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Chapter 3: Problem 70

The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains \(500 . \mathrm{mg} \mathrm{C}_{9} \mathrm{H}_{\mathrm{g}} \mathrm{O}_{4} .\) 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
The molar mass of aspirin (acetylsalicylic acid) is approximately 180.154 g/mol. A 500-mg tablet contains approximately 0.00277 moles of aspirin, which is equivalent to \(1.67 \times 10^{21}\) molecules.

Step by step solution

01

Calculate the molar mass of aspirin.

To calculate the molar mass of aspirin, we sum up the molar masses of every atom in the molecule. Aspirin has the molecular formula \(C_9H_8O_4\). Thus, the molar mass can be calculated as follows: Molar mass = 9(Molar mass of C) + 8(Molar mass of H) + 4(Molar mass of O) Using the atomic masses from the periodic table: the molar mass of C = 12.01 g/mol, H = 1.008 g/mol, and O = 16.00 g/mol, we can plug these values into the equation: Molar mass = 9(12.01\(\ g/mol\)) + 8(1.008\(\ g/mol\)) + 4(16.00\(\ g/mol\)) Molar mass = 108.09\(\ g/mol\) + 8.064\(\ g/mol\) + 64.00\(\ g/mol\) Molar mass = 180.154\(\ g/mol\)
02

Convert mass of aspirin to moles.

Given that a typical aspirin tablet contains 500 mg of aspirin, we need to convert this mass into moles. To do this, we'll use the molar mass calculated in the previous step. First, convert 500 mg to grams: 500 mg = 0.5 g Then, we can use the molar mass to find the number of moles: Moles = mass (g) / molar mass (g/mol) Moles = \( \tfrac{0.5\ g}{180.154\ g/mol} \) Moles ≈ 0.00277 moles
03

Calculate the number of molecules of aspirin.

To find the number of molecules of aspirin, we'll use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles/mol. Number of molecules = Moles × Avogadro's number Number of molecules = 0.00277 moles × \(6.022 \times 10^{23}\) molecules/mol Number of molecules ≈ \(1.67 \times 10^{21}\) molecules So, a 500-mg tablet contains approximately \(1.67 \times 10^{21}\) molecules of acetylsalicylic acid.

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Most popular questions from this chapter

Ammonia reacts with \(\mathrm{O}_{2}\) to form either \(\mathrm{NO}(g)\) or \(\mathrm{NO}_{2}(g) \mathrm{ac}-\) cording to these unbalanced equations: $$ \begin{array}{l} \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \\ \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ In a certain experiment \(2.00\) moles of \(\mathrm{NH}_{3}(g)\) and \(10.00 \mathrm{moles}\) of \(\mathrm{O}_{2}(g)\) are contained in a closed flask. After the reaction is complete, \(6.75\) moles of \(\mathrm{O}_{2}(g)\) remains. Calculate the number of moles of \(\mathrm{NO}(g)\) in the product mixture: (Hint: You cannot do this problem by adding the balanced equations because you cannot assume that the two reactions will occur with equal probability.)

ABS plastic is a tough, hard plastic used in applications requiring shock resistance. The polymer consists of three monomer units: acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}\right)\), butadiene \(\left(\mathrm{C}_{4} \mathrm{H}_{6}\right)\), and styrene \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\). a. A sample of ABS plastic contains \(8.80 \% \mathrm{~N}\) by mass. It took \(0.605 \mathrm{~g}\) of \(\mathrm{Br}_{2}\) to react completely with a \(1.20-\mathrm{g}\) sample of ABS plastic. Bromine reacts \(1: 1\) (by moles) with the butadiene molecules in the polymer and nothing else. What is the percent by mass of acrylonitrile and butadiene in this polymer? b. What are the relative numbers of each of the monomer units in this polymer?

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