Chapter 2

Empirical and molecular formulas. (a) Fluorocarbonyl hypofluorite is composed of \(14.6 \% \mathrm{C}, 39.0 \%\) O, and \(46.3 \%\) F. The molar mass of the compound is \(82 \mathrm{g} / \mathrm{mol}\). Determine the empirical and molecular formulas of the compound. (b) Azulene, a beautiful blue hydrocarbon, is \(93.71 \%\) C and has a molar mass of \(128.16 \mathrm{g} / \mathrm{mol} .\) What are the empirical and molecular formulas of azulene?

Cacodyl, a compound containing arsenic, was reported in 1842 by the German chemist Robert Wilhelm Bunsen. It has an almost intolerable garlic-like odor. Its molar mass is \(210 \mathrm{g} / \mathrm{mol},\) and it is \(22.88 \% \mathrm{C}\) \(5.76 \% \mathrm{H},\) and \(71.36 \%\) As. Determine its empirical and molecular formulas.

The action of bacteria on meat and fish produces a compound called cadaverine. As its name and origin imply, it stinks! (It is also present in bad breath and adds to the odor of urine.) It is \(58.77 \%\) C, \(13.81 \%\) H and \(27.40 \%\) N. Its molar mass is \(102.2 \mathrm{g} / \mathrm{mol}\) Determine the molecular formula of cadaverine.

Transition metals can combine with carbon monoxide (CO) to form compounds such as \(\mathrm{Fe}_{x}(\mathrm{CO})_{y}\) (Study Question 123). Assume that you combine 0.125 g of nickel with CO and isolate \(0.364 \mathrm{g}\) of \(\mathrm{Ni}(\mathrm{CO})_{x} .\) What is the value of \(x ?\)

A compound called MMT was once used to boost the octane rating of gasoline. What is the empirical formula of MMT if it is \(49.5 \% \mathrm{C}, 3.2 \% \mathrm{H}, 22.0 \% \mathrm{O}\) and \(25.2 \%\) Mn?

Chromium is obtained by heating chromium(III) oxide with carbon. Calculate the mass percent of chromium in the oxide, and then use this value to calculate the quantity of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) required to produce \(850 \mathrm{kg}\) of chromium metal.

Stibnite, \(\mathrm{Sb}_{2} \mathrm{S}_{3},\) is a dark gray mineral from which antimony metal is obtained. What is the mass percent of antimony in the sulfide? If you have \(1.00 \mathrm{kg}\) of an ore that contains \(10.6 \%\) antimony, what mass of \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) (in grams) is in the ore?

Direct reaction of iodine \(\left(I_{2}\right)\) and chlorine \(\left(C l_{2}\right)\) produces an iodine chloride, \(I_{x} C l_{y},\) a bright yellow solid. If you completely consume \(0.678 \mathrm{g}\) of \(\mathrm{I}_{2}\) in a reaction with excess \(\mathrm{Cl}_{2}\) and produce \(1.246 \mathrm{g}\) of \(\mathrm{I}_{x} \mathrm{Cl}_{y}\) what is the empirical formula of the compound? A later experiment showed that the molar mass of \(\mathrm{I}_{x} \mathrm{Cl}_{y}\) was \(467 \mathrm{g} / \mathrm{mol} .\) What is the molecular formula of the compound?

In a reaction, \(2.04 \mathrm{g}\) of vanadium combined with \(1.93 \mathrm{g}\) of sulfur to give a pure compound. What is the empirical formula of the product?

Iron pyrite, often called "fool's gold," has the formula FeS\(_{2} .\) If you could convert \(15.8 \mathrm{kg}\) of iron pyrite to iron metal, what mass of the metal would your obtain?

Which of the following statements about \(57.1 \mathrm{g}\) of octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) is (are) not true? (a) \(57.1 \mathrm{g}\) is 0.500 mol of octane. (b) The compound is \(84.1 \%\) C by weight. (c) The empirical formula of the compound is \(\mathbf{C}_{4} \mathbf{H}_{9}\) (d) \(57.1 \mathrm{g}\) of octane contains \(28.0 \mathrm{g}\) of hydrogen atoms.

The formula of barium molybdate is \(\mathrm{BaMoO}_{4}\). Which of the following is the formula of sodium molybdate? (a) \(\mathrm{Na}_{4} \mathrm{MoO}\) (b) NaMoO (c) \(\mathrm{Na}_{2} \mathrm{MoO}_{3}\) (d) \(\mathrm{Na}_{2} \mathrm{MoO}_{4}\) (e) \(\mathrm{Na}_{4} \mathrm{MoO}_{4}\)

Pepto-Bismol, which can help provide relief for an upset stomach, contains \(300 .\) mg of bismuth subsalicylate, \(\mathrm{C}_{21} \mathrm{H}_{15} \mathrm{Bi}_{3} \mathrm{O}_{12},\) per tablet. If you take two tablets for your stomach distress, what amount (in moles) of the "active ingredient" are you taking? What mass of Bi are you consuming in two tablets?

