# 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:
>
>$$ \ce{
CH2O + NO3- -> HCO3- + N2 + CO2
} $$


4. 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 $\ce{\gamma-MnO2}$ & $K=\pu{e41}$
>
>$$\ce{
\gamma-MnO2 + 4 H+ + 2 -> Mn^2+ + 2 H2O
} $$

5. 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 $\ce{H2(g)}$.

6. 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.