Problem 37 - Chemistry The Science in Context

Question

Nitrite ion reacts with ozone in aqueous solution, producing nitrate ion and oxygen: $$ \mathrm{NO}_{2}^{-}(a q)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{O}_{2}(g) $$ The following data were collected for this reaction at \(298 \mathrm{K}\) Calculate the average reaction rate between 0.0 and \(100.0 \mu \mathrm{s}\) (microseconds) and between 200.0 and \(300.0 \mu \mathrm{s}\) $$\begin{array}{cc} \text { Time }(\mu \mathrm{s}) & {\left[\mathrm{O}_{3}\right](\mathrm{M})} \\ 0.0 & 1.13 \times 10^{-2} \\ \hline 100.0 & 9.93 \times 10^{-3} \\ \hline 200.0 & 8.70 \times 10^{-3} \\ \hline 300.0 & 8.15 \times 10^{-3} \\ \hline \end{array}$$

Step-by-Step Solution

Answer

Question: Calculate the average reaction rate between 0.0 to 100.0 microseconds and between 200.0 to 300.0 microseconds for the given concentration of ozone data. Answer: The average reaction rate between 0.0 and 100.0 microseconds is $$-\frac{1.97 \times 10^{-3}\ \text{M}}{100.0 \mu s}$$, and between 200.0 and 300.0 microseconds is $$-\frac{5.50 \times 10^{-4}\ \text{M}}{100.0 \mu s}$$.

Step 1: Understand average reaction rate formula

Average reaction rate is calculated using the formula: $$\text{Average reaction rate} = \frac{\Delta [\text{concentration}]}{\Delta \text{time}}$$ where \(\Delta [\text{concentration}]\) represents the change in concentration, and \(\Delta \text{time}\) represents the change in time.

Step 2: Calculate the change in concentration for both time intervals

In the first time interval, from 0.0 to 100.0 microseconds, the change in concentration of ozone, Δ[O₃], is: $$\Delta [\mathrm{O}_{3}] = [\mathrm{O}_{3}]_{100.0 \mu s}-[\mathrm{O}_{3}]_{0.0 \mu s} = (9.93 \times 10^{-3}\ \text{M})-(1.13 \times 10^{-2}\ \text{M})$$ Similarly, for the second time interval, from 200.0 to 300.0 microseconds: $$\Delta [\mathrm{O}_{3}] = [\mathrm{O}_{3}]_{300.0 \mu s}-[\mathrm{O}_{3}]_{200.0 \mu s} = (8.15 \times 10^{-3}\ \text{M})-(8.70 \times 10^{-3}\ \text{M})$$

Step 3: Calculate the change in time for both time intervals

The change in time for the first time interval (0.0 to 100.0 microseconds) is: $$\Delta \text{time} = 100.0 \mu s - 0.0 \mu s$$ For the second time interval (200.0 to 300.0 microseconds): $$\Delta \text{time} = 300.0 \mu s - 200.0 \mu s$$

Step 4: Calculate the average reaction rate for both time intervals

For the first time interval (0.0 to 100.0 microseconds), the average reaction rate is: $$\text{Average reaction rate} = \frac{(9.93 \times 10^{-3}-1.13 \times 10^{-2})\ \text{M}}{100.0 \mu s} = -\frac{1.97 \times 10^{-3}\ \text{M}}{100.0 \mu s}$$ For the second time interval (200.0 to 300.0 microseconds): $$\text{Average reaction rate} = \frac{(8.15 \times 10^{-3}-8.70 \times 10^{-3})\ \text{M}}{100.0 \mu s} = -\frac{5.50 \times 10^{-4}\ \text{M}}{100.0 \mu s}$$

Step 5: Report the average reaction rates

The average reaction rate between 0.0 and 100.0 microseconds is $$-\frac{1.97 \times 10^{-3}\ \text{M}}{100.0 \mu s}$$, and between 200.0 and 300.0 microseconds is $$-\frac{5.50 \times 10^{-4}\ \text{M}}{100.0 \mu s}$$. The negative sign indicates that the concentration of ozone is decreasing over time, which is expected for a reactant in a chemical reaction.

Key Concepts

Chemical Kinetics

Chemical kinetics is a fascinating branch of chemistry that focuses on the rates at which chemical reactions occur and the steps by which they proceed. It answers not only 'how' and 'when' a chemical reaction happens, but also 'how fast.' Kinetics can offer insight into the reaction mechanism—the series of steps that lead to the formation of products from reactants.

By studying the speed of chemical reactions, scientists can understand which factors influence this speed, like temperature, concentration of reactants, and the presence of catalysts. A grasp of chemical kinetics is indispensable for controlling reactions in industrial processes, understanding biological pathways, and even for predicting the stability of medications and substances over time.

Concentration Change Over Time

The rate of a chemical reaction is closely linked to the changes in concentration of the reactants or products over time. When a reactant is consumed, its concentration decreases, whereas the concentration of a product increases. These changes form the basis for determining the reaction rate. For example, if the concentration of ozone in a reaction decreases from \(1.13 \times 10^{-2} M\) to \(9.93 \times 10^{-3} M\), it shows that ozone is being used up to form products.

Students can improve their understanding by tracking concentration changes graphically or with data tables, noting the time and concentration at specific intervals. This real-life data then becomes the bedrock for calculating reaction rates and can also hint at the order of the reaction and its kinetics.

Reaction Rate Calculation

To calculate the average reaction rate, you need to consider the change in concentration over a specific time interval. The formula for the average reaction rate is \(\text{Average reaction rate} = \frac{\Delta [\text{concentration}]}{\Delta \text{time}}\), where delta represents the change in a given parameter. It's essential to understand that a positive rate denotes the formation of products, while a negative rate indicates the consumption of reactants.

To master reaction rate calculations, practice with different time intervals and observe how rates can vary over the course of a reaction. This helps in understanding the progression of the reaction and the importance of time precision in kinetics studies. Remember, being meticulous in your calculations and understanding the sign of your results will give you clearer insights into the behavior of reactions.