Chapter 3

Write "true" or "false" for each statement. (a) We balance chemical equations as we do because energy must be conserved. (b) If the reaction \(2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)\) goes to completion and all \(\mathrm{O}_{3}\) is converted to \(\mathrm{O}_{2}\), then the mass of \(\mathrm{O}_{3}\) at the beginning of the reaction must be the same as the mass of \(\mathrm{O}_{2}\) at the end of the reaction. (c) You can balance the "water-splitting" reaction \(\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) by writing it this way: \(\mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\).

A key step in balancing chemical equations is correctly identifying the formulas of the reactants and products. For example, consider the reaction between calcium oxide, \(\mathrm{CaO}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) to form aqueous calcium hydroxide. (a) Write a balanced chemical equation for this combination reaction, having correctly identified the product as \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)\). (b) Is it possible to balance the equation if you incorrectly identify the product as \(\mathrm{CaOH}(a q)\), and if so, what is the equation?

Balance the following equations: (a) \(\mathrm{SiCl}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Si}(\mathrm{OH})_{4}(s)+\mathrm{HCl}(a q)\) (b) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(l) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Balance the following equations: (a) \(\mathrm{HClO}_{4}(a q)+\mathrm{P}_{4} \mathrm{O}_{10}(s) \longrightarrow \mathrm{HPO}_{3}(a q)+\mathrm{Cl}_{2} \mathrm{O}_{7}(l)\) (b) \(\mathrm{Au}_{2} \mathrm{~S}_{3}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Au}(s)+\mathrm{H}_{2} \mathrm{~S}(g)\) (c) \(\mathrm{Ba}_{3} \mathrm{~N}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(a q) \longrightarrow \mathrm{Ba}(\mathrm{OH})_{2}(a q)+\mathrm{NH}_{3}(g)\) (d) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)\)

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) \(\mathrm{FeS}_{2}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{2}(g)\)

Balance the following equations: (a) \(\mathrm{CF}_{4}(l)+\mathrm{Br}_{2}(g) \longrightarrow \mathrm{CBr}_{4}(l)+\mathrm{F}_{2}(g)\) (b) \(\mathrm{Cu}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{MnO}_{2}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{MnCl}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cl}_{2}(g)\) (d) \(\mathrm{KOH}(a q)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{K}_{3} \mathrm{PO}_{4}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Write balanced chemical equations corresponding to each of the following descriptions: (a) Potassium cyanide reacts with an aqueous solution of sulfuric acid to form hydrogen cyanide gas. (b) When an aqueous solution of ammonium nitrite \(\left(\mathrm{NH}_{4} \mathrm{NO}_{2}\right)\) reacts with an aqueous solution of potassium hydroxide, ammonia gas, water and metal nitrate is formed. (c) When hydrogen gas is passed over solid hot iron(III) oxide, the resulting reaction produces iron and gaseous water. (d) When liquid ethanoic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) is combusted, carbon dioxide and water are formed.

Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(\mathrm{B}_{2} \mathrm{~S}_{3}(s),\) reacts violently with water to form dissolved boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3},\) and hydrogen sulfide gas. (c) Phosphine, \(\mathrm{PH}_{3}(g)\), combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen. (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

(a) When the metallic element lithium combines with the nonmetallic element chlorine, \(\mathrm{Cl}_{2}(g),\) what is the chemical formula of the product? (b) Is the product a solid, liquid, or gas at room temperature? (c) In the balanced chemical equation for this reaction, what is the coefficient in front of the product if the coefficient in front of \(\mathrm{Cl}_{2}(g)\) is \(1 ?\)

(a) When a compound containing C, H, and O is completely combusted in air, what reactant besides the hydrocarbon is involved in the reaction? (b) What products form in this reaction? (c) What is the sum of the coefficients in the balanced chemical equation for the combustion of one mole of acetone, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l),\) in air?

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (b) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),\) is combusted in air.

