Chapter 3

Balance the following equations using the method outlined in Section 3.7 . (a) \(\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}+\mathrm{O}_{2}\) (b) \(\mathrm{KNO}_{3} \longrightarrow \mathrm{KNO}_{2}+\mathrm{O}_{2}\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3} \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{NH}_{4} \mathrm{NO}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{NaHCO}_{3} \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (f) \(\mathrm{P}_{4} \mathrm{O}_{10}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}\) (g) \(\mathrm{HCl}+\mathrm{CaCO}_{3} \longrightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (h) \(\mathrm{Al}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2}\) (i) \(\mathrm{CO}_{2}+\mathrm{KOH} \longrightarrow \mathrm{K}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}\) (j) \(\mathrm{CH}_{4}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (k) \(\mathrm{Be}_{2} \mathrm{C}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Be}(\mathrm{OH})_{2}+\mathrm{CH}_{4}\) (l) \(\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) \((\mathrm{m}) \mathrm{S}+\mathrm{HNO}_{3} \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{NH}_{3}+\mathrm{CuO} \longrightarrow \mathrm{Cu}+\mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\)

On what law is stoichiometry based? Why is it essential to use balanced equations in solving stoichiometric problems?

Describe the steps involved in the mole method.

Consider the combustion of carbon monoxide (CO) in oxygen gas: $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$Starting with 3.60 moles of \(\mathrm{CO}\), calculate the number of moles of \(\mathrm{CO}_{2}\) produced if there is enough oxygen gas to react with all of the CO.

Silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) can be prepared by heating \(\mathrm{Si}\) in chlorine gas:$$\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(l)$$In one reaction, 0.507 mole of \(\mathrm{SiCl}_{4}\) is produced. How many moles of molecular chlorine were used in the reaction?

Ammonia is a principal nitrogen fertilizer. It is prepared by the reaction between hydrogen and nitrogen.$$3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$In a particular reaction, 6.0 moles of \(\mathrm{NH}_{3}\) were produced. How many moles of \(\mathrm{H}_{2}\) and how many moles of \(\mathrm{N}_{2}\) were reacted to produce this amount of \(\mathrm{NH}_{3} ?\)

Certain race cars use methanol (CH \(_{3} \mathrm{OH}\), also called wood alcohol) as a fuel. The combustion of methanol occurs according to the following equation:$$2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$$In a particular reaction, 9.8 moles of \(\mathrm{CH}_{3} \mathrm{OH}\) are reacted with an excess of \(\mathrm{O}_{2}\). Calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) formed.

How many grams of sulfur (S) are needed to react completely with \(246 \mathrm{~g}\) of mercury (Hg) to form \(\mathrm{HgS} ?\)

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is$$\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)$$How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2} ?\)

When baking soda (sodium bicarbonate or sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\) ) is heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, donuts, and bread. (a) Write a balanced equation for the decomposition of the compound (one of the products is \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) ). (b) Calculate the mass of \(\mathrm{NaHCO}_{3}\) required to produce \(20.5 \mathrm{~g}\) of \(\mathrm{CO}_{2}\)

If chlorine bleach is mixed with other cleaning products containing ammonia, the toxic gas \(\mathrm{NCl}_{3}(g)\) can form according to the equation $$3 \mathrm{NaClO}(a q)+\mathrm{NH}_{3}(a q) \longrightarrow 3 \mathrm{NaOH}(a q)+\mathrm{NCl}_{3}(g)$$ When \(2.94 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) reacts with an excess of \(\mathrm{NaClO}\) according to the preceding reaction, how many grams of \(\mathrm{NCl}_{3}\) are formed?

Fermentation is a complex chemical process of wine making in which glucose is converted into ethanol and carbon dioxide: $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{CO}_{2}$$ Starting with \(500.4 \mathrm{~g}\) of glucose, what is the maximum amount of ethanol in grams and in liters that can be obtained by this process? (Density of ethanol \(=0.789 \mathrm{~g} / \mathrm{mL} .)\)

Each copper(II) sulfate unit is associated with five water molecules in crystalline copper(II) sulfate pentahydrate \(\left(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\right)\). When this compound is heated in air above \(100^{\circ} \mathrm{C},\) it loses the water \(\mathrm{mol}-\) ecules and also its blue color:$$\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CuSO}_{4}+5 \mathrm{H}_{2} \mathrm{O}$$ If \(9.60 \mathrm{~g}\) of \(\mathrm{CuSO}_{4}\) are left after heating \(15.01 \mathrm{~g}\) of the blue compound, calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) originally present in the compound.

