Essential Ideas

Check Your Learning (a) To three decimal places, what is the volume of a cube \(\left( {c{m^2}{\rm{ }}} \right)\) with an edge length of \(0.843{\rm{ }}cm\)? (b) If the cube in part (a) is copper and has a mass of \(5.34{\rm{ }}g,\) what is the density of copper to two decimal places

A very good 197-lb weight lifter lifted 192 kg in a move called the clean and jerk. What was the mass of theweight lifted in pounds?

Question: In terms of the kinetic molecular theory, in what ways are liquids similar to solids? In what ways are liquids different from solids?

Question: Show by suitable net ionic equations that each of the following species can act as a Bronsted-Lowry acid: (a) \({H_3}{O^ + }\)(b) \(HCl\) (c)\(N{H_3}\)(d) \(C{H_3}C{O_2}H\) (e) \(NH_4^ + \)(f) \(HSO_4^ - \)

How do the concentrations of \(P{b^{2 + }}\)  \(and {S^{2 - }}\)  change when  \({K_2}\;S\)   is added to a saturated solution of PbS? 

How much heat is produced when 100 mL of 0.250 M HCl (density, 1.00 g/mL) and 200 mL of 0.150 M NaOH (density, 1.00 g/mL) are mixed?

\({\bf{HCl(aq)  +   NaOH(aq)}} \to {\bf{NaCl(aq)   +  }}{{\bf{H}}_{\bf{2}}}{\bf{O(l)           \Delta H}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ =  - 58kJ}}\)

If both solutions are at the same temperature and the heat capacity of the products is 4.19 J/g °C, how much will the temperature increase? What assumption did you make in your calculation?

Does the standard enthalpy of formation of \({{\bf{H}}_{\bf{2}}}{\bf{O}}\left( {\bf{g}} \right)\)differ from ΔH° for the reaction \({\bf{2}}{{\bf{H}}_{\bf{2}}}\left( {\bf{g}} \right){\bf{  +  }}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right) \to {\bf{2}}{{\bf{H}}_{\bf{2}}}{\bf{O}}\left( {\bf{g}} \right)\)?

Both graphite and diamond burn.

\({\bf{C}}\left( {{\bf{s, diamond}}} \right){\bf{  +  }}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right) \to {\bf{C}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right)\)

For the conversion of graphite to diamond:

\({\bf{C}}\left( {{\bf{s, graphite}}} \right) \to {\bf{C}}\left( {{\bf{s, diamond}}} \right){\bf{                 \Delta {\rm H}}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = 1}}{\bf{.90 kJ}}\)

Which produces more heat, the combustion of graphite or the combustion of a diamond?

Which produces more heat?

\({\bf{Os}}\left( {\bf{s}} \right) \to {\bf{2}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right) \to {\bf{Os}}{{\bf{O}}_{\bf{4}}}\left( {\bf{s}} \right)\)

or

\({\bf{Os}}\left( {\bf{s}} \right) \to {\bf{2}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right) \to {\bf{Os}}{{\bf{O}}_{\bf{4}}}\left( {\bf{g}} \right)\)

for the phase change \({\bf{Os}}{{\bf{O}}_{\bf{4}}}\left( {\bf{s}} \right) \to {\bf{Os}}{{\bf{O}}_{\bf{4}}}\left( {\bf{g}} \right){\bf{                 \Delta H =  56}}{\bf{.4 kJ}}\)

Calculate \({\bf{\Delta {\rm H}}}_{{\bf{298K}}}^{\bf{^\circ }}\) for the process

\({\bf{Sb(s)  + }}\frac{{\bf{5}}}{{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{(g)}} \to {\bf{SbC}}{{\bf{l}}_{\bf{5}}}\left( {\bf{g}} \right)\)

from the following information:

\({\bf{Sb(s)  + }}\frac{{\bf{3}}}{{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{(g)}} \to {\bf{SbC}}{{\bf{l}}_{\bf{3}}}\left( {\bf{g}} \right){\bf{                 \Delta {\rm H}}}_{{\bf{298K}}}^{\bf{^\circ }}{\bf{ =   - 314kJ}}\)