The weight percent of oxygen in an oxide that has the formula \(\mathrm{MO}_{2}\) is \(15.2 \% .\) What is the molar mass of this compound? What element or elements are possible for M?

The mass of 2.50 mol of a compound with the formula ECl, in which E is a nonmetallic element, is \(385 \mathrm{g} .\) What is the molar mass of \(\mathrm{ECl}_{4} ?\) What is the identity of E?

The elements A and Z combine to produce two different compounds: \(\mathrm{A}_{2} \mathrm{Z}_{3}\) and \(\mathrm{AZ}_{2}\). If 0.15 mol of \(\mathrm{A}_{2} \mathrm{Z}_{3}\) has a mass of \(15.9 \mathrm{g}\) and \(0.15 \mathrm{mol}\) of \(\mathrm{AZ}_{2}\) has a mass of \(9.3 \mathrm{g},\) what are the atomic masses of \(\mathrm{A}\) and \(\mathrm{Z} ?\)

Polystyrene can be prepared by heating styrene with tribromobenzoyl peroxide in the absence of air. A sample prepared by this method has the empirical formula \(\mathrm{Br}_{3} \mathrm{C}_{6} \mathrm{H}_{3}\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)_{n},\) where the value of \(n\) can vary from sample to sample. If one sample has \(0.105 \%\) Br, what is the value of \(n ?\)

A sample of hemoglobin is found to be \(0.335 \%\) iron. What is the molar mass of hemoglobin if there are four iron atoms per molecule?

Consider an atom of \(^{64} \mathrm{Zn}\). (a) Calculate the density of the nucleus in grams per cubic centimeter, knowing that the nuclear radius is \(4.8 \times 10^{-6} \mathrm{nm}\) and the mass of the \(^{64} \mathrm{Zn}\) atom is \(1.06 \times 10^{-22} \mathrm{g} .\) (Recall that the volume of a sphere is \(\left.[4 / 3] \pi r^{3} .\right)\) (b) Calculate the density of the space occupied by the electrons in the zinc atom, given that the atomic radius is \(0.125 \mathrm{nm}\) and the electron mass is \(9.11 \times 10^{-28} \mathrm{g}\) (c) Having calculated these densities, what statement can you make about the relative densities of the parts of the atom?

Estimating the radius of a lead atom. (a) You are given a cube of lead that is \(1.000 \mathrm{cm}\) on each side. The density of lead is \(11.35 \mathrm{g} / \mathrm{cm}^{3} .\) How many atoms of lead are in the sample? (b) Atoms are spherical; therefore, the lead atoms in this sample cannot fill all the available space. As an approximation, assume that \(60 \%\) of the space of the cube is filled with spherical lead atoms. Calculate the volume of one lead atom from this information. From the calculated volume (V) and the formula \((4 / 3) \pi r^{3}\) for the volume of a sphere, estimate the radius ( \(r\) ) of a lead atom.

A piece of nickel foil, \(0.550 \mathrm{mm}\) thick and \(1.25 \mathrm{cm}\) square, is allowed to react with fluorine, \(F_{2},\) to give a nickel fluoride. (a) How many moles of nickel foil were used? (The density of nickel is \(8.902 \mathrm{g} / \mathrm{cm}^{3} .\) ) (b) If you isolate \(1.261 \mathrm{g}\) of the nickel fluoride, what is its formula? (c) What is its complete name?

Uranium is used as a fuel, primarily in the form of uranium(IV) oxide, in nuclear power plants. This question considers some uranium chemistry. (a) A small sample of uranium metal \((0.169 \mathrm{g})\) is heated to between 800 and \(900^{\circ} \mathrm{C}\) in air to give \(0.199 \mathrm{g}\) of a dark green oxide, \(\mathrm{U}_{x} \mathrm{O}_{y} .\) How many moles of uranium metal were used? What is the empirical formula of the oxide, \(\mathrm{U}_{x} \mathrm{O}_{y} ?\) What is the name of the oxide? How many moles of \(\mathrm{U}_{x} \mathrm{O}_{y}\) must have been obtained? (b) The naturally occurring isotopes of uranium are \(^{234} \mathrm{U},^{235} \mathrm{U},\) and \(^{238} \mathrm{U} .\) Knowing that uranium's atomic weight is \(238.02 \mathrm{g} / \mathrm{mol},\) which isotope must be the most abundant? (c) If the hydrated compound \(\mathrm{UO}_{2}\left(\mathrm{NO}_{3}\right)_{2} \cdot z \mathrm{H}_{2} \mathrm{O}\) is heated gently, the water of hydration is lost. If you have \(0.865 \mathrm{g}\) of the hydrated compound and obtain \(0.679 \mathrm{g}\) of \(\mathrm{UO}_{2}\left(\mathrm{NO}_{3}\right)_{2}\) on heating, how many waters of hydration are in each formula unit of the original compound? (The oxide \(\mathrm{U}_{x} \mathrm{O}_{y}\) is obtained if the hydrate is heated to temperatures over \(800^{\circ} \mathrm{C}\) in the air.)

