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Chapter 18: Problem 18

Assign oxidation numbers to all the atoms in each of the following: a. \(\mathrm{HNO}_{3} \quad\) g. \(\mathrm{PbSO}_{4}\) b. \(\mathrm{CuCl}_{2} \quad\) h. \(\mathrm{PbO}_{2}\) c. \(\mathrm{O}_{2} \quad\) i. \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) d. \(\mathrm{H}_{2} \mathrm{O}_{2} \quad\) j. \(\mathrm{CO}_{2}\) e. \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \quad \mathrm{k} .\left(\mathrm{NH}_{0}\right)_{2} \mathrm{Ce}\left(\mathrm{SO}_{4}\right)_{3}\) f. \(\mathrm{Ag} \quad\) l. \(\mathrm{Cr}_{2} \mathrm{O}_{3}\)

Short Answer

Expert verified
Oxidation numbers for the given compounds: a. \(\mathrm{HNO}_{3}\): H(+1), N(+5), O(-2) b. \(\mathrm{CuCl}_{2}\): Cu(+2), Cl(-1) c. \(\mathrm{O}_{2}\): O(0) d. \(\mathrm{H}_{2} \mathrm{O}_{2}\): H(+1), O(-1) e. \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\): H(+1), O(-2), C(+4) f. \(\mathrm{Ag}\): Ag(0) g. \(\mathrm{PbSO}_{4}\): Pb(+2), S(+6), O(-2) h. \(\mathrm{PbO}_{2}\): Pb(+4), O(-2) i. \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\): Na(+1), C(+3), O(-2) j. \(\mathrm{CO}_{2}\): C(+4), O(-2) k. \(\left(\mathrm{NH}_{0}\right)_{2} \mathrm{Ce}\left(\mathrm{SO}_{4}\right)_{3}\): N(-3), H(+1), O(-2), Ce(+3), S(+6) l. \(\mathrm{Cr}_{2} \mathrm{O}_{3}\): Cr(+3), O(-2)

Step by step solution

01

Rule for assigning oxidation numbers

The oxidation number of an atom is assigned according to the following rules: 1. The oxidation number of an element in its free (uncombined) state is zero. 2. The oxidation number of a monatomic ion is equal to its charge. 3. The sum of all oxidation numbers in a neutral compound is zero. 4. The sum of all oxidation numbers in a polyatomic ion is equal to the charge of the ion. 5. The oxidation number of hydrogen in a compound is +1, except in metal hydrides, where it is -1. 6. The oxidation number of oxygen in a compound is -2, except in peroxides, where it is -1. 7. The oxidation number of an atom in a compound can also be determined by considering the electronegativity of the elements. Now let's assign the oxidation numbers to the atoms in each compound: a. \(\mathrm{HNO}_{3}\)
02

Assign H, N, and O oxidation numbers based on the rules

Using the rules explained above, we can determine the oxidation numbers of H, N, and O in \(\mathrm{HNO}_{3}\): 1. Hydrogen (H): +1 2. Oxygen (O): -2 3. Nitrogen (N): Unknown
03

Apply the rule that the sum of oxidation numbers is zero

Now we can use the rule that the sum of oxidation numbers in a neutral compound is zero to find the oxidation number of nitrogen: (+1) + x + (-2)(3) = 0 Solving for x, x = +5 Therefore, the oxidation numbers for \(\mathrm{HNO}_{3}\) are: H(+1), N(+5), and O(-2). We will now follow the same procedure for the remaining compounds: b. \(\mathrm{CuCl}_{2}\) Cu: +2 (from the charge of the ion) Cl: -1 (from the charge of the ion) c. \(\mathrm{O}_{2}\) (element in its free state) O: 0 d. \(\mathrm{H}_{2} \mathrm{O}_{2}\) (remember that this is a peroxide) H: +1 O: -1 (since it's a peroxide) e. \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) H: +1 O: -2 C: +4 (calculated based on the rules) f. \(\mathrm{Ag}\) (element in its free state) Ag: 0 g. \(\mathrm{PbSO}_{4}\) Pb: +2 (from the charge of the ion) S: +6 (calculated based on the rules) O: -2 h. \(\mathrm{PbO}_{2}\) Pb: +4 (from the charge of the ion) O: -2 i. \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) Na: +1 C: +3 (calculated based on the rules) O: -2 j. \(\mathrm{CO}_{2}\) C: +4 (calculated based on the rules) O: -2 k. \(\left(\mathrm{NH}_{0}\right)_{2} \mathrm{Ce}\left(\mathrm{SO}_{4}\right)_{3}\) N: -3 (calculated based on the rules) H: +1 O: -2 Ce: +3 (from the charge of the ion) S: +6 (calculated based on the rules) l. \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) Cr: +3 (calculated based on the rules) O: -2