\({\bf{SbC}}{{\bf{l}}_{\bf{3}}}\left( {\bf{g}} \right){\bf{ + C}}{{\bf{l}}_{\bf{2}}}{\bf{(g) }} \to {\bf{ SbC}}{{\bf{l}}_{\bf{5}}}\left( {\bf{g}} \right){\bf{               \Delta {\rm H}}}_{{\bf{298K}}}^{\bf{^\circ }}{\bf{ =   - 80kJ}}\)

Calculate\({\bf{\Delta H}}_{{\bf{298 }}}^{\bf{^\circ }}\) for the process Zn(s) + S(s) + 2O₂(g)⟶ZnSO₄(s)

from the following information:

\({\bf{Zn}}\left( {\bf{s}} \right){\bf{  +   S}}\left( {\bf{s}} \right) \to {\bf{ZnS}}\left( {\bf{s}} \right){\bf{  \Delta H}}_{{\bf{298 }}}^{\bf{^\circ }}{\bf{ =   - 206}}{\bf{.0 kJ}}\)

\({\bf{ZnS}}\left( {\bf{s}} \right){\bf{  +   2}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right) \to {\bf{ZnS}}{{\bf{O}}_{\bf{4}}}\left( {\bf{s}} \right){\bf{      \Delta H}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{  =   - 776}}{\bf{.8 kJ}}\)

Calculate the standard molar enthalpy of formation of NO(g) from the following data:

\({{\bf{N}}_{\bf{2}}}\left( {\bf{g}} \right){\bf{  +  2}}{{\bf{O}}_{\bf{2}}} \to {\bf{2N}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right){\bf{\;\;\;\;\;\Delta H}}_{{\bf{298 }}}^{\bf{^\circ }}{\bf{ = 66}}{\bf{.4kJ}}\) 

\({\bf{2NO}}\left( {\bf{g}} \right){\bf{  +  }}{{\bf{O}}_{\bf{2}}} \to {\bf{2N}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right){\bf{\;\;\;\;\Delta H}}_{{\bf{298 }}}^{\bf{^\circ }}{\bf{ =   - 114}}{\bf{.1kJ}}\)

The oxidation of the sugar glucose, \({{\bf{C}}_{\bf{6}}}{{\bf{H}}_{{\bf{12}}}}{{\bf{O}}_{\bf{6}}}\), is described by the following equation:

\({{\bf{C}}_{\bf{6}}}{{\bf{H}}_{{\bf{12}}}}{{\bf{O}}_{\bf{6}}}{\bf{(s)  +   6}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{6C}}{{\bf{O}}_{\bf{2}}}{\bf{(g)   +   6}}{{\bf{H}}_{\bf{2}}}{\bf{O(l)}};{\bf{ \Delta H =   - 2816 kJ}}\)

The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body.

(a) How much heat in kilojoules can be produced by the metabolism of 1.0 g of glucose?

(b) How many calories can be produced by the metabolism of 1.0 g of glucose?

Question: Show by suitable net ionic equations that each of the following species can act as a Bronsted-Lowry base:

\({\rm{a) H}}{{\rm{S}}^ - }\)

\({\rm{b)\;PO}}_4^{3 - }\) 

\({\rm{c) NH}}_2^ - \)

\({\rm{d)}}{{\rm{C}}_2}{{\rm{H}}_5}{\rm{OH}}\)

\({\rm{e)}}{{\rm{O}}^{2 - }}\)

\({\rm{f) }}{{\rm{H}}_2}{\rm{PO}}_4^ - \) 

Which molecule has a molecular mass of 28.05 amu?

(a) \({\rm{HC}} \equiv {\rm{CH}}\)

(b)

(c) 

Among the solubility rules previously discussed is the statement: All chlorides are soluble except \(H{g_2}C{l_2},\;AgC{l_{^2}},\;PbC{l_2}\) and \({\rm{CuCl}}.\)

(a) Write the expression for the equilibrium constant for the reaction represented by the equation \({\mathop{\rm AgCl}\nolimits} (s) \rightleftharpoons  {\rm{A}}{{\rm{g}}^ + }(aq) + {\rm{C}}{{\rm{l}}^ - }(aq)\). Is \({K_c} > 1,\; < 1\), or \( \approx 1\)? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation \({\rm{P}}{{\rm{b}}^{2 + }}(aq) + 2{\rm{C}}{{\rm{l}}^ - }(aq) \rightleftharpoons  {\rm{PbC}}{{\rm{l}}_2}(s)\). Is \({K_c} > 1,\; < 1\) or \( \approx 1\)? Explain your answer.