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I) oxide decomposes into silver metal and oxygen gas when heated; \((\mathbf{c})\) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air;(d) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{C}_{7} \mathrm{H}_{16}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{Li}_{3} \mathrm{~N}(s)+\mathrm{BN}(s) \longrightarrow \mathrm{Li}_{3} \mathrm{BN}_{2}(s)\) (c) \(\mathrm{Zn}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{O}_{2}(g)\)

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{NaClO}_{3}(s) \longrightarrow \mathrm{NaCl}(s)+\mathrm{O}_{2}(g)\) (b) \(\mathrm{NH}_{4} \mathrm{OH}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NH}_{3}(g)\) (c) \(\mathrm{K}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{KCl}(s)\) (d) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(l)\)

Determine the formula weights of each of the following compounds: (a) lead (IV) chloride; (b) copper(II) oxide; (c) iodic acid, \(\mathrm{HIO}_{3} ;(\mathbf{d})\) sodium perchlorate, \(\mathrm{NaClO}_{4}\); (e) indium nitride, (f) phosphorus pentoxide, \(\mathrm{P}_{4} \mathrm{O}_{10} ;(\mathbf{g})\) boron trichloride.

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."

Calculate the percentage by mass of oxygen in the following compounds: (a) vanillin, \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3} ;(\mathbf{b})\) isopropyl alcohol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\); (c) acetaminophen, \(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2}\); (d) cyclopropanone, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O} ;\) (e) dioxin, \(\mathrm{C}_{12} \mathrm{H}_{4} \mathrm{Cl}_{4} \mathrm{O}_{2} ;(\mathbf{f})\) penicillin, \(\mathrm{C}_{16} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{4} \mathrm{~S}\).

Calculate the percentage by mass of the indicated element in the following compounds: (a) hydrogen in methane, \(\mathrm{CH}_{4}\), the major hydrocarbon in natural gas; (b) oxygen in vitamin E, \(\mathrm{C}_{29} \mathrm{H}_{50} \mathrm{O}_{2} ;\) (c) sulphur in magnesium sulphate, \(\mathrm{MgSO}_{4}\), a substance used as a drying agent; (d) nitrogen in epinephrine, \(\mathrm{C}_{9} \mathrm{H}_{13} \mathrm{NO}_{3},\) also known as adrenalin, a hormone that is important for the fightor-flight response; \((\mathbf{e})\) oxygen in the insect pheromone sulcatol, \(\mathrm{C}_{8} \mathrm{H}_{16} \mathrm{O} ;(\mathbf{f})\) carbon in sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11},\) the compound that is responsible for the sweet taste of table sugar.

(a) Write "true" or "false" for each statement. (a) A mole of ducks contain a mole of feathers. (b) A mole of ammonia gas has a mass of 17.0 g. \((\mathbf{c})\) The mass of 1 ammonia molecule is 17.0 g. (d) A mole of \(\mathrm{MgSO}_{4}(s)\) contains 4 moles of oxygen atoms.

(a) What is the mass, in grams, of one mole of \({ }^{79} \mathrm{Br}\) ? (b) How many bromine atoms are present in one mole of \({ }^{79} \mathrm{Br}\) ?

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing numbers of atoms: \(0.5 \mathrm{~mol} \mathrm{BCl}_{3}\) molecules, \(197 \mathrm{~g}\) gold, \(6.0 \times 10^{23} \mathrm{CCl}_{4}\) molecules.

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing numbers of atoms: \(0.2 \mathrm{~mol} \mathrm{PCl}_{5}\), molecules, \(80 \mathrm{~g} \mathrm{Fe}_{2} \mathrm{O}_{3}, 3.0 \times 10^{23} \mathrm{CO}\) molecules.

What is the mass, in kilograms, of an Avogadro's number of people, if the average mass of a person is \(160 \mathrm{lb}\) ? How does this compare with the mass of Earth, \(5.98 \times 10^{24} \mathrm{~kg}\) ?

If Avogadro's number of pennies is divided equally among the 321 million men, women, and children in the United States, how many dollars would each receive? How does this compare with the gross domestic product (GDP) of the United States, which was \(\$ 17.419\) trillion in \(2015 ?\) (The GDP is the total market value of the nation's goods and services.)

Calculate the following quantities: (a) mass, in grams, of 0.105 mol sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) (b) moles of \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\) in \(143.50 \mathrm{~g}\) of this substance (c) number of molecules in \(1.0 \times 10^{-6} \mathrm{~mol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (d) number of \(\mathrm{N}\) atoms in \(0.410 \mathrm{~mol} \mathrm{NH}_{3}\)

(a) What is the mass, in grams, of \(2.50 \times 10^{-3} \mathrm{~mol}\) of ammonium phosphate? (b) How many moles of chloride ions are in \(0.2550 \mathrm{~g}\) of aluminum chloride? (c) What is the mass, in grams, of \(7.70 \times 10^{20}\) molecules of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\) (d) What is the molar mass of cholesterol if 0.00105 mol has a mass of \(0.406 \mathrm{~g}\) ?

