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Chapter 3: Problem 88

(a) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). How many moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in a 0.500 -g tablet of aspirin? (b) How many molecules of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in this tablet? (c) How many carbon atoms are in the tablet?

Short Answer

Expert verified
In the short version, the moles of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) in a 0.500-g aspirin tablet are approximately 0.002777 mol. There are approximately \(1.672 \times 10^{21}\) molecules of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) in the tablet, with around \(1.50 \times 10^{22}\) carbon atoms.

Step by step solution

01

Calculate the molar mass of acetylsalicylic acid.

First, we need to find the molar mass of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\). We can do this by multiplying the number of atoms of each element by their respective atomic masses and summing them up. Molar mass of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) = (number of C atoms \(\times\) atomic mass of C) + (number of H atoms \(\times\) atomic mass of H) + (number of O atoms \(\times\) atomic mass of O) Molar mass of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) = (9 \(\times\) 12.01 g/mol) + (8 \(\times\) 1.01 g/mol) + (4 \(\times\) 16.00 g/mol) = 180.17 g/mol.
02

Determine the moles of acetylsalicylic acid in the tablet.

To find the moles of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\), we will use the given mass of the aspirin tablet (0.500 g) and the calculated molar mass (180.17 g/mol) using the formula: Moles of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) = mass of tablet/molar mass of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) Moles of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) = 0.500 g / 180.17 g/mol = 0.002777 mol
03

Find the number of molecules in the tablet.

To determine the number of molecules in the tablet, we will use Avogadro's number, which is approximately \(6.022 \times 10^{23}\). Number of molecules of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) = moles of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) \(\times\) Avogadro's number Number of molecules of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) = 0.002777 mol \(\times\) \(6.022 \times 10^{23}\) = \(1.672 \times 10^{21}\)
04

Calculate the number of carbon atoms in the tablet

The molecular formula of acetylsalicylic acid shows that it has 9 carbon atoms per molecule. Therefore, Number of carbon atoms in the tablet = number of molecules of \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\) \(\times\) 9 Number of carbon atoms in the tablet = \(1.672 \times 10^{21}\) \(\times\) 9 = \(15.05 \times 10^{21}\) ≈ \(1.50 \times 10^{22}\)

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Most popular questions from this chapter

The fizz produced when an Alka-Seltzer \(^{\circledast}\) tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment \(1.00 \mathrm{~g}\) of sodium bicarbonate and \(1.00 \mathrm{~g}\) of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?

Give the empirical formula of each of the following compounds if a sample contains (a) \(0.0130 \mathrm{~mol} \mathrm{C}, 0.0390 \mathrm{~mol} \mathrm{H},\) and \(0.0065 \mathrm{~mol} \mathrm{O} ;\) (b) \(11.66 \mathrm{~g}\) iron and \(5.01 \mathrm{~g}\) oxygen; (c) \(40.0 \% \mathrm{C}, 6.7 \% \mathrm{H},\) and \(53.3 \% \mathrm{O}\) by mass.

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl},\) in the atmosphere in a chemical plant is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). How many moles of vinyl chloride in each liter does this represent? How many molecules per liter?

A compound, \(\mathrm{KBrO}_{x}\), where \(x\) is unknown, is analyzed and found to contain \(52.92 \%\) Br. What is the value of \(x ?\)

Write a balanced chemical equation for the reaction that occurs when (a) calcium metal undergoes a combination reaction with \(\mathrm{O}_{2}(g) ;\) (b) copper(II) hydroxide decomposes into copper(II) oxide and water when heated; (c) heptane, \(\mathrm{C}_{7} \mathrm{H}_{16}(l),\) burns in air; (d) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l)\) burns in air.
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