The edge length of the unit cell of KCl (NaCl-like structure, FCC) is 6.28 Å. Assuming anion-cation contact along the cell edge, calculate the radius of the potassium ion. The radius of the chloride ion is 1.82 Å.

A medical laboratory catalog describes the pressure in a cylinder of gas as 14.82MPa. What is the pressure of this gas in atmospheres and torr?

Explain why a carbon atom cannot form five bonds using \({\rm{s}}{{\rm{p}}^{\rm{3}}}{\rm{d}}\) hybrid orbitals.

Indicate the most important types of intermolecular attractions in each of the following solutions: 

1. NO (g) in CO (l) 
2. \({\bf{C}}{{\bf{l}}_{\bf{2}}}\) (g) in \({\bf{B}}{{\bf{r}}_{\bf{2}}}\) (l) 
3. HCl(g) in benzene \({{\bf{C}}_{\bf{6}}}{{\bf{H}}_{\bf{6}}}\) (l) 
4. Methanol \({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH}}\) (l) in \({{\bf{H}}_{\bf{2}}}{\bf{O}}\) (l)

Suppose you are presented with a clear solution of sodium thiosulfate, \({\bf{N}}{{\bf{a}}_{\bf{2}}}{{\bf{S}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}\). How could you determine whether the solution is unsaturated, saturated, or supersaturated?

Calculate the percent by mass of KBr in a saturated solution of KBr in water at 10 °C. See Figure for useful data, and report the computed percentage to one significant digit.

Iron(II) can be oxidized to iron(III) by dichromate ion, which is reduced to chromium(III) in acid solution. A 2.5000-g sample of iron ore is dissolved and the iron converted into iron(II). Exactly 19.17 mL of 0.0100 M \(N{a_2}C{r_2}{O_7}\)is required in the titration. What percentage of the ore sample was iron?

Write the symbol for each of the following ions: (a) the ion with a \(3 + \) charge, \(28\) electrons, and a mass number of \(71\)(b) the ion with \(36\) electrons, \(35\) protons, and \(45\) neutrons (c) the ion with \(86\) electrons, \(142\) neutrons, and a \(4 + \) charge (d) the ion with a \(2 + \) charge, atomic number \(38,\) and mass number \(87\) 

Question:  Which of the various particles (\(\alpha \)  particles, \(\beta \) particles, and so on) that may be produced in a nuclear reaction are actually nuclei?

Find the potentials of the following electrochemical cell:

\(Cd|C{d^{2 + }},M = 0.10||N{i^{2 + }},M = 0.50|Ni\)

Calculate the ionization constant for each of the following acids or bases from the ionization constant of its conjugate base or conjugate acid:

1. \({F^ - }\)
2. \(NH_4^ + \)
3. \(AsO_4^{3 - }\)
4. \({\left( {C{H_3}} \right)_2}NH_2^ + \)
5. \(N{O_2}\)
6. \(H{C_2}O_4^ - \) (asabase)

A 500-mL bottle of water at room temperature and a 2-L bottle of water at the same temperature were placed in a refrigerator. After 30 minutes, the 500-mL bottle of water had cooled to the temperature of the refrigerator. An hour later, the 2-L of water had cooled to the same temperature. When asked which sample of water lost the most heat, one student replied that both bottles lost the same amount of heat because they started at the same temperature and finished at the same temperature. A second student thought that the 2-L bottle of water lost more heat because there was more water. A third student believed that the 500-mL bottle of water lost more heat because it cooled more quickly. A fourth student thought that it was not possible to tell because we do not know the initial temperature and the final temperature of the water. Indicate which of these answers is correct and describe the error in each of the other answers.

Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when. Does it have a quantum number of 1?