(a) What is the mass, in grams, of \(1.223 \mathrm{~mol}\) of iron(III) sulfate? (b) How many moles of ammonium ions are in \(6.955 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(1.50 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} ?\) (d) What is the molar mass of diazepam (Valium \(^{\circledast}\) ) if 0.05570 mol has a mass of \(15.86 \mathrm{~g}\) ?

The molecular formula of saccharin, an artificial sweetener, is \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{~S} .(\mathbf{a})\) What is the molar mass of saccharin? (b) How many moles of sachharin are in \(2.00 \mathrm{mg}\) of this substance?(c) How many molecules are in \(2.00 \mathrm{mg}\) of this substance? (d) How many C atoms are present in \(2.00 \mathrm{mg}\) of saccharin?

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? \((\mathbf{c})\) 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?

A sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) contains \(1.250 \times 10^{21}\) carbon atoms. (a) How many atoms of hydrogen does it contain? (b) How many molecules of glucose does it contain? (c) How many moles of glucose does it contain? (d) What is the mass of this sample in grams?

A sample of the male sex hormone testosterone, \(\mathrm{C}_{19} \mathrm{H}_{28} \mathrm{O}_{2}\), contains \(3.88 \times 10^{21}\) hydrogen atoms. (a) How many atoms of carbon does it contain? (b) How many molecules of testosterone does it contain? (c) How many moles of testosterone does it contain? (d) What is the mass of this sample in grams?

At least \(25 \mu \mathrm{g}\) of tetrahydrocannabinol \((\mathrm{THC}),\) the active ingredient in marijuana, is required to produce intoxication. The molecular formula of \(\mathrm{THC}\) is \(\mathrm{C}_{21} \mathrm{H}_{30} \mathrm{O}_{2}\). How many moles of THC does this \(25 \mu \mathrm{g}\) represent? How many molecules?

Give the empirical formula of each of the following compounds if a sample contains (a) \(0.052 \mathrm{~mol} \mathrm{C}, 0.103 \mathrm{~mol}\) \(\mathrm{H}\), and \(0.017 \mathrm{~mol} \mathrm{O} ;\) (b) \(2.10 \mathrm{~g}\) nickel and \(0.58 \mathrm{~g}\) oxygen; (c) \(26.56 \% \mathrm{~K}, 35.41 \% \mathrm{Cr}\), and \(38.03 \% \mathrm{O}\) by mass.

Determine the empirical formula of each of the following compounds if a sample contains (a) \(3.92 \mathrm{~mol} \mathrm{C}, 5.99 \mathrm{~mol} \mathrm{H}\) and \(2.94 \mathrm{~mol} \mathrm{O} ;(\mathbf{b}) 12.0 \mathrm{~g}\) calcium and \(2.8 \mathrm{~g}\) nitrogen; \((\mathbf{c})\) \(89.14 \%\) Au and \(10.86 \%\) O by mass.

Determine the empirical formulas of the compounds with the following compositions by mass: (a) \(74.0 \% \mathrm{C}, 8.7 \% \mathrm{H},\) and \(17.3 \% \mathrm{~N}\) (b) \(57.5 \% \mathrm{Na}, 40.0 \% \mathrm{O},\) and \(2.5 \% \mathrm{H}\) (c) \(41.1 \% \mathrm{~N}, 11.8 \% \mathrm{H},\) and the remainder \(\mathrm{S}\)

Determine the empirical formulas of the compounds with the following compositions by mass: (a) \(42.1 \% \mathrm{Na}, 18.9 \% \mathrm{P}\), and \(39.0 \% \mathrm{O}\) (b) \(18.7 \% \mathrm{Li}, 16.3 \% \mathrm{C},\) and \(65.0 \% \mathrm{O}\) (c) \(60.0 \% \mathrm{C}, 4.4 \% \mathrm{H},\) and the remainder \(\mathrm{O}\)

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. What is the atomic mass of \(X\) ?

The compound \(\mathrm{XCl}_{4}\) contains \(75.0 \% \mathrm{Cl}\) by mass. What is the element X?

