Chapter 2

An element has four naturally occurring isotopes with the masses and natural abundances given here. Find the atomic mass of the element and identify it. $$ \begin{array}{ccc} \text { Isotope } & \text { Mass (amu) } & \text { Abundance (\%) } \\ \hline 1 & 135.90714 & 0.19 \\ \hline 2 & 137.90599 & 0.25 \\ \hline 3 & 139.90543 & 88.43 \\ \hline 4 & 141.90924 & 11.13 \\ \hline \end{array} $$

How many sulfur atoms are there in 5.52 mol of sulfur?

How many moles of aluminum do \(3.7 \times 10^{24}\) aluminum atoms represent?

What is the amount, in moles, of each elemental sample? a. \(11.8 \mathrm{~g} \mathrm{Ar}\) b. \(3.55 \mathrm{~g} \mathrm{Zn}\) c. \(26.1 \mathrm{~g}\) Ta d. \(0.211 \mathrm{~g}\) Li

What is the mass, in grams, of each elemental sample? a. \(2.3 \times 10^{-3} \mathrm{~mol} \mathrm{Sb}\) b. \(0.0355 \mathrm{~mol} \mathrm{Ba}\) c. \(43.9 \mathrm{~mol} \mathrm{Xe}\) d. \(1.3 \mathrm{~mol} \mathrm{~W}\)

Calculate the number of atoms in each sample. a. \(5.18 \mathrm{~g} \mathrm{P}\) b. \(2.26 \mathrm{~g} \mathrm{Hg}\) c. \(1.87 \mathrm{~g}\) Bi d. \(0.082 \mathrm{~g} \mathrm{Sr}\)

Calculate the number of atoms in each sample. a. \(14.955 \mathrm{~g} \mathrm{Cr}\) b. \(39.733 \mathrm{~g} \mathrm{~S}\) c. \(12.899 \mathrm{~g} \mathrm{Pt}\) d. \(97.552 \mathrm{~g} \mathrm{Sn}\)

Calculate the mass, in \(\mathrm{kg}\), of each sample. a. \(7.55 \times 10^{26}\) cadmium atoms b. \(8.15 \times 10^{27}\) nickel atoms c. \(1.22 \times 10^{27}\) manganese atoms d. \(5.48 \times 10^{29}\) lithium atoms

A 7.83 g sample of \(\mathrm{HCN}\) contains \(0.290 \mathrm{~g}\) of \(\mathrm{H}\) and \(4.06 \mathrm{~g}\) of \(\mathrm{N}\). Find the mass of carbon in a sample of HCN with a mass of \(3.37 \mathrm{~g}\).

The ratio of oxygen to carbon by mass in carbon monoxide is \(1.33: 1.00 .\) Find the formula of an oxide of carbon in which the ratio by mass of oxygen to carbon is 2.00: 1.00 .

The ratio of the mass of a nitrogen atom to the mass of an atom of \({ }^{12} \mathrm{C}\) is \(7: 6,\) and the ratio of the mass of nitrogen to oxygen in \(\mathrm{N}_{2} \mathrm{O}\) is \(7: 4 .\) Find the mass of \(1 \mathrm{~mol}\) of oxygen atoms.

Naturally occurring iodine has an atomic mass of 126.9045 amu. \(\mathrm{A} 12.3849 \mathrm{~g}\) sample of iodine is accidentally contaminated with an additional \(1.00070 \mathrm{~g}\) of \({ }^{129} \mathrm{I}\), a synthetic radioisotope of iodine used in the treatment of certain diseases of the thyroid gland. The mass of \({ }^{129} \mathrm{I}\) is 128.9050 amu. Find the apparent "atomic mass" of the contaminated iodine.

Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately \(2.7 \mathrm{fm}\) (femtometers), and the radius of the atom is approximately \(70 \mathrm{pm}\) (picometers). Calculate the volume of the nucleus and the volume of the atom. What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.)

A penny has a thickness of approximately \(1.0 \mathrm{~mm} .\) If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in \(\mathrm{km}\) )? [For comparison, the sun is about 150 million \(\mathrm{km}\) from Earth, and the nearest star (Proxima Centauri) is about 40 trillion \(\mathrm{km}\) from Earth.]

Use the concepts in this chapter to obtain an estimate for the number of atoms in the universe. Make the following assumptions: (a) All of the atoms in the universe are hydrogen atoms in stars. (This is not a ridiculous assumption because over threefourths of the atoms in the universe are in fact hydrogen. Gas and dust between the stars represent only about \(15 \%\) of the visible matter of our galaxy, and planets compose a far tinier fraction.) (b) The sun is a typical star composed of pure hydrogen with a density of \(1.4 \mathrm{~g} / \mathrm{cm}^{3}\) and a radius of \(7 \times 10^{8} \mathrm{~m}\). (c) Each of the roughly 100 billion stars in the Milky Way galaxy contains the same number of atoms as our sun. (d) Each of the 10 billion galaxies in the visible universe contains the same number of atoms as our Milky Way galaxy.

The ratio of oxygen to nitrogen by mass in \(\mathrm{NO}_{2}\) is \(2.29 .\) The ratio of fluorine to nitrogen by mass in \(\mathrm{NF}_{3}\) is \(4.07 .\) Find the ratio of oxygen to fluorine by mass in \(\mathrm{OF}_{2}\).