Using the relevant \({\bf{S}}_{{\bf{298}}}^{\bf{^\circ }}\)values listed in Appendix G, calculate \({\bf{\Delta S}}_{{\bf{298}}}^{\bf{^\circ }}\)for the following changes:

(a) \({{\bf{N}}_{\bf{2}}}{\bf{(g) + 3}}{{\bf{H}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2N}}{{\bf{H}}_{\bf{3}}}{\bf{(g)}}\)

(b) \({{\bf{N}}_{\bf{2}}}{\bf{(g) + }}\frac{{\bf{5}}}{{\bf{2}}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {{\bf{N}}_{\bf{2}}}{{\bf{O}}_{\bf{5}}}{\bf{(g)}}\)

From the following information, determine \({\bf{\Delta S}}_{{\bf{298}}}^{\bf{^\circ }}\)for the following:

\(\begin{array}{*{20}{c}}{{\bf{N(g) + O(g)}} \to {\bf{NO(g)}}}&{{\bf{\Delta S}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = ?}}}\\{{\bf{\;}}{{\bf{N}}_{\bf{2}}}{\bf{(g) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2NO(g)}}}&{{\bf{\Delta S}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = 24}}{\bf{.8\;J/K}}}\\{{{\bf{N}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2\;N(g)}}}&{{\bf{\Delta S}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = 115}}{\bf{.0\;J/K}}}\\{{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2O(g)}}}&{{\bf{\Delta S}}_{{\bf{298}}}^{\bf{^\circ }}{\bf{ = 117}}{\bf{.0\;J/K}}}\end{array}\)

Use the standard entropy data in Appendix \(G\) to determine the change in entropy for each of the reactions listed in Exercise 16.33. All are run under standard state conditions and\({\bf{2}}{{\bf{5}}^{\bf{^\circ }}}{\bf{C}}\).

Use the standard entropy data in Appendix \(G\)to determine the change in entropy for each of the reactions listed in Exercise 16.34. All are run under standard state conditions and \({\bf{2}}{{\bf{5}}^{\bf{^\circ }}}{\bf{C}}\).

Carbon dioxide decomposes into \({\bf{CO}}\) and \({{\bf{O}}_{\bf{2}}}\)at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at \({\bf{100}}{{\bf{0}}^{\bf{^\circ }}}{\bf{C}}\) for which the initial pressure of \({\bf{C}}{{\bf{O}}_{\bf{2}}}\)was \({\bf{1}}{\bf{.15\;atm}}\)?

Determine the standard free energy change,  ΔG_f^°  , for the formation of \({{\rm{S}}^{2 - }}(aq)\) given that the ΔG_f^° for \({\rm{A}}{{\rm{g}}^ + }(aq)\) and \({\rm{A}}{{\rm{g}}_2}\;{\rm{S}}(s)\) are \(77.1\;{\rm{kJ}}/mole\) and \( - 39.5\;{\rm{kJ}}/{\rm{mole}}\) respectively, and the solubility product for \(Ag{\rm{S}}(s)\) is \(8 \times {10^{ - 51}}.\)

In glycolysis, the reaction of glucose (Glu) to form glucose-6-phosphate (G6P) requires ATP to be present as described by the following equation:

Glu + ATP → G6P + ADP

ΔG^°₂₉₈ = -17kJ

In this process, ATP becomes ADP summarized by the following equation:

ATP → ADP  ΔG^°₂₉₈ = -30kJ 

Determine the standard free energy change for the following reaction, and explain why ATP is necessary to drive this process:

Glu → G6P  ΔG^°₂₉₈ =  ?

Predict the sign of the enthalpy change for the following processes. Give a reason for your prediction.

(a) \({\bf{NaN}}{{\bf{O}}_{\bf{3}}}{\bf{(s)}} \to {\bf{N}}{{\bf{a}}^{\bf{ + }}}{\bf{(aq) + N}}{{\bf{O}}_{\bf{3}}}^{\bf{ - }}{\bf{(aq)}}\)

(b) the freezing of liquid water

(c) \({\bf{C}}{{\bf{O}}_{\bf{2}}}{\bf{(s)}} \to {\bf{C}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

(d) \({\bf{CaCO(s)}} \to {\bf{CaO(s) + C}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

Use standard enthalpy and entropy data from Appendix G to calculate the standard free energy change forthe reaction shown here (298 K). What does the computed value for ΔG° say about the spontaneity of thisprocess?

\({{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{6}}}{\bf{(g)}} \to {{\bf{H}}_{\bf{2}}}{\bf{(g) + }}{{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}{\bf{(g)}}\)

The following are properties of isotopes of two elements that are essential in our diet. Determine the number of protons, neutrons and electrons in each and name them. (a) atomic number 26, mass number 58, charge of 2⁺(b) atomic number 53, mass number 127, charge of 1⁻

If a 2.5 A current is run through a circuit for 35 minutes, how many coulombs of charge moved through the circuit?