What is the molecular formula of each of the following compounds? (a) empirical formula CH, molar mass \(=78.0 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula OH, molar mass \(=34.0 \mathrm{~g} / \mathrm{mol}\)

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{CH}_{3} \mathrm{O},\) molar mass \(=62.0 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{NH}_{2}\), molar mass \(=32.0 \mathrm{~g} / \mathrm{mol}\)

Determine the empirical and molecular formulas of each of the following substances: (a) Styrene, a compound used to make Styrofoam \(^{\circ}\) 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 \(49.5 \%\) 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 \(169 \mathrm{~g} / \mathrm{mol}\)

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains \(75.69 \% \mathrm{C}\) \(8.80 \% \mathrm{H},\) and \(15.51 \% \mathrm{O}\) by mass and has a molar mass of \(206 \mathrm{~g} / \mathrm{mol}\). (b) Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains \(58.55 \% \mathrm{C}\), \(13.81 \% \mathrm{H},\) and \(27.40 \% \mathrm{~N}\) by mass; its molar mass is \(102.2 \mathrm{~g} / \mathrm{mol}\) (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains \(59.0 \%\) C, \(7.1 \%\) H, \(26.2 \%\) O, and \(7.7 \%\) N by mass; its molar mass is about \(180 \mathrm{u}\).

(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?

(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of \(2.78 \mathrm{mg}\) of ethyl butyrate produces \(6.32 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(2.58 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound? (b) Nicotine, a component of tobacco, is composed of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{N}\). A \(5.250-\mathrm{mg}\) sample of nicotine was combusted, producing \(14.242 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(4.083 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\). What is the empirical formula for nicotine? If nicotine has a molar mass of \(160 \pm 5 \mathrm{~g} / \mathrm{mol}\), what is its molecular formula?

Valproic acid, used to treat seizures and bipolar disorder, is composed of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O} .\) A \(0.165-\mathrm{g}\) sample is combusted to produce \(0.166 \mathrm{~g}\) of water and \(0.403 \mathrm{~g}\) of carbon dioxide. What is the empirical formula for valproic acid? If the molar mass is \(144 \mathrm{~g} / \mathrm{mol}\), what is the molecular formula?

Propenoic acid, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2},\) is a reactive organic liquid that is used in the manufacturing of plastics, coatings, and adhesives. An unlabeled container is thought to contain this liquid. A 0.275 -g sample of the liquid is combusted to produce \(0.102 \mathrm{~g}\) of water and \(0.374 \mathrm{~g}\) carbon dioxide. Is the unknown liquid propenoic acid? Support your reasoning with calculations.

Washing soda, a compound used to prepare hard water for washing laundry, is a hydrate, which means that a certain number of water molecules are included in the solid structure. Its formula can be written as \(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot x \mathrm{H}_{2} \mathrm{O},\) where \(x\) is the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) When a \(2.558-g\) sample of washing soda is heated at \(125^{\circ} \mathrm{C},\) all the water of hydration is lost, leaving \(0.948 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) What is the value of \(x ?\)

Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O},\) where \(x\) indicates the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{MgSO}_{4}\). When \(5.061 \mathrm{~g}\) of this hydrate is heated to \(250^{\circ} \mathrm{C},\) all the water of hydration is lost, leaving \(2.472 \mathrm{~g}\) of \(\mathrm{MgSO}_{4}\). What is the value of \(x ?\)

Hydrofluoric acid, HF \((a q)\), cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the \(\mathrm{HF}(a q)\). Sodium silicate \(\left(\mathrm{Na}_{2} \mathrm{SiO}_{3}\right)\), for example, reacts as follows: $$ \mathrm{Na}_{2} \mathrm{SiO}_{3}(s)+8 \mathrm{HF}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SiF}_{6}(a q)+2 \mathrm{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) How many moles of HF are needed to react with 0.300 mol of \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (b) How many grams of NaF form when \(0.500 \mathrm{~mol}\) of HF reacts with excess \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (c) How many grams of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) can react with \(0.800 \mathrm{~g}\) of HF?

The reaction between potassium superoxide, \(\mathrm{KO}_{2}\), and \(\mathrm{CO}_{2}\), $$ 4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2} $$ is used as a source of \(\mathrm{O}_{2}\) and absorber of \(\mathrm{CO}_{2}\) in selfcontained breathing equipment used by rescue workers. (a) How many moles of \(\mathrm{O}_{2}\) are produced when \(0.400 \mathrm{~mol}\) of \(\mathrm{KO}_{2}\) reacts in this fashion? (b) How many grams of \(\mathrm{KO}_{2}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) ?