Chapter 2

A 1.0 -g sample of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is fully decomposed into its elements, yielding \(0.273 \mathrm{~g}\) of carbon and \(0.727 \mathrm{~g}\) of oxygen. (a) What is the ratio of the mass of \(\mathrm{O}\) to \(\mathrm{C} ?(\mathbf{b})\) If a sample of a different compound decomposes into \(0.429 \mathrm{~g}\) of carbon and \(0.571 \mathrm{~g}\) of oxygen, what is its ratio of the mass of \(\mathrm{O}\) to \(\mathrm{C} ?(\mathbf{c})\) According to Dalton's atomic theory, what is the empirical formula of the second compound?

A chemist finds that \(30.82 \mathrm{~g}\) of nitrogen will react with 17.60 , 35.20,70.40 , or \(88.00 \mathrm{~g}\) of oxygen to form four different compounds. (a) Calculate the mass of oxygen per gram of nitrogen in each compound. (b) How do the numbers in part (a) support Dalton's atomic theory?

In a series of experiments, a chemist prepared three different compounds that contain only iodine and fluorine and determined the mass of each element in each compound: $$ \begin{array}{lcc} \hline \text { Compound } & \text { Mass of Iodine (g) } & \text { Mass of Fluorine (g) } \\ \hline 1 & 4.75 & 3.56 \\ \hline 2 & 7.64 & 3.43 \\ 3 & 9.41 & 9.86 \\ \hline \end{array} $$ (a) Calculate the mass of fluorine per gram of iodine in each compound. (b) How do the numbers in part (a) support the atomic theorv?

What fraction of the \(\alpha\) particles in Rutherford's gold foil experiment are scattered at large angles? Assume the gold foil is two layers thick, as shown in Figure \(2.9,\) and that the approximate diameters of a gold atom and its nucleus are 270 \(\mathrm{pm}\) and \(1.0 \times 10^{-2} \mathrm{pm}\), respectively. Hint: Calculate the cross sectional area occupied by the nucleus as a fraction of that occupied by the atom. Assume that the gold nuclei in each layer are offset from each other.

Millikan determined the charge on the electron by studying the static charges on oil drops falling in an electric field (Figure 2.5 ). A student carried out this experiment using several oil drops for her measurements and calculated the charges on the drops. She obtained the following data: $$ \begin{array}{lc} \hline \text { Droplet } & \text { Calculated Charge (C) } \\ \hline \text { A } & 1.60 \times 10^{-19} \\ \text {B } & 3.15 \times 10^{-19} \\ \text {C } & 4.81 \times 10^{-19} \\ \text {D } & 6.31 \times 10^{-19} \\ \hline \end{array} $$ (a) What is the significance of the fact that the droplets carried different charges? (b) What conclusion can the student draw from these data regarding the charge of the electron? (c) What value (and to how many significant figures) should she report for the electronic charge?

he radius of an atom of tungsten (W) is about \(2.10 \AA\). (a) Express this distance in nanometers (nm) and in picometers (pm). (b) How many tungsten atoms would have to be lined up to create a wire of \(2.0 \mathrm{~mm} ?(\mathbf{c})\) If the atom is assumed to be a sphere, what is the volume in \(\mathrm{m}^{3}\) of a single \(\mathrm{W}\) atom?

The radius of an atom of copper (Cu) is about 140 pm. (a) EXpress this distance in millimeters (mm) and in angstroms \((\AA)\). (b) How many Cu atoms would have to be placed side by side to span a distance of \(5.0 \mathrm{~mm} ?(\mathbf{c})\) If you assume that the Cu atom is a sphere, what is the volume in \(\mathrm{cm}^{3}\) of a single atom?

Answer the following questions without referring to Table 2.1: (a) What are the main subatomic particles that make up the atom? (b) What is the relative charge (in multiples of the electronic charge) of each of the particles? (c) Which of the particles is the most massive? (d) Which is the least massive?