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Redox Reactions
Redox reactions, short for reduction-oxidation reactions, are processes in which electrons are transferred between chemical species. Understanding these reactions is important because they are fundamental to various chemical, biological, and industrial processes. In a redox reaction, one species undergoes oxidation, losing electrons, while another species undergoes reduction, gaining those electrons.

This electron transfer leads to changes in the oxidation states of the elements involved. For instance, when looking at the example of the compound a) \(\mathrm{HNO}_3\), during the assignment of oxidation numbers, we recognized that hydrogen had an oxidation state of +1, nitrogen was +5, and oxygen was -2. In potential redox reactions involving this compound, these oxidation states might change as electrons are transferred.
  • Oxidation: Increase in oxidation number (loses electrons).
  • Reduction: Decrease in oxidation number (gains electrons).
It's crucial to note that many reactions in everyday life, like combustion or rusting, are redox processes. Understanding the concept of oxidation and reduction is key to predicting how different chemical compounds behave in redox reactions.
Chemical Compounds
Chemical compounds are substances formed by the chemical combination of two or more elements. These elements are bonded together in specific ratios, creating distinct chemical and physical properties. Understanding chemical compounds involves knowing their composition and how the elements within them interact based on chemical principles.

For instance, the compound \(\mathrm{CuCl}_2\) consists of copper (Cu) and chlorine (Cl) atoms. By assigning oxidation numbers, we find that copper carries a +2 charge, while chlorine carries a -1 charge. The compound is neutral overall, demonstrating the balance of charges in chemical compounds.

Chemical compounds can be classified into different categories, such as:
  • Ionic compounds: Formed through ionic bonding.
  • Covalent compounds: Formed through covalent bonding.
The nomenclature and formulae of chemical compounds provide essential information about the proportion of elements and their chemical environment. This fundamental understanding helps predict how compounds react with each other, affecting properties like reactivity and stability.
Chemical Bonding
Chemical bonding is the force that holds atoms together in a compound. Understanding the types of bonds and how they form is essential for explaining the behaviors of different materials and substances.

There are several types of chemical bonds:
  • Ionic Bonds: Formed when electrons are transferred from one atom to another, resulting in positively and negatively charged ions, like in \(\mathrm{CuCl}_2\).
  • Covalent Bonds: Occur when two atoms share one or more pairs of electrons. These bonds are common in organic compounds, such as \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\).
  • Metallic Bonds: Found in metals, where electrons are free to move throughout a lattice of metal cations.
Chemical bonding directly influences the structure and properties of a compound. For example, the ionic bonds in \(\mathrm{CuCl}_2\) contribute to its properties such as high melting point and conductivity when dissolved in water. Understanding the underlying bonding principles helps predict how compounds will interact and behave.
Periodic Table
The periodic table is a systematic way of organizing elements according to their atomic number, electron configurations, and recurring chemical properties. It is a valuable tool for chemists, providing critical information about the elements, including trends in atomic size, electronegativity, and ionization energy.

When assigning oxidation numbers to elements in compounds, the periodic table offers insights into possible oxidation states based on an element's position. For instance, elements in Group 1, like Sodium in \(\mathrm{Na}_2\mathrm{C}_2\mathrm{O}_4\), typically have an oxidation state of +1 due to their tendency to lose one electron.

