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5.4 Practice Problems

5.4 Practice Problems#

  1. Determine the oxidation number of each atom in the following compounds and ion: (a) \(\ce{SO2}\), (b) \(\ce{NaH}\), (c) \(\ce{CO3^2-}\), (d) \(\ce{N2O5}\).

  2. Rank the following sets of chemical compounds from the most oxidized to the most reduced form:

    1. \(\ce{NH3}\), \(\ce{NO3-}\), \(\ce{NO2-}\), \(\ce{N2}\)

    2. \(\ce{H2SO4}\), \(\ce{SO4^2-}\), \(\ce{H2S}\), \(\ce{SO2}\), \(\ce{SO3}\)

    3. \(\ce{Cr(s)}\), \(\ce{K2Cr2O7}\), \(\ce{H2CrO4}\), \(\ce{Cr(OH)2-}\)

  3. Balance the reactions below. Identify the oxidizing and reducing agents in the balanced reactions.

(a) Permanganate ion (\(\ce{MnO4^-}\)) and iodide (\(\ce{I-}\)) ion react in basic solution to produce manganese(IV) oxide (\(\ce{MnO2}\)) and molecular iodine (\(\ce{I2}\)) as follows:

\[ \ce{ MnO4^- + I- -> MnO2 + I2 } \]

(b) One of the common ways to treat groundwater contaminated with \(\ce{Cr(VI)}\) is by using \(\ce{Fe}\) minerals, as shown by the following reaction:

\[\ce{ Fe^2+ + Cr2O7^2- -> Fe^3+ + Cr^3+ } \]

(c) \(\ce{SO2(g)}\) in air is mainly responsible for the phenomenon of acid rain. Typically, \(\ce{SO2}\) generated at the source can be treated by scrubbing the acid rain with a standard permanganate solution as follows:

\[ \ce{ SO2 + MnO4- -> SO4^2- + Mn^2+ } \]

(d) The concentration of a hydrogen peroxide (\(\ce{H2O2}\)) solution can be conveniently determined by titration against a standardized permanganate (\(\ce{MnO4-}\)) solution in an acidic medium according to the following unbalanced equation:

\[\ce{ MnO4- + H2O2 -> O2 + Mn^2+ } \]

(e) Organic matter present in soils and natural water has a strong influence on redox processes. In the reaction below, organic matter (\(\ce{CH2O}\)) is represented in a simplified form:

\[ \ce{ CH2O + NO3- -> HCO3- + N2 + CO2 } \]

  1. Calculate \(pe\) in the following examples:

(a) Calculate \(pe\) for natural water at \(p\ce{H} = 7.5\) in equilibrium with atmosphere. \(P_{\ce{O2}} = \pu{0.21 atm}\) & \(K=\pu{e83}\)

\[\ce{ O2 + 4 H+ + 4 -> 2 H2O } \]

(b) Calculate \(pe\) for natural water at \(p\ce{H} = 8\) containing \(\ce{Mn^2+} = \pu{e-5 M}\) at equilibrium with \(\ce{\gamma-MnO2}\) & \(K=\pu{e41}\)

\[\ce{ \gamma-MnO2 + 4 H+ + 2 -> Mn^2+ + 2 H2O } \]

  1. Show the \(pe-p\ce{H}\) relationships for the following systems:

    1. Oxidation of \(\ce{H2O(l)}\) to \(\ce{O2(g)}\).

    2. Reduction of \(\ce{H2O(l)}\) to \(\ce{H2(g)}\).

  2. Sulfur is commonly present in coastal environments, such as those near Charleston, SC. Three of the most common forms of \(\ce{S}\) in these environments are \(\ce{SO4^2-}\), \(\ce{S (s)}\), and \(\ce{H2S}\). Answer the following questions:

    1. Write three balanced half-reactions between each pair of \(\ce{S}\) species, listed above.

    2. Write the \(pe\) expressions for all of the above half-reactions.

    3. If \(\log K =4.8\) and \(36.2\) for fully balanced \(\ce{S(s)}-\ce{H2S}\) and \(\ce{SO4^2-}-\ce{S(s)}\) half-reactions, respectively, determine \(\log K\) for the balanced half-reaction \(\ce{SO4^2-}-\ce{H2S}\).

    4. Of all forms of S present in these coastal environments, which form of \(\ce{S}\) will predominate at \(p\ce{H} = 4\) and \(pe = -3\)? Hint: Substitute these values in the 3 \(pe\) expressions in part (2).

    5. If the concentrations of \(\ce{S}\) species in each redox couple (see parts (1) and (2) of this problem) are equal, write the new \(pe\) expressions.