Determine whether each of the following statements is true or false. If false, correct the statement to make it true: \((\mathbf{a})\) The nucleus has most of the mass and comprises most of the volume of an atom. (b) Every atom of a given element has the same number of protons. (c) The number of electrons in an atom equals the number of neutrons in the atom. (d) The protons in the nucleus of the helium atom are held together by a force called the strong nuclear force.

Consider an atom of \({ }^{58} \mathrm{Ni}\). (a) How many protons, neutrons, and electrons does this atom contain? (b) What is the symbol of the ion obtained by removing two electrons from \({ }^{58} \mathrm{Ni}\) ? (c) What is the symbol for the isotope of \({ }^{58} \mathrm{Ni}\) that possesses 33 neutrons?

(a) Define atomic number and mass number. (b) Which of these can vary without changing the identity of the element?

(a) Which two of the following are isotopes of the same element: \(106 \mathrm{X},{ }_{46}^{107} \mathrm{X},{ }_{4}^{107} \mathrm{X} ?(\mathbf{b})\) What is the identity of the element whose isotopes you have selected?

Each of the following isotopes is used in medicine. Indicate the number of protons and neutrons in each isotope: (a) samarium-153, \((\mathbf{b})\) lutetium-177, \((\mathbf{c})\) bismuth- \(213,\) (d) molybdenum-99, \((\mathbf{e})\) lead-212, \((\mathbf{f})\) caesium- \(131 .\)

Fill in the gaps in the following table, assuming each column represents a neutral atom. $$ \begin{array}{l|c|c|c|c|c} \hline \text { Symbol } & 159 & & & & \\ \text { Protons } & & 29 & & & 37 \\ \text { Neutrons } & & 34 & 53 & & \\ \text { Electrons } & & & 42 & 34 & \\ \text { Mass no. } & & & & 79 & 85 \\ \hline \end{array} $$

Fill in the gaps in the following table, assuming each column represents a neutral atom. $$ \begin{array}{l|l|l|l|l|l} \hline \text { Symbol } & { }^{89} \mathrm{Y} & & & & \\ \text { Protons } & & 78 & & & 89 \\ \text { Neutrons } & & & 123 & & \\ \text { Electrons } & & & 81 & 50 & \\ \text { Mass no. } & & 195 & & 119 & 227 \\ \hline \end{array} $$

One way in which Earth's evolution as a planet can be understood is by measuring the amounts of certain isotopes in rocks. One quantity recently measured is the ratio of \({ }^{129} \mathrm{Xe}\) to \({ }^{130} \mathrm{Xe}\) in some minerals. In what way do these two isotopes differ from one another? In what respects are they the same?

(a) What isotope is used as the standard in establishing the atomic mass scale? (b) The atomic weight of boron is reported as 10.81 , yet no atom of boron has the mass of \(10.81 \mathrm{u}\). Explain.

(a) What is the mass in \(\mathrm{u}\) of a carbon- 12 atom? (b) Why is the atomic weight of carbon reported as 12.011 in the table of elements and the periodic table in the front inside cover of this text?

Iron has three major isotopes: \({ }^{54} \mathrm{Fe}\) (atomic mass = \(53.9396 \mathrm{u}\); abundance \(5.85 \%),{ }^{56} \mathrm{Fe}\) (atomic mass = 55.9349u; abundance 91.75\%), and \({ }^{57} \mathrm{Fe}\) (atomic mass \(=56.9354 \mathrm{u} ;\) abundance \(2.12 \%) .\) Calculate the atomic weight (average atomic mass) of iron.

Bromine has two naturally occurring isotopes, bromine- 79 (atomic mass \(=78.9183 \mathrm{u} ; \quad\) abundance \(=50.69 \%)\) a \(\mathrm{nd}\) bromine- \(81 \quad\) (atomic mass \(=80.9163\) u; abundance = \(49.31 \%)\). Calculate the atomic weight of bromine.

