g/mol) + 4*(16.00~g/mol) = 180.17~g/mol\) b. The amount (moles) of aspirin in a 500 mg tablet is: \(Amount~(moles)~of~aspirin = 0.5~g / 180.17~g/mol = 2.775 \times 10^{-3}~moles\) The number of molecules of aspirin in the tablet is: \(Number~of~molecules~of~aspirin = 2.775 \times 10^{-3}~moles * 6.022 \times 10^{23}~molecules/mol = 1.67 \times 10^{21}~molecules\)

Step by step solution

01

Calculate the molar mass of aspirin

Using the molecular formula of aspirin, \(C_9H_8O_4\), we can calculate its molar mass using the atomic weights of carbon (C), hydrogen (H), and oxygen (O). The atomic weights can be found in a periodic table: Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.01 g/mol, Oxygen (O) = 16.00 g/mol. Molar mass of aspirin = 9*(Molar mass of Carbon) + 8*(Molar mass of Hydrogen) + 4*(Molar mass of Oxygen) Molar mass of aspirin = 9*(12.01 g/mol) + 8*(1.01 g/mol) + 4*(16.00 g/mol)
02

Convert the mass of aspirin from mg to grams

The mass of aspirin in a tablet is given in mg: 500 mg. To calculate the amount (moles), we need to convert it into grams. Since 1g = 1000 mg, we can do this conversion: Mass of aspirin in grams = 500 mg / 1000 mg/g = 0.5 g
03

Determine the amount (moles) of aspirin in a 500 mg tablet

Now that we have the mass of aspirin in grams and its molar mass, we can calculate the amount (moles) of aspirin in a 500 mg tablet using the formula: moles = mass (g) / molar mass (g/mol) Amount (moles) of aspirin = 0.5 g / Molar mass of aspirin
04

Calculate the number of molecules of aspirin

Finally, we can determine the number of molecules of aspirin in the tablet using Avogadro's number, which is \(6.022 \times 10^{23}\) molecules per mole. Number of molecules of aspirin = Amount (moles) of aspirin * Avogadro's number By following these steps systematically, we can answer the given questions and find the molar mass, amount (moles), and the number of molecules of aspirin in a 500 mg tablet.

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Most popular questions from this chapter

Several important compounds contain only nitrogen and oxygen. Place the following compounds in order of increasing mass percent of nitrogen. a. NO, a gas formed by the reaction of \(\mathrm{N}_{2}\) with \(\mathrm{O}_{2}\) in internal combustion engines b. \(\mathrm{NO}_{2}\), a brown gas mainly responsible for the brownish color of photochemical smog c. \(\mathrm{N}_{2} \mathrm{O}_{4}\), a colorless liquid used as fuel in space shuttles d. \(\mathrm{N}_{2} \mathrm{O}\), a colorless gas sometimes used as an anesthetic by dentists (known as laughing gas)

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