If Epsom salt, \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O},\) is heated to \(250^{\circ} \mathrm{C},\) all the water of hydration is lost. On heating a \(1.687-\mathrm{g}\) sample of the hydrate, \(0.824 \mathrm{g}\) of \(\mathrm{MgSO}_{4}\) remains. How many molecules of water occur per formula unit of \(\mathrm{MgSO}_{4} ?\)

The "alum" used in cooking is potassium aluminum sulfate hydrate, \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2} \cdot x \mathrm{H}_{2} \mathrm{O} .\) To find the value of \(x,\) you can heat a sample of the compound to drive off all of the water and leave only \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2}\). Assume you heat \(4.74 \mathrm{g}\) of the hydrated compound and that the sample loses \(2.16 \mathrm{g}\) of water. What is the value of \(x ?\)

When analyzed, an unknown compound gave these experimental results: \(\mathbf{C}, 54.0 \% ; \mathbf{H}, \mathbf{6} .00 \% ;\) and \(\mathbf{O}, 40.0 \%\) Four different students used these values to calculate the empirical formulas shown here. Which answer is correct? Why did some students not get the correct answer? (a) \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{O}_{2}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{3}\) (c) \(\mathrm{C}_{7} \mathrm{H}_{10} \mathrm{O}_{4}\) (d) \(\mathrm{C}_{9} \mathrm{H}_{12} \mathrm{O}_{5}\)

Two general chemistry students working together in the lab weigh out \(0.832 \mathrm{g}\) of \(\mathrm{CaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) into a crucible. After heating the sample for a short time and allowing the crucible to cool, the students determine that the sample has a mass of \(0.739 \mathrm{g} .\) They then do a quick calculation. On the basis of this calculation, what should they do next? (a) Congratulate themselves on a job well done. (b) Assume the bottle of \(\mathrm{CaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) was mislabeled; it actually contained something different. (c) Heat the crucible again, and then reweigh it.

Mass spectrometric analysis showed that there are four isotopes of an unknown element having the following masses and abundances: $$\begin{array}{cccc} \text { Isotope } & \text { Mass Number } & \text { Isotope Mass } & \text { Abundance (\%) } \\ \hline 1 & 136 & 135.9090 & 0.193 \\ 2 & 138 & 137.9057 & 0.250 \\ 3 & 140 & 139.9053 & 88.48 \\ 4 & 142 & 141.9090 & 11.07 \end{array}$$Three elements in the periodic table that have atomic weights near these values are lanthanum (La), atomic number \(57,\) atomic weight \(138.9055 ;\) cerium (Ce) atomic number \(58,\) atomic weight \(140.115 ;\) and praeseodymium (Pr), atomic number 59 , atomic weight \(140.9076 .\) Using the data above, calculate the atomic weight, and identify the element if possible.

The highest mass peaks in the mass spectrum of \(\mathrm{Br}_{2}\) occur at \(m / Z 158,160,\) and \(162 .\) The ratio of intensities of these peaks is approximately \(1: 2: 1 .\) Bromine has two stable isotopes, \(^{79} \mathrm{Br}(50.7 \% \text { abundance })\) and \(^{81} \mathrm{Br}\) \((49.3 \% \text { abundance })\) (a) What molecular species gives rise to each of these peaks? (b) Explain the relative intensities of these peaks. (Hint: Consider the probabilities of each atom combination.)

Identify, from the list below, the information needed to calculate the number of atoms in \(1.00 \mathrm{cm}^{3}\) of iron. Outline the procedure used in this calculation. (a) the structure of solid iron (b) the molar mass of iron (c) Avogadro's number (d) the density of iron (e) the temperature (f) iron's atomic number (g) the number of iron isotopes

Cobalt(II) chloride hexahydrate, dissolves readily in water to give a red solution. If we use this solution as an "ink," we can write secret messages on paper. The writing is not visible when the water evaporates from the paper. When the paper is heated, however, the message can be read. Explain the chemistry behind this observation. (IMAGE CAN'T COPY)