Naturally occurring lead has the following isotopic abundances: $$ \begin{array}{lcc} \hline \text { Isotope } & \text { Abundance (\%) } & \text { Atomic mass (u) } \\ \hline{ }^{204} \mathrm{~Pb} & 1.4 & 203.9730 \\ { }^{206} \mathrm{~Pb} & 24.1 & 205.9744 \\ { }^{207} \mathrm{~Pb} & 22.1 & 206.9759 \\ { }^{208} \mathrm{~Pb} & 52.4 & 207.9766 \\ \hline \end{array} $$ (a) What is the average atomic mass of \(\mathrm{Pb}\) ? (b) Sketch the mass spectrum of \(\mathrm{Pb}\).

Mass spectrometry is more often applied to molecules than to atoms. We will see in Chapter 3 that the molecular weight of a molecule is the sum of the atomic weights of the atoms in the molecule. The mass spectrum of \(\mathrm{H}_{2}\) is taken under conditions that prevent decomposition into \(\mathrm{H}\) atoms. The two naturally occurring isotopes of hydrogen are \({ }^{1} \mathrm{H}\) (atomic mass \(=1.00783 \mathrm{u}\); abundance \(\left.99.9885 \%\right)\) and \({ }^{2} \mathrm{H}(\) atomic mass \(=2.01410 \mathrm{u} ;\) abundance \(0.0115 \%)\). (a) How many peaks will the mass spectrum have? (b) Give the relative atomic masses of each of these peaks. (c) Which peak will be the largest, and which the smallest?

For each of the following elements, write its chemical sym. bol, locate it in the periodic table, give its atomic number and indicate whether it is a metal, metalloid, or nonmetal (a) radon, (b) tellurium, (c) cadmium, (d) chromium (e) barium, (f) selenium, (g) sulphur.

Locate each of the following elements in the periodic table; give its name and atomic number, and indicate whether it is a metal, metalloid, or nonmetal: \((\mathbf{a}) \mathrm{Hg},(\mathbf{b})\) At, \((\mathbf{c})\) Mo, \((\mathbf{d})\) \(\mathrm{W},(\mathbf{e}) \mathrm{Sn},(\mathbf{f}) \mathrm{V},(\mathbf{g}) \mathrm{K}\)

For each of the following elements, write its chemical symbol, determine the name of the group to which it belongs (Table 2.3), and indicate whether it is a metal, metalloid, or nonmetal: (a) polonium, (b) strontium, (c) neon, (d) rubidium, (e) bromine.

The elements of group 14 show an interesting change in properties moving down the group. Give the name and chemical symbol of each element in the group and label it as a nonmetal, metalloid, or metal.

Two substances have the same molecular and empirical formulas. Does this mean that they must be the same compound?

Write the empirical formula corresponding to each of the following molecular formulas: \((\mathbf{a}) \mathrm{Al}_{2} \mathrm{Br}_{6},(\mathbf{b}) \mathrm{C}_{8} \mathrm{H}_{10},\) (c) \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\) (d) \(\mathrm{P}_{4} \mathrm{O}_{10}\) (e) \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2},\) (f) \(\mathrm{B}_{3} \mathrm{~N}_{3} \mathrm{H}_{6}\).

Determine the molecular and empirical formulas of the following: (a) the organic solvent benzene, which has six carbon atoms and six hydrogen atoms; \((\mathbf{b})\) the compound silicon tetrachloride, which has a silicon atom and four chlorine atoms and is used in the manufacture of computer chips; \((\mathbf{c})\) the reactive substance diborane, which has two boron atoms and six hydrogen atoms; (d) the sugar called glucose, which has six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.