For many years the recovery of gold-that is, the separation of gold from other materials-involved the use of potassium cyanide: $$4 \mathrm{Au}+8 \mathrm{KCN}+\mathrm{O}_{2}+2 \mathrm{H}_{2} \mathrm{O} \underset{4 \mathrm{KAu}(\mathrm{CN})_{2}+4 \mathrm{KOH}}{\longrightarrow}$$ What is the minimum amount of KCN in moles needed to extract \(29.0 \mathrm{~g}\) (about an ounce) of gold?

limestone \(\left(\mathrm{CaCO}_{3}\right)\) is decomposed by heating to quicklime \((\mathrm{CaO})\) and carbon dioxide. Calculate how many grams of quicklime can be produced from \(1.0 \mathrm{~kg}\) of limestone.

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) is also called "laughing gas." It can be prepared by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\). The other product is \(\mathrm{H}_{2} \mathrm{O}\). (a) Write a balanced equation for this reaction. (b) How many grams of \(\mathrm{N}_{2} \mathrm{O}\) are formed if 0.46 mole of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is used in the reaction?

The fertilizer ammonium sulfate \(\left[\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\right]\) is prepared by the reaction between ammonia (NH \(_{3}\) ) and sulfuric acid:$$2 \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(a q)$$How many kilograms of \(\mathrm{NH}_{3}\) are needed to produce \(1.00 \times 10^{5} \mathrm{~kg}\) of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} ?\)

Define limiting reactant and excess reactant. What is the significance of the limiting reactant in predicting the amount of the product obtained in a reaction? Can there be a limiting reactant if only one reactant is present?

Give an everyday example that illustrates the limiting reactant concept.

Nitric oxide (NO) reacts with oxygen gas to form nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\), a dark-brown gas: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ In one experiment 0.886 mole of NO is mixed with 0.503 mole of \(\mathrm{O}_{2}\). Calculate which of the two reactants is the limiting reactant. Calculate also the number of moles of \(\mathrm{NO}_{2}\) produced.

Ammonia and sulfuric acid react to form ammonium sulfate. (a) Write an equation for the reaction. (b) Determine the starting mass (in grams) of each reactant if \(20.3 \mathrm{~g}\) of ammonium sulfate is produced and \(5.89 \mathrm{~g}\) of sulfuric acid remains unreacted.

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is a component of natural gas and is used in domestic cooking and heating. (a) Balance the following equation representing the combustion of propane in air.$$\mathrm{C}_{3} \mathrm{H}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}$$ (b) How many grams of carbon dioxide can be produced by burning 3.65 moles of propane? Assume that oxygen is the excess reactant in this reaction.

Consider the reaction $$\mathrm{MnO}_{2}+4 \mathrm{HCl} \longrightarrow \mathrm{MnCl}_{2}+\mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O} $$If 0.86 mole of \(\mathrm{MnO}_{2}\) and \(48.2 \mathrm{~g}\) of \(\mathrm{HCl}\) react, which reactant will be used up first? How many grams of \(\mathrm{Cl}_{2}\) will be produced?

Why is the theoretical yield of a reaction determined only by the amount of the limiting reactant?

Why is the actual yield of a reaction almost always smaller than the theoretical yield?

Hydrogen fluoride is used in the manufacture of Freons (which destroy ozone in the stratosphere) and in the production of aluminum metal. It is prepared by the reaction$$\mathrm{CaF}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{CaSO}_{4}+2 \mathrm{HF}$$ In one process, \(6.00 \mathrm{~kg}\) of \(\mathrm{CaF}_{2}\) are treated with an excess of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and yield \(2.86 \mathrm{~kg}\) of \(\mathrm{HF}\). Calculate the percent yield of HF.

Nitroglycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)\) is a powerful explosive. Its decomposition may be represented by$$4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9} \longrightarrow 6 \mathrm{~N}_{2}+12 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} $$This reaction generates a large amount of heat and many gaseous products. It is the sudden formation of these gases, together with their rapid expansion, that produces the explosion. (a) What is the maximum amount of \(\mathrm{O}_{2}\) in grams that can be obtained from \(2.00 \times 10^{2} \mathrm{~g}\) of nitroglycerin? (b) Calculate the percent yield in this reaction if the amount of \(\mathrm{O}_{2}\) generated is found to be \(6.55 \mathrm{~g}\).

Titanium(IV) oxide \(\left(\mathrm{TiO}_{2}\right)\) is a white substance produced by the action of sulfuric acid on the mineral ilmenite \(\left(\mathrm{FeTiO}_{3}\right)\) $$\mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow\mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O}$$Its opaque and nontoxic properties make it suitable as a pigment in plastics and paints. In one process, \(8.00 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{FeTiO}_{3}\) yielded \(3.67 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{TiO}_{2} .\) What is the percent yield of the reaction?

Ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) an important industrial organic chemical, can be prepared by heating hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) at \(800^{\circ} \mathrm{C}:$$$\mathrm{C}_{6} \mathrm{H}_{14} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}+\text { other products }$$ If the yield of ethylene production is 42.5 percent, what mass of hexane must be reacted to produce \)481 \mathrm{~g}$ of ethylene?

When heated, lithium reacts with nitrogen to form lithium nitride: $$6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{~N}(s)$$What is the theoretical yield of \(\mathrm{Li}_{3} \mathrm{~N}\) in grams when \(12.3 \mathrm{~g}\) of \(\mathrm{Li}\) are heated with \(33.6 \mathrm{~g}\) of \(\mathrm{N}_{2} ?\) If the actual yield of \(\mathrm{Li}_{3} \mathrm{~N}\) is \(5.89 \mathrm{~g},\) what is the percent yield of the reaction?

Disulfide dichloride \(\left(\mathrm{S}_{2} \mathrm{Cl}_{2}\right)\) is used in the vulcanization of rubber, a process that prevents the slippage of rubber molecules past one another when stretched. It is prepared by heating sulfur in an atmosphere of chlorine:$$\mathrm{S}_{8}(l)+4 \mathrm{Cl}_{2}(g) \longrightarrow 4 \mathrm{~S}_{2} \mathrm{Cl}_{2}(l)$$What is the theoretical yield of \(\mathrm{S}_{2} \mathrm{Cl}_{2}\) in grams when \(4.06 \mathrm{~g}\) of \(\mathrm{S}_{8}\) are heated with \(6.24 \mathrm{~g}\) of \(\mathrm{Cl}_{2} ?\) If the actual yield of \(\mathrm{S}_{2} \mathrm{Cl}_{2}\) is \(6.55 \mathrm{~g}\), what is the percent yield?

Rubidium is used in "atomic clocks" and other precise electronic equipment. The average atomic mass of \({ }_{37}^{85} \mathrm{Rb}(84.912 \mathrm{amu})\) and \({ }_{37}^{87} \mathrm{Rb}(86.909 \mathrm{amu})\) is 85.47 amu. Calculate the natural abundances of the rubidium isotopes.

Consider the reaction of hydrogen gas with oxygen gas: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$

Ethylene reacts with hydrogen chloride to form ethyl chloride: $$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(g) $$Calculate the mass of ethyl chloride formed if \(4.66 \mathrm{~g}\) of ethylene reacts with an 89.4 percent yield.

Write balanced equations for the following reactions described in words. (a) Pentane burns in oxygen to form carbon dioxide and water. (b) Sodium bicarbonate reacts with hydrochloric acid to form carbon dioxide, sodium chloride, and water. (c) When heated in an atmosphere of nitrogen, lithium forms lithium nitride. (d) Phosphorus trichloride reacts with water to form phosphorus acid and hydrogen chloride. (e) Copper(II) oxide heated with ammonia will form copper, nitrogen gas, and water.

