# 6.3 Practice Problems

1. Consider the following reaction, 

$$\ce{4 NO2 + O2 -> 2 N2O5}$$
>At a particular time during the reaction, is being consumed at the rate of $\pu{1.3e-3 mol L-1 s-1}$. (a)  At what rate is being consumed? (b) At what rate is being produced? **Answer**: (a) $\pu{-3.25e-4mol L-1 s-1}$, (b) $\pu{6.5e-4 mol L-1 s-1}$
 
2. The solvent methylene chloride ($\ce{CH2Cl2}$) reacts with bisulfide ($\ce{HS-}$) to form dithiomethane ($\ce{CH2(SH)2}$) as shown in this reaction: 

$$\ce{CH2Cl2 + 2 HS- -> CH2(SH)2 + 2 Cl-}$$
>This reaction is monitored by measuring the rate of production. If after $\pu{2 min}$, appears at a rate of $\pu{10 mmol L-1 min-1}$, what is the reaction rate at which is being consumed? **Answer**: $\pu{-5 mmol L-1 min-1}$

3. Write the rate expressions and determine the reaction order in the following reactions.

$$
\begin{align}
\ce{
2 A &-> C\\
2 A + B &-> C
}
\end{align}$$
>**Answer**: (1) 2, 2 (2) 2, 1, 3

4. The decomposition of hydrogen peroxide is first order in $\ce{H2O2}$. 

$$\ce{
2 H2O2 -> 2 H2O + O2
}$$
>The rate constant for this reaction at $\pu{20 ^\circ C}$ is $\pu{1.8e-5 s-1}$. The starting concentration of is $\pu{0.75 M}$. Determine (a) the concentration of remaining after $\pu{3 h}$.  **Answer**: $\pu{0.62 M}$ and (b) how long it will take for the concentration to drop to $\pu{0.10 M}$. **Answer**: $\pu{31 h}$.

5. The decomposition of ethane ($\ce{C2H6}$) to methyl radicals ($\ce{.CH3}$) is a first-order reaction with a rate constant of $\pu{5.36e-1 s-1}$ at $\pu{700 ^\circ C}$. Calculate the half-life of this reaction in minutes. **Answer**: $\pu{21.5 min}$

6. Auto-oxidation of $\ce{Fe^2+}$ occurs when exposed to the atmosphere due to the presence of $\ce{O2(g)}$. The table below shows the observed $\ce{Fe^2+}$ oxidation data. Determine (a) the reaction order, (b) the rate constant for this reaction, and (c) the half-life of $\ce{Fe^2+}$.

| Time, $\pu{min}$ | Conc, $\pu{\mu g L-1}$ |
|-----------|----------------------------------|
| 0         | 500                              |
| 10        | 320                              |
| 20        | 200                              |
| 30        | 130                              |
| 40        | 80                               |
| 60        | 35                               |

7. A researcher has monitored the treatment of an organic pollutant using a naturally-occurring mineral compound. The table below shows the kinetics data. Determine (a) the reaction order, (b) the rate constant for this reaction, and (c) the half-life of pollutant.

| Time, $\pu{h}$ | Conc, $\pu{\mu mol L-1}$ |
|---------|-------------------------|
| 1.5     | 137                     |
| 18      | 98.6                    |
| 42.5    | 68                      |
| 71.5    | 38.4                    |
| 91.5    | 23.7                    |
| 115     | 12.2                    |
| 138.5   | 8.4                     |