Some useful periodic trends include:
  • Metallic character: Decreases from left to right across a period.
  • Electronegativity: Increases across a period and decreases down a group.
  • Atomic radii: Decreases across a period and increases down a group.
The periodic table is not only crucial for identifying elements but also for predicting how they might bond and react based on their properties and interactions with other elements. It's a foundational tool for making sense of chemical behavior and reactivity.

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Most popular questions from this chapter

Sketch the galvanic cells based on the following overall reactions. Show the direction of electron flow, the direction of ion migration through the salt bridge, and identify the cathode and anode. Give the overall balanced equation. Assume that all concentrations are 1.0 \(M\) and that all partial pressures are 1.0 atm. a. \(\mathrm{IO}_{3}^{-}(a q)+\mathrm{Fe}^{2+}(a q) \Longrightarrow \mathrm{Fe}^{3+}(a q)+\mathrm{I}_{2}(a q)\) b. \(\mathrm{Zn}(s)+\mathrm{Ag}^{+}(a q) \rightleftharpoons \mathrm{Zn}^{2+}(a q)+\mathrm{Ag}(s)\)

Consider the following electrochemical cell: a. If silver metal is a product of the reaction, is the cell a galvanic cell or electrolytic cell? Label the cathode and anode, and describe the direction of the electron flow. b. If copper metal is a product of the reaction, is the cell a galvanic cell or electrolytic cell? Label the cathode and anode, and describe the direction of the electron flow. c. If the above cell is a galvanic cell, determine the standard cell potential. d. If the above cell is an electrolytic cell, determine the minimum external potential that must be applied to cause the reaction to occur.

The black silver sulfide discoloration of silverware can be removed by heating the silver article in a sodium carbonate solution in an aluminum pan. The reaction is $$3 \mathrm{Ag}_{2} \mathrm{S}(s)+2 \mathrm{Al}(s) \rightleftharpoons 6 \mathrm{Ag}(s)+3 \mathrm{S}^{2-}(a q)+2 \mathrm{Al}^{3+}(a q)$$ a. Using data in Appendix \(4,\) calculate \(\Delta G^{\circ}, K,\) and \(\mathscr{E}^{\circ}\) for the above reaction at \(25^{\circ} \mathrm{C} .\left[\text { For } \mathrm{Al}^{3+}(a q), \Delta G_{\mathrm{f}}^{\circ}=-480 . \mathrm{kJ} / \mathrm{mol.}\right]\) b. Calculate the value of the standard reduction potential for the following half-reaction: $$2 \mathrm{e}^{-}+\mathrm{Ag}_{2} \mathrm{S}(s) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)$$

When copper reacts with nitric acid, a mixture of \(\mathrm{NO}(g)\) and \(\mathrm{NO}_{2}(g)\) is evolved. The volume ratio of the two product gases depends on the concentration of the nitric acid according to the equilibrium $$2 \mathrm{H}^{+}(a q)+2 \mathrm{NO}_{3}^{-}(a q)+\mathrm{NO}(g) \rightleftharpoons 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$$ Consider the following standard reduction potentials at \(25^{\circ} \mathrm{C} :\) $$3 \mathrm{e}^{-}+4 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ $$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \mathscr{E}^{\circ}=0.957 \mathrm{V}$$ $$\mathrm{e}^{-}+2 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ $$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \mathscr{E}^{\circ}=0.775 \mathrm{V}$$ a. Calculate the equilibrium constant for the above reaction. b. What concentration of nitric acid will produce a NO and NO \(_{2}\) mixture with only 0.20\(\% \mathrm{NO}_{2}\) (by moles) at \(25^{\circ} \mathrm{C}\) and 1.00 atm? Assume that no other gases are present and that the change in acid concentration can be neglected.

In the electrolysis of a sodium chloride solution, what volume of \(\mathrm{H}_{2}(g)\) is produced in the same time it takes to produce 257 \(\mathrm{L} \mathrm{Cl}_{2}(g),\) with both volumes measured at \(50 .^{\circ} \mathrm{C}\) and 2.50 \(\mathrm{atm}\) ?
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