Industrially, nitric acid is produced by the Ostwald process represented by the following equations: $$ \begin{aligned} 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{NO}_{2}(g) \\\2 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{HNO}_{3}(a q)+\mathrm{HNO}_{2}(a q) \end{aligned}$$What mass of \(\mathrm{NH}_{3}\) (in grams) must be used to produce 1.00 ton of \(\mathrm{HNO}_{3}\) by the above procedure, assuming an 80 percent yield in each step? ( 1 ton = \(2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

A sample of a compound of \(\mathrm{Cl}\) and \(\mathrm{O}\) reacts with an excess of \(\mathrm{H}_{2}\) to give \(0.233 \mathrm{~g}\) of \(\mathrm{HCl}\) and \(0.403 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Determine the empirical formula of the \(\mathrm{com}-\) pound.

How many grams of \(\mathrm{H}_{2} \mathrm{O}\) will be produced from the complete combustion of \(26.7 \mathrm{~g}\) of butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right) ?\)

A 26.2-g sample of oxalic acid hydrate \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right.\). \(2 \mathrm{H}_{2} \mathrm{O}\) ) is heated in an oven until all the water is driven off. How much of the anhydrous acid is left?

The atomic mass of element X is 33.42 amu. A 27.22-g sample of X combines with \(84.10 \mathrm{~g}\) of another element Y to form a compound XY. Calculate the atomic mass of Y.

How many moles of \(\mathrm{O}\) are needed to combine with 0.212 mole of \(\mathrm{C}\) to form (a) \(\mathrm{CO}\) and (b) \(\mathrm{CO}_{2}\) ?

A research chemist used a mass spectrometer to study the two isotopes of an element. Over time, she recorded a number of mass spectra of these isotopes. On analysis, she noticed that the ratio of the taller peak (the more abundant isotope) to the shorter peak (the less abundant isotope) gradually increased with time. Assuming that the mass spectrometer was functioning normally, what do you think was causing this change?

The aluminum sulfate hydrate \(\left[\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot x \mathrm{H}_{2} \mathrm{O}\right]\)contains 8.10 percent \(\mathrm{Al}\) by mass. Calculate \(x-\) that is, the number of water molecules associated with each \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) unit.

The explosive nitroglycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)\) has also been used as a drug to treat heart patients to relieve pain (angina pectoris). We now know that nitroglycerin produces nitric oxide (NO), which causes muscles to relax and allows the arteries to dilate. If each nitroglycerin molecule releases one NO per atom of \(\mathrm{N},\) calculate the mass percent of NO available from nitroglycerin.

An iron bar weighed \(664 \mathrm{~g}\). After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right) .\) Calculate the final mass of the iron bar and rust.

A certain metal oxide has the formula \(\mathrm{MO},\) where \(\mathrm{M}\) denotes the metal. A \(39.46-\mathrm{g}\) sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, \(31.70 \mathrm{~g}\) of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.

An impure sample of zinc (Zn) is treated with an excess of sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)\) to form zinc sulfate \(\left(\mathrm{ZnSO}_{4}\right)\) and molecular hydrogen \(\left(\mathrm{H}_{2}\right) .\) (a) Write a balanced equation for the reaction. (b) If \(0.0764 \mathrm{~g}\) of \(\mathrm{H}_{2}\) is obtained from \(3.86 \mathrm{~g}\) of the sample, calculate the percent purity of the sample. (c) What assumptions must you make in (b)?

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is$$\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2}$$Suppose that \(1.64 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{Fe}\) are obtained from a \(2.62 \times 10^{3} \mathrm{~kg}\) sample of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). Assuming that the reaction goes to completion, what is the percent purity of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the original sample?

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of \(\mathrm{CO}_{2}\) in the atmosphere. Carbon dioxide is also the end product of metabolism (see Example 3.13 ). Using glucose as an example of food, calculate the annual human production of \(\mathrm{CO}_{2}\) in grams, assuming that each person consumes \(5.0 \times 10^{2} \mathrm{~g}\) of glucose per day. The world's population is 7.2 billion, and there are 365 days in a year.

Carbohydrates are compounds containing carbon, hydrogen, and oxygen in which the hydrogen to oxygen ratio is \(2: 1 .\) A certain carbohydrate contains 40.0 percent carbon by mass. Calculate the empirical and molecular formulas of the compound if the approximate molar mass is \(178 \mathrm{~g}\)