Naturally occurring magnesium has an atomic mass of 24.312 and consists of three isotopes. The major isotope is \({ }^{24} \mathrm{Mg},\) natural abundance \(78.99 \%\), relative atomic mass 23.98504 . The next most abundant isotope is \({ }^{26} \mathrm{Mg},\) relative atomic mass \(25.98259 .\) The third most abundant isotope is \({ }^{25} \mathrm{Mg},\) whose natural abundance is in the ratio of 0.9083 to that of \({ }^{26} \mathrm{Mg}\). Find the relative atomic mass of \({ }^{25} \mathrm{Mg}\).

Which answer is an example of the law of multiple proportions? Explain. a. Two different samples of water are found to have the same ratio of hydrogen to oxygen. b. When hydrogen and oxygen react, the mass of water formed is exactly equal to the mass of hydrogen and oxygen that reacted. c. The mass ratio of oxygen to hydrogen in water is \(8: 1 .\) The mass ratio of oxygen to hydrogen in hydrogen peroxide (a compound that only contains hydrogen and oxygen) is 16:1.

Lithium has two naturally occurring isotopes: Li-6 (natural abundance \(7.5 \%\) ) and Li-7 (natural abundance \(92.5 \%\) ). Using circles to represent protons and squares to represent neutrons, draw the nucleus of each isotope. How many Li-6 atoms are present, on average, in a 1000 -atom sample of lithium?

As we saw in the previous problem, lithium has two naturally occurring isotopes: Li-6 (natural abundance 7.5\%; mass 6.0151 amu) and Li-7 (natural abundance \(92.5 \% ;\) mass 7.0160 amu). Without doing any calculations, determine which mass is closest to the atomic mass of Li. a. 6.00 amu b. 6.50 amu c. 7.00 amu

The mole is defined as the amount of a substance containing the same number of particles as exactly \(12 \mathrm{~g}\) of \(\mathrm{C}-12 .\) The amu is defined as \(1 / 12\) of the mass of an atom of \(\mathrm{C}-12 .\) Why is it important that both of these definitions reference the same isotope? What would be the result, for example, of defining the mole with respect to \(\mathrm{C}-12\), but the amu with respect to Ne- \(20 ?\)

The atomic radii of the isotopes of an element are identical to one another. However, the atomic radii of the ions of an element are significantly different from the atomic radii of the neutral atom of the element. Explain.

Discuss these questions with the group and record your consensus answer. The table shown here includes data similar to those used by Mendeleev when he created the periodic table. On a small card, write the symbol, atomic mass, and a stable compound formed by each element. Without consulting a periodic table, arrange the cards so that atomic mass increases from left to right and elements with similar properties are above and below each other. Copy the periodic table you have invented onto a piece of paper. There is one element missing. Predict its mass and a stable compound it might form. $$ \begin{array}{ccc} \text { Element } & \text { Atomic Mass } & \text { Stable Compound } \\ \hline \text { Be } & 9 & \text { BeCI }_{2} \\ \hline \text { S } & 32 & \mathrm{H}_{2} \mathrm{~S} \\ \hline \mathrm{F} & 19 & \mathrm{~F}_{2} \\ \hline \mathrm{Ca} & 40 & \mathrm{CaCl}_{2} \\ \hline \mathrm{Li} & 7 & \mathrm{LiCl} \\ \hline \mathrm{Si} & 28 & \mathrm{SiH}_{4} \\ \hline \mathrm{Cl} & 35.4 & \mathrm{Cl}_{2} \\ \hline \mathrm{B} & 10.8 & \mathrm{BH}_{3} \\ \hline \mathrm{Ge} & 72.6 & \mathrm{GeH}_{4} \\ \hline \mathrm{N} & 14 & \mathrm{NF}_{3} \\ \hline \mathrm{O} & 16 & \mathrm{H}_{2} \mathrm{O} \\ \hline \mathrm{Ga} & 69.7 & \mathrm{GaH}_{3} \\ \hline \hline \text { As } & 75 & \text { AsF }_{3} \\ \hline \text { C } & 12 & \text { CH }_{4} \\ \hline \text { K } & 39 & \text { KCl } \\ \hline \text { Mg } & 24.3 & \text { MgCl }_{2} \\ \hline \text { Se } & 79 & \text { H }_{2} \text { Se } \\ \hline \text { Al } & 27 & \text { AlH }_{3} \\ \hline \text { Br } & 80 & \text { Br }_{2} \\ \hline \text { Na } & 23 & \text { NaCl } \\ \hline \end{array} $$

In complete sentences, describe the similarities and differences between: a. different isotopes of an element b. a neutral atom and an ion of the same element

Calculate the mass in grams of one mole of each of the following (the mass of a single item is given in parentheses): electrons \(\left(9.10938 \times 10^{-28} \mathrm{~g}\right),\) protons \(\left(1.67262 \times 10^{-24} \mathrm{~g}\right),\) neutrons \(\left(1.67493 \times 10^{-24} \mathrm{~g}\right),\) atoms of carbon- \(12\left(1.992646 \times 10^{-23} \mathrm{~g}\right)\) and doughnuts \((74 \mathrm{~g})\). Compare the mass of one mole of carbon-12 atoms to the sum of the masses of the particles that it contains. If the doughnut mentioned in this question were made entirely of carbon, how many atoms would it contain?