Given the following pairs of balanced half-reactions, determine the balanced reaction for each pair of half reactions in an acidic solution.

(a) \({\rm{Ca}} \to {\rm{C}}{{\rm{a}}^{2 + }} + 2{{\rm{e}}^ - },\quad {{\rm{F}}_2} + 2{{\rm{e}}^ - } \to 2\;{{\rm{F}}^ - }\)

(b) \({\rm{Li}} \to {\rm{L}}{{\rm{i}}^ + } + {{\rm{e}}^ - },\quad {\rm{C}}{{\rm{l}}_2} + 2{{\rm{e}}^ - } \to 2{\rm{C}}{{\rm{l}}^ - }\)

(c) \({\rm{Fe}} \to {\rm{F}}{{\rm{e}}^{3 + }} + 3{{\rm{e}}^ - },\quad {\rm{B}}{{\rm{r}}_2} + 2{{\rm{e}}^ - } \to 2{\rm{B}}{{\rm{r}}^ - }\)

(d) \({\rm{Ag}} \to {\rm{A}}{{\rm{g}}^ + } + {{\rm{e}}^ - },\quad {\rm{MnO}}_4^ -   + 4{{\rm{H}}^ + } + 3{{\rm{e}}^ - } \to {\rm{Mn}}{{\rm{O}}_2} + 2{{\rm{H}}_2}{\rm{O}}\)

Explain why hydrogen sulfide is a gas at room temperature, whereas water, which has a lower molecular mass, is a liquid.

98. Explain why sulfuric acid,\({{\rm{H}}_2}{\rm{S}}{{\rm{O}}_4}\) , which is a covalent molecule, dissolves in water and produces a solution that contains ions.

Predict the products of the following reactions and balance the equations.

(a) Zn is added to a solution of Cr₂(SO₄)₃ in acid.

(b) FeCl₂ is added to a solution containing an excess of Cr₂O₇²⁻ in hydrochloric acid.

(c) Cr²⁺ is added to Cr₂O₇²⁻ in acid solution.

(d) Mn is heated with CrO₃.

(e) CrO is added to 2HNO₃ in water.

(f) FeCl3 is added to an aqueous solution of NaOH.

Most barium compounds are very poisonous; however, barium sulfate is often administered internally as an aid in the X-ray examination of the lower intestinal tract (Figure 15.4). This use of \(BaS{O_4}\) is possible because of its low solubility. Calculate the molar solubility of \(BaS{O_4}\)and the mass of barium present in \(1.00\;L\)of water saturated with\(BaS{O_4}\).

Question: The following nuclei do not lie in the band of stability. How would they be expected to decay? 

(a) \({}_{{\rm{15}}}^{{\rm{28}}}{\rm{P}}\)

(b) \({}_{{\rm{92}}}^{{\rm{235}}}{\rm{U}}\)

(c) \({}_{20}^{{\rm{37}}}{\rm{Ca}}\)

(d) \({}_3^{\rm{9}}{\rm{Li}}\)

(e) \({}_{96}^{{\rm{245}}}{\rm{Cm}}\)

Question: Predict by what mode(s) of spontaneous radioactive decay each of the following unstable isotopes might proceed: 

(a) \({}_2^{\rm{6}}He\)

(b) \({}_{30}^{60}Zn\)

(c) \({}_{91}^{{\rm{235}}}Pa\)

(d) \({}_{94}^{241}{\rm{Np}}\)

(e) \({}^{18}{\rm{F}}\)

(f) \({}^{129}Ba\)

(g) \({}^{237}{\rm{Pu}}\)

What are the allowed values for each of the four quantum numbers: n, l, ml, and ms? 

A compound with a molar mass of about \({\rm{28 g/mol}}\) contains \({\rm{85}}{\rm{.7 \% }}\) carbon and \({\rm{14}}{\rm{.3 \% }}\) hydrogen by mass. Write the Lewis structure for a molecule of the compound.

(a) What are the mass, volume and density of the yellow block?

(b) What are the mass, volume and density of the red block?

(c) List the block colors in order from smallest to largest mass.

(d) List the block colors in order from lowest to highest density.

(e) How are mass and density related for blocks of the same volume?