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Chapter 3: Problem 90

(a) Ibuprofen is a common over-the-counter analgesic with the formula \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2} .\) How many moles of \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\) are in a 500-mg tablet of ibuprofen? Assume the tablet is composed entirely of ibuprofen. (b) How many molecules of $\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}$ are in this tablet? (c) How many oxygen atoms are in the tablet?

Short Answer

Expert verified
(a) There are 0.00242 moles of ibuprofen in the 500-mg tablet. (b) There are \(1.46 \times 10^{21}\) molecules of ibuprofen in the tablet. (c) There are \(2.92 \times 10^{21}\) oxygen atoms in the tablet.

Step by step solution

01

Calculate the molecular weight of ibuprofen

To find the molecular weight of ibuprofen, we need to add the atomic masses of all the atoms in the molecule, i.e. 13 carbon atoms, 18 hydrogen atoms, and 2 oxygen atoms. Using the atomic weights: Carbon (C): 12.01 g/mol Hydrogen (H): 1.01 g/mol Oxygen (O): 16.00 g/mol Molecular weight of ibuprofen = (13 × 12.01 g/mol) + (18 × 1.01 g/mol) + (2 × 16.00 g/mol) = 206.29 g/mol
02

Convert the mass of the tablet to grams

The mass of the tablet is given in milligrams (mg). We need to convert it to grams (g) to match the molecular weight. Mass of the tablet in grams = 500 mg × (1 g / 1000 mg) = 0.5 g
03

Calculate the number of moles of ibuprofen in the tablet

To find the number of moles, we will use the formula: Number of moles = (mass of the tablet) / (molecular weight of ibuprofen) Number of moles = (0.5 g) / (206.29 g/mol) = 0.00242 mol
04

Calculate the number of molecules of ibuprofen in the tablet

To find the number of molecules, we will use Avogadro's number (6.022 × 10^23 molecules/mol): Number of molecules = (number of moles) × (Avogadro's number) Number of molecules = (0.00242 mol) × (6.022 × 10^23 molecules/mol) = 1.46 × 10^21 molecules
05

Calculate the number of oxygen atoms in the tablet

Since there are 2 oxygen atoms in each ibuprofen molecule, we can find the total number of oxygen atoms by multiplying the number of ibuprofen molecules by 2: Number of oxygen atoms = (number of ibuprofen molecules) × 2 Number of oxygen atoms = (1.46 × 10^21 molecules) × 2 = 2.92 × 10^21 oxygen atoms So, (a) there are 0.00242 moles of ibuprofen in the 500-mg tablet, (b) there are 1.46 × 10^21 molecules of ibuprofen in the tablet, and (c) there are 2.92 × 10^21 oxygen atoms in the tablet.

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Most popular questions from this chapter

Balance the following equations: (a) $\mathrm{CaS}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{HS})_{2}(a q)+\mathrm{Ca}(\mathrm{OH})_{2}(a q)$ (b) $\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{FeCl}_{3}(s)+\mathrm{Na}_{2} \mathrm{CO}_{3}(a q) \longrightarrow \mathrm{Fe}_{2}\left(\mathrm{CO}_{3}\right)_{3}(s)+\mathrm{NaCl}(a q)$ (d) $\mathrm{FeS}_{2}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{2}(g)$

Determine the empirical and molecular formulas of each of the following substances: (a) Styrene, a compound used to make Styrofoam \(^{*}\) cups and insulation, contains \(92.3 \% \mathrm{C}\) and \(7.7 \% \mathrm{H}\) by mass and has a molar mass of \(104 \mathrm{~g} / \mathrm{mol}\). (b) Caffeine, a stimulant found in coffee, contains \(49.5 \% \mathrm{C}\), \(5.15 \% \mathrm{H}, 28.9 \% \mathrm{~N},\) and \(16.5 \% \mathrm{O}\) by mass and has a molar mass of \(195 \mathrm{~g} / \mathrm{mol}\) (c) Monosodium glutamate (MSG), a flavor enhancer in certain foods, contains \(35.51 \% \mathrm{C}, 4.77 \% \mathrm{H}, 37.85 \% \mathrm{O},\) $8.29 \% \mathrm{~N},\( and \)13.60 \% \mathrm{Na},\( and has a molar mass of \)169 \mathrm{~g} / \mathrm{mol} .$

An iron ore sample contains \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) together with other substances. Reaction of the ore with CO produces iron metal: $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) $$ (a) Balance this equation. (b) Calculate the number of grams of CO that can react with $0.350 \mathrm{~kg}\( of \)\mathrm{Fe}_{2} \mathrm{O}_{3}$ (c) Calculate the number of grams of Fe and the number of grams of \(\mathrm{CO}_{2}\) formed when \(0.350 \mathrm{~kg}\) of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ reacts. (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

An organic compound was found to contain only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{Cl}\). When a \(1.50-\mathrm{g}\) sample of the compound was completely combusted in air, \(3.52 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) was formed. In a separate experiment, the chlorine in a \(1.00-g\) sample of the compound was converted to \(1.27 \mathrm{~g}\) of AgCl. Determine the empirical formula of the compound.

An element \(\mathrm{X}\) forms an iodide \(\left(\mathrm{XI}_{3}\right)\) and a chloride \(\left(\mathrm{XCl}_{3}\right)\). The iodide is quantitatively converted to the chloride when it is heated in a stream of chlorine: $$ 2 \mathrm{XI}_{3}+3 \mathrm{Cl}_{2} \longrightarrow 2 \mathrm{XCl}_{3}+3 \mathrm{I}_{2} $$ If \(0.5000 \mathrm{~g}\) of \(\mathrm{XI}_{3}\) is treated with chlorine, $0.2360 \mathrm{~g}\( of \)\mathrm{XCl}_{3}$ is obtained. (a) Calculate the atomic weight of the element X. (b) Identify the element X.
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