How many hydrogen atoms are in each of the following: (a) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (b) \(\mathrm{Ca}\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\) (c) \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4} ?\)

How many of the indicated atoms are represented by each chemical formula: (a) carbon atoms in \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{COOCH}_{3}\), (b) oxygen atoms in \(\mathrm{Ca}\left(\mathrm{ClO}_{3}\right)_{2},(\mathbf{c})\) hydrogen atoms in \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} ?\)

Write the molecular and structural formulas for the compounds represented by the following models: $$ \begin{array}{l|c|c|c|c} \hline \text { Symbol } & { }^{58} \mathrm{Fe}^{2+} & & & \\ \hline \text { Protons } & & 50 & & 40 \\ \text { Neutrons } & & 68 & 78 & 50 \\ \text { Electrons } & & & 54 & 38 \\ \text { Net charge } & & 4+ & 2- & \\ \hline \end{array} $$

Each of the following elements is capable of forming an ion in chemical reactions. By referring to the periodic table, predict the charge of the most stable ion of each: (a) Be, (b) Rb, (c) As, (d) In, (e) At.

Using the periodic table, predict the charge of the most stable ion of the following elements: \((\mathbf{a}) \mathrm{Li},(\mathbf{b}) \mathrm{Ba},(\mathbf{c})\) Po,(d) I, \((\mathbf{e})\) Sb.

Using the periodic table to guide you, predict the chemical formula and name of the compound formed by the following elements: \((\mathbf{a})\) Ga and \(\mathrm{F},(\mathbf{b}) \mathrm{Li}\) and \(\mathrm{H},(\mathbf{c}) \mathrm{Al}\) and \(\mathrm{I},(\mathbf{d}) \mathrm{K}\) and \(\mathrm{S}\).

The most common charge associated with selenium is \(2-\). Indicate the chemical formulas you would expect for compounds formed between selenium and (a) barium, (b) lithium, (c) aluminum.

Predict the chemical formulas of the ionic compound formed by (a) \(\mathrm{Fe}^{3+}\) and \(\mathrm{OH}^{-},\) (b) \(\mathrm{Cs}^{+}\) and \(\mathrm{NO}_{3}^{-}\), (c) \(\mathrm{V}^{2+}\) and \(\mathrm{CH}_{3} \mathrm{COO}^{-},(\mathbf{d}) \mathrm{Li}^{+}\) and \(\mathrm{PO}_{4}^{3-},(\mathbf{e}) \mathrm{In}^{3+}\) and \(\mathrm{O}^{2-} .\)

Predict the chemical formulas of the compounds formed by the following pairs of ions: (a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{CN}^{-}\), (b) \(\mathrm{Mn}^{2+}\) and \(\mathrm{ClO}_{4}^{-}\), (c) \(\mathrm{Na}^{+}\) and \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\), (d) \(\mathrm{Cd}^{2+}\) and \(\mathrm{CO}_{3}^{2-}\), (e) \(\mathrm{Ti}^{4+}\) and \(\mathrm{O}^{2-}\).

Complete the table by filling in the formula for the ionic compound formed by each pair of cations and anions, as shown for the first pair. $$ \begin{array}{l|l|l|l|l} \hline \text { Ion } & \mathrm{K}^{+} & \mathrm{NH}_{4}^{+} & \mathrm{Mg}^{2+} & \mathrm{Fe}^{3+} \\ \hline \mathrm{Cl}^{-} & \mathrm{KCl} & & & \\ \mathrm{OH}^{-} & & & & \\ \mathrm{CO}_{3}^{2-} & & & & \\ \mathrm{PO}_{4}^{3-} & & & & \\ \hline \end{array} $$

Complete the table by filling in the formula for the ionic compound formed by each pair of cations and anions, as shown for the first pair. $$ \begin{array}{c|c|c|c|c} \hline \text { Ion } & \mathrm{Na}^{+} & \mathrm{Ca}^{2+} & \mathrm{Fe}^{2+} & \mathrm{Al}^{3+} \\ \hline \mathrm{O}^{2-} & \mathrm{Na}_{2} \mathrm{O} & & & \\ \mathrm{NO}_{3}^{-} & & & & \\ \mathrm{SO}_{4}^{2-} & & & & \\ \mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-} & & & & \\ \hline \end{array} $$

