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Chapter 3: Problem 47

Ibuprofen, the active ingredient in Advil \(^{\text {m }}\), is made up of carbon, hydrogen, and oxygen atoms. When a sample of ibuprofen, weighing \(5.000 \mathrm{~g}\), burns in oxygen, \(13.86 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(3.926 \mathrm{~g}\) of water are obtaine \(\mathrm{d} .\) What is the simplest formula of ibuprofen?

Short Answer

Expert verified
Answer: The simplest formula for Ibuprofen is C6H9O.

Step by step solution

01

Calculate the moles of Carbon Dioxide and Water

Using the given weights of Carbon Dioxide (CO2) and Water (H2O), calculate the number of moles of each product. For CO2: (13.86 g) / (44.01 g/mol) = 0.315 moles For H2O: (3.926 g) / (18.02 g/mol) = 0.218 moles
02

Determine the moles of Carbon and Hydrogen in Ibuprofen

The moles of Carbon and Hydrogen in Ibuprofen can be found using the mole ratio of CO2 and H2O. In CO2, there is 1 mole of Carbon for every 1 mole of CO2. In H2O, there are 2 moles of Hydrogen for every 1 mole of H2O. Moles of Carbon = moles of CO2 = 0.315 moles Moles of Hydrogen = 2 x moles of H2O = 2 x 0.218 moles = 0.436 moles
03

Calculate the weight of Carbon and Hydrogen in Ibuprofen

Using the moles of Carbon and Hydrogen found in step 2, calculate the weight of Carbon and Hydrogen in Ibuprofen. Weight of Carbon = (0.315 moles) x (12.01 g/mol) = 3.783 g Weight of Hydrogen = (0.436 moles) x (1.01 g/mol) = 0.440 g
04

Calculate the weight of Oxygen in Ibuprofen

Subtract the weights of Carbon and Hydrogen from the total weight of Ibuprofen to find the weight of Oxygen. Total weight of Ibuprofen = 5.000 g Weight of Oxygen = Total weight - (Weight of Carbon + Weight of Hydrogen) = 5.000 g - (3.783 g + 0.440 g) = 0.777 g
05

Calculate the moles of Oxygen in Ibuprofen

Divide the weight of Oxygen by its molar mass to find the moles of Oxygen in Ibuprofen. Moles of Oxygen = (0.777 g) / (16.00 g/mol) = 0.0486 moles
06

Find the ratio of moles of Carbon, Hydrogen, and Oxygen in Ibuprofen

Divide the moles of each element by the smallest number of moles among the three elements to find the mole ratio. Mole ratio of C : H : O = (0.315 : 0.436 : 0.0486) / 0.0486 = 6.48 : 8.97 : 1 Since the mole ratio should be integer values, round the ratios to the nearest whole numbers. Mole ratio of C : H : O ≈ 6 : 9 : 1
07

Write the simplest formula of Ibuprofen

Use the mole ratio found in step 6 to write the simplest formula for Ibuprofen. Ibuprofen simplest formula: C6H9O1 (or simply C6H9O) The simplest formula for Ibuprofen is C6H9O.

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Most popular questions from this chapter

Write balanced equations for the reaction of sulfur with the following metals to form solids that you can take to be ionic when the anion is \(\mathrm{S}^{2-}\). (a) potassium (b) magnesium (c) aluminum (d) calcium (e) iron (forming \(\mathrm{Fe}^{2+}\) ions)

The active ingredient of some antiperspirants is \(\mathrm{Al}_{2}(\mathrm{OH})_{5} \mathrm{Cl} .\) Calculate the mass percent of each element in this ingredient.

Calculate the mass in grams of \(2.688 \mathrm{~mol}\) of (a) chlorophyll, \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{~N}_{4} \mathrm{O}_{5} \mathrm{Mg}\), responsible for the green color of leaves. (b) sorbitol, \(\mathrm{C}_{9} \mathrm{H}_{14} \mathrm{O}_{6}\), an artificial sweetener. (c) indigo, \(\mathrm{C}_{16} \mathrm{H}_{10} \mathrm{~N}_{2} \mathrm{O}_{2}\), a blue dye.

Diborane, \(\mathrm{B}_{2} \mathrm{H}_{6}\), can be prepared by the following reaction: $$ 3 \mathrm{NaBH}_{4}(s)+4 \mathrm{BF}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{~B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{NaBF}_{4}(s) $$ (a) How many moles of \(\mathrm{NaBH}_{4}\) react with \(1.299 \mathrm{~mol}\) of \(\mathrm{BF}_{3} ?\) (b) How many moles of \(\mathrm{B}_{2} \mathrm{H}_{6}\) can be obtained from \(0.893 \mathrm{~mol}\) of \(\mathrm{NaBH}_{4} ?\) (c) If \(1.987 \mathrm{~mol}\) of \(\mathrm{B}_{2} \mathrm{H}_{6}\) is obtained, how many moles of \(\mathrm{NaBF}_{4}\) are produced? (d) How many moles of \(\mathrm{BF}_{3}\) are required to produce \(4.992 \mathrm{~mol}\) of \(\mathrm{NaBF}_{4} ?\)

Perhaps the simplest way to calculate Avogadro's number is to compare the charge on the electron, first determined by Robert Millikan in 1909, with the charge on a mole of electrons, determined electrochemically (Chapter 18). These charges, in coulombs (C), are given in Appendix 1 . Use them to calculate Avogadro's number to five significant figures.
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