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Chapter 3: Problem 40

The molecular formula of salicylic acid, a compound commonly found in facial cleanser, is \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\). (a) What is the molar mass of salicylic acid? (b) How many moles of salicylic acid are present in \(0.5 \mathrm{mg}\) of this substance? (c) How many molecules of salicylic acid are in \(0.5 \mathrm{mg}\) of this substance? (d) How many oxygen atoms are present in \(0.5 \mathrm{mg}\) of salicylic acid?

Short Answer

Expert verified
(a) The molar mass of salicylic acid is 138.13 g/mol. (b) There are 3.62 x 10^(-6) moles of salicylic acid in 0.5 mg of the substance. (c) There are 2.18 x 10^(18) molecules of salicylic acid in 0.5 mg of the substance. (d) There are 6.53 x 10^(18) oxygen atoms in 0.5 mg of salicylic acid.

Step by step solution

01

Calculate the molar mass of salicylic acid

To calculate the molar mass of salicylic acid (C₇H₆O₃), we need to find the sum of the molar mass of each of its elements (C, H, and O) as they appear in the molecular formula: Molar mass of salicylic acid = (7 x molar mass of Carbon) + (6 x molar mass of Hydrogen) + (3 x molar mass of Oxygen) Using the standard atomic weights: Carbon: 12.01 g/mol Hydrogen: 1.01 g/mol Oxygen: 16 g/mol Molar mass of salicylic acid = (7 x 12.01) + (6 x 1.01) + (3 x 16) = 84.07 + 6.06 + 48 = 138.13 g/mol
02

(b) Calculate the number of moles of salicylic acid in 0.5 mg

To find the number of moles of salicylic acid in 0.5 mg, we will use the following formula: Number of moles = mass of substance / molar mass First, convert 0.5 mg to grams: 0.5 mg = 0.0005 g Now, divide the mass of substance by its molar mass: Number of moles = 0.0005 g / 138.13 g/mol = 3.62 x 10^(-6) moles
03

(c) Calculate the number of molecules of salicylic acid in 0.5 mg

To find the number of molecules of salicylic acid in 0.5 mg, we will use Avogadro's number, which is approximately 6.022 x 10^(23) particles (atoms, ions, or molecules) per mole. Number of molecules = number of moles x Avogadro's number Number of molecules = 3.62 x 10^(-6) moles x 6.022 x 10^(23) molecules/mole = 2.18 x 10^(18) molecules
04

(d) Calculate the number of oxygen atoms in 0.5 mg of salicylic acid

To find the number of oxygen atoms in 0.5 mg of salicylic acid, we will first determine the number of moles of oxygen present in our given amount of salicylic acid. Since there are 3 oxygen atoms in one molecule of salicylic acid, the number of moles of oxygen will be three times the number of moles of salicylic acid. Number of moles of oxygen = 3 x 3.62 x 10^(-6) moles = 10.86 x 10^(-6) moles Now, we will multiply the number of moles of oxygen by Avogadro's number to obtain the total number of oxygen atoms: Number of oxygen atoms = 10.86 x 10^(-6) moles x 6.022 x 10^(23) atoms/mole = 6.53 x 10^(18) oxygen atoms

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Most popular questions from this chapter

(a) Combustion analysis of toluene, a common organic solvent, gives $5.86 \mathrm{mg}\( of \)\mathrm{CO}_{2}\( and \)1.37 \mathrm{mg}\( of \)\mathrm{H}_{2} \mathrm{O} .$ If the compound contains only carbon and hydrogen, what is its empirical formula? (b) Menthol, the substance we can smell in mentholated cough drops, is composed of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\). A \(0.1005-g\) sample of menthol is combusted, producing \(0.2829 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.1159 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula for menthol? If menthol has a molar mass of $156 \mathrm{~g} / \mathrm{mol}$, what is its molecular formula?

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally $\mathrm{N}_{2}(\sim 79 \%)\( and \)\mathrm{O}_{2}(\sim 20 \%) .$ In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NO \(_{x}\) " gases. In 2009 , the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{x}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) into \(\mathrm{CO}_{2}\) and water. If \(85 \%\) of the oxygen in an engine is used to combust octane and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of \(500 \mathrm{~g}\) of octane.

A mixture containing $\mathrm{KClO}_{3}, \mathrm{~K}_{2} \mathrm{CO}_{3}, \mathrm{KHCO}_{3},\( and \)\mathrm{KCl}\( was heated, producing \)\mathrm{CO}_{2}, \mathrm{O}_{2}\(, and \)\mathrm{H}_{2} \mathrm{O}$ gases according to the following equations: $$ \begin{aligned} 2 \mathrm{KClO}_{3}(s) & \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g) \\\ 2 \mathrm{KHCO}_{3}(s) & \longrightarrow \mathrm{K}_{2} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{CO}_{2}(g) \\ \mathrm{K}_{2} \mathrm{CO}_{3}(s) & \longrightarrow \mathrm{K}_{2} \mathrm{O}(s)+\mathrm{CO}_{2}(g) \end{aligned} $$ The KCl does not react under the conditions of the reaction. If $100.0 \mathrm{~g}\( of the mixture produces \)1.80 \mathrm{~g}\( of \)\mathrm{H}_{2} \mathrm{O}, 13.20 \mathrm{~g}\( of \)\mathrm{CO}_{2}$, and \(4.00 \mathrm{~g}\) of \(\mathrm{O}_{2}\), what was the composition of the original mixture? (Assume complete decomposition of the mixture.)

Determine the formula weights of each of the following compounds: (a) Butyric acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH},\) which is responsible for the rotten smell of spoiled food; (b) sodium perborate, \(\mathrm{NaBO}_{3}\), a substance used as bleach; (c) calcium carbonate, \(\mathrm{CaCO}_{3},\) a substance found in marble. (c) $\mathrm{CF}_{2} \mathrm{Cl}_{2},\( a refrigerant known as Freon; \)(\mathbf{d}) \mathrm{NaHCO}_{3},$ known as baking soda and used in bread and pastry baking; \((\mathbf{e})\) iron pyrite, \(\mathrm{FeS}_{2}\) which has a golden appearance and is known as "Fool's Gold."

Solutions of sulfuric acid and lead(II) acetate react to form solid lead(II) sulfate and a solution of acetic acid. If \(5.00 \mathrm{~g}\) of sulfuric acid and \(5.00 \mathrm{~g}\) of lead(II) acetate are mixed, calculate the number of grams of sulfuric acid, lead(II) acetate, lead(II) sulfate, and acetic acid present in the mixture after the reaction is complete.
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