Predict whether each of the following compounds is molecular or ionic: \((\mathbf{a}) \mathrm{BI}_{3}(\mathbf{b}) \mathrm{N}\left(\mathrm{CH}_{3}\right)_{3}(\mathbf{c}) \mathrm{Zr}\left(\mathrm{NO}_{3}\right)_{2}(\mathbf{d}) \mathrm{N}_{2} \mathrm{H}_{4}(\mathbf{e})\) \(\mathrm{OsCO}_{3}(\mathbf{f}) \mathrm{H}_{2} \mathrm{SO}_{4}(\mathbf{g}) \mathrm{HgS}(\mathbf{h}) \mathrm{IOH} .\)

Give the chemical formula for (a) chromate ion (b) bromide ion (c) nitrite ion (d) sulphite ion (e) permanganate ion.

Selenium, an element required nutritionally in trace quantities, forms compounds analogous to sulfur. Name the following ions: (a) \(\mathrm{SeO}_{4}^{2-},(\mathbf{b}) \mathrm{Se}^{2-}\), (c) \(\mathrm{HSe}^{-}\), (d) \(\mathrm{HSeO}_{3}^{-}\).

Selenium, an element required nutritionally in trace quantities, forms compounds analogous to sulfur. Name the following ions: \((\mathbf{a}) \mathrm{SeO}_{4}^{2-},(\mathbf{b}) \mathrm{Se}^{2-},(\mathbf{c}) \mathrm{HSe}^{-},(\mathbf{d}) \mathrm{HSeO}_{3}^{-}\).

Give the names and charges of the cation and anion in each of the following compounds: (a) CuS, (b) \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\), (c) \(\mathrm{Al}\left(\mathrm{ClO}_{3}\right)_{3}\), (d) \(\mathrm{Co}(\mathrm{OH})_{2}\), (e) \(\mathrm{PbCO}_{3}\).

Name the following ionic compounds: (a) \(\mathrm{Li}_{2} \mathrm{O}\), (b) \(\mathrm{FeCl}_{3}\), (c) \(\mathrm{NaClO},(\mathbf{d}) \mathrm{CaSO}_{3},(\mathbf{e}) \mathrm{Cu}(\mathrm{OH})_{2},\), (f) \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}\), (g) \(\mathrm{Ca}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2}\), (h) \(\mathrm{Cr}_{2}\left(\mathrm{CO}_{3}\right)_{3},(\mathbf{i}) \mathrm{K}_{2} \mathrm{CrO}_{4},(\mathbf{j})\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\).

Name the following ionic compounds: \((\mathbf{a}) \mathrm{KCN},(\mathbf{b}) \mathrm{NaBrO}_{2},\) (c) \(\mathrm{Sr}(\mathrm{OH})_{2}\), (d) CoTe, (e) \(\mathrm{Fe}_{2}\left(\mathrm{CO}_{3}\right)_{3},\), (f) \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\), (h) \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\), (i) \(\mathrm{KMnO}_{4}\), (g) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3},\), , (j) \(\mathrm{Ag}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\).

Write the chemical formulas for the following compounds: (a) aluminum hydroxide, (b) potassium sulfate, (c) copper(I) oxide, \((\mathbf{d})\) zinc nitrate, \((\mathbf{e})\) mercury(II) bromide, (f) iron(III) carbonate, \((\mathbf{g})\) sodium hypobromite.

Give the chemical formula for each of the following ionic compounds: (a) sodium phosphate, (b) zinc nitrate, (c) barium bromate, \((\mathbf{d})\) iron(II) perchlorate, \((\mathbf{e})\) cobalt(II) hydrogen carbonate, (f) chromium(III) acetate, \((\mathbf{g})\) potassium dichromate.

Give the name or chemical formula, as appropriate, for each of the following acids: \((\mathbf{a}) \mathrm{HBrO}_{3},(\mathbf{b}) \mathrm{HBr},(\mathbf{c}) \mathrm{H}_{3} \mathrm{PO}_{4},(\mathbf{d})\) hypochlorous acid, \((\mathbf{e})\) iodic acid, \((\mathbf{f})\) sulfurous acid.