# 5.4 Practice Problems

1. Determine the oxidation number of each atom in the following compounds and ions: 
	1. $\ce{SO2}$
	2. $\ce{NaH}$
	3. $\ce{CO3^2-}$
	4. $\ce{N2O5}$

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.
	1. 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} $
	2. 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+} $
	3. $\ce{SO2(g)}$ 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+} $
	4. 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+} $
	5. Organic matter in soils and natural water strongly influences 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:
	1. Calculate $pe$ for natural water at $p\ce{H} = 7.5$ in equilibrium with atmosphere. $P_{\ce{O2}} = \pu{0.21 atm}$ & $K=\pu{e83}$.  The half-reaction: $\ce{O2 + 4 H+ + 4 e- -> 2 H2O} $
	2. Calculate $pe$ for natural water at $p\ce{H} = 8$ containing $\ce{Mn^2+} = \pu{e-5 M}$ at equilibrium with $\ce{\gamma-MnO2}$ & $K=\pu{e41}$. The half-reaction: $\ce{\gamma-MnO2 + 4 H+ + 2 e- -> 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.