Chapter 2

A drop of water has a volume of about 0.050 mL. How many molecules of water are in a drop of water? (Assume water has a density of \(1.00 \mathrm{g} / \mathrm{cm}^{3} .\) )

Capsaicin, the compound that gives the hot taste to chili peppers, has the formula \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\) (a) Calculate its molar mass. (b) If you eat 55 mg of capsaicin, what amount (moles) have you consumed? (c) Calculate the mass percent of each element in the compound. (d) What mass of carbon (in milligrams) is there in \(55 \mathrm{mg}\) of capsaicin?

Calculate the molar mass and the mass percent of each element in the blue solid compound \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} .\) What is the mass of copper and the mass of water in 10.5 g of the compound?

Malic acid, an organic acid found in apples, contains \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) in the following ratios: \(\mathrm{C}_{1} \mathrm{H}_{1.50} \mathrm{O}_{1.25} .\) What is the empirical formula of malic acid?

A compound composed of iron and carbon monoxide, \(\mathrm{Fe}_{x}(\mathrm{CO})_{y},\) is \(30.70 \%\) iron. What is the empirical formula for the compound?

Name each of the following compounds and indicate which ones are best described as ionic: (a) \(\mathrm{ClF}_{3}\) (b) \(\mathrm{NCl}_{3}\) (c) \(\mathrm{SrSO}_{4}\) (d) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) (e) \(\mathrm{XeF}_{4}\) (f) \(\mathrm{OF}_{2}\) (g) KI (h) \(\mathrm{Al}_{2} \mathrm{S}_{3}\) (i) \(\quad \mathrm{PCl}_{3}\) (j) \(\mathrm{K}_{3} \mathrm{PO}_{4}\)

Write the formula for each of the following compounds and indicate which ones are best described as ionic: (a) sodium hypochlorite (b) boron triiodide (c) aluminum perchlorate (d) calcium acetate (e) potassium permanganate (f) ammonium sulfite (g) potassium dihydrogen phosphate (h) disulfur dichloride (i) chlorine trifluoride (j) phosphorus trifluoride

Empirical and molecular formulas. (a) Fluorocarbonyl hypofluorite is composed of \(14.6 \% \mathrm{C}, 39.0 \% \mathrm{O},\) 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 \(128.16 \mathrm{g} /\) 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 \(22.88 \%\) C, \(5.76 \%\) 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.

In the laboratory you combine 0.125 g of nickel with CO and isolate 0.364 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 \(49.5 \%\) C, \(3.2 \%\) \(\mathrm{H}, 22.0 \% \mathrm{O},\) and \(25.2 \% \mathrm{Mn} ?\)

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 \(\left(\mathrm{I}_{2}\right)\) and chlorine \(\left(\mathrm{Cl}_{2}\right)\) produces an iodine chloride, \(\mathrm{I}_{x} \mathrm{Cl}_{y},\) a bright yellow solid. If you completely consume 0.678 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 g of vanadium combined with 1.93 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 \(\mathrm{FeS}_{2}\). If you could convert \(15.8 \mathrm{kg}\) of iron pyrite to iron metal, what mass of the metal would you 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 \(\mathrm{C}_{4} \mathrm{H}_{3}\) (d) \(57.1 \mathrm{g}\) of octane contains \(28.0 \mathrm{g}\) of hydrogen atoms.

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

A metal M forms a compound with the formula MCl_t.If the compound is 74.75\% chlorine, what is the identity of \(\mathrm{M} ?\)

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 \(\mathrm{M}\) ?

The mass of 2.50 mol of a compound with the formula \(\mathrm{ECl}_{4},\) in which \(\mathrm{E}\) 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 weights of A and 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 \(0.105 \% \mathrm{Br},\) 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, \(\mathrm{F}_{2},\) 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 g) is heated to between 800 and \(900^{\circ} \mathrm{C}\) in air to give 0.199 g of a dark green oxide, Ux \(\mathrm{O}_{y}\) 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 \(^{238}\) 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 \(\left.800^{\circ} \mathrm{C} \text { in the air. }\right)\)

In an experiment, you need 0.125 mol of sodium metal. Sodium can be cut easily with a knife (Figure \(2.5),\) so if you cut out a block of sodium, what should the volume of the block be in cubic centimeters? If you cut a perfect cube, what is the length of the edge of the cube? (The density of sodium is \(\left.0.97 \mathrm{g} / \mathrm{cm}^{3} .\right)\)

Mass spectrometric analysis showed that there are four isotopes of an unknown element having the following masses and abundances: $$\begin{array}{|c|c|c|c|}\hline \text { Isotope } & \begin{array}{c}\text { Mass } \\\\\text { Number }\end{array} & \begin{array}{c}\text { Isotope } \\\\\text { Mass }\end{array} & \begin{array}{c}\text { Abundance } \\\\(\%)\end{array} \\\\\hline 1 & 136 & 135.9090 & 0.193 \\\\\hline 2 & 138 & 137.9057 & 0.250 \\\\\hline 3 & 140 & 139.9053 & 88.48 \\\\\hline 4 & 142 & 141.9090 & 11.07 \\\\\hline\end{array}$$ 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 praseodymium \((\mathrm{Pr}),\) atomic number \(59,\) atomic weight \(140.9076 .\) Using the data above, calculate the atomic weight, and identify the element if possible.

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 -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 \(x ?\)

Tin metal (Sn) and purple iodine (I_2) combine to form orange, solid tin iodide with an unknown formula. $$\text { Sn metal }+\text { solid } \mathrm{I}_{2} \rightarrow \text { solid } \mathrm{Sn}_{x} \mathrm{I}_{y}$$ Weighed quantities of Sn and \(\mathrm{I}_{2}\) are combined, where the quantity of Sn is more than is needed to react with all of the iodine. After \(\operatorname{Sn}_{x}\) I has been formed, it is isolated by filtration. The mass of excess tin is also determined. The following data were collected: Mass of tin (Sn) in the original mixture \(1.056 \mathrm{g}\) Mass of iodine \(\left(\mathrm{I}_{2}\right)\) in the original mixture \(1.947 \mathrm{g}\) Mass of tin (Sn) recovered after reaction \(0.601 \mathrm{g}\) What is the empirical formula of the tin iodide obtained?

When analyzed, an unknown compound gave these experimental results: \(\mathrm{C}, 54.0 \% ; \mathrm{H}, 6.00 \%\) and \(\mathrm{O}, 40.0 \% .\) 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) \(\mathrm{C}_{9} \mathrm{H}_{12} \mathrm{O}_{5}\)

To find the empirical formula of tin oxide, you first react tin metal with nitric acid in a porcelain crucible. The metal is converted to tin nitrate, but, on heating the nitrate strongly, brown nitrogen dioxide gas is evolved and tin oxide is formed. In the laboratory you collect the following data: Mass of crucible Mass of crucible plus tin \(14.710 \mathrm{g}\) Mass of crucible after heating \(15.048 \mathrm{g}\) What is the empirical formula of tin oxide?

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

A jar contains some number of jelly beans. To find out precisely how many are in the jar, you could dump them out and count them. How could you estimate their number without counting each one? (Chemists need to do just this kind of "bean counting" when they work with atoms and molecules. Atoms and molecules are too small to count one by one, so chemists have worked out other methods to determine the number of atoms in a sample.