Problem 37 - Chemistry: An Atoms-Focused Approach

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 and \(100 \mu \mathrm{s}(\text { microseconds })\) and between 200 and \(300 \mu \mathrm{s}\) $$\begin{array}{cc}\text { Time }(\mu \mathrm{s}) & {\left[\mathrm{O}_{3}\right](\mathrm{M})} \\\0 & 1.13 \times 10^{-2} \\\\\hline 100 & 9.93 \times 10^{-3} \\\\\hline 200 & 8.70 \times 10^{-3} \\\\\hline 300 & 8.15 \times 10^{-3} \\\\\hline\end{array}$$

Step-by-Step Solution

Answer

Answer: The average reaction rates for the given time intervals are: - \(2.00 \times 10^4\) M s\(^{-1}\) between 0 and 100 μs - \(5.5 \times 10^3\) M s\(^{-1}\) between 200 and 300 μs.

Step 1: Calculate the change in the concentration of O3

First, let's find the change in concentration of O3 for both given time intervals (0 to 100 μs and 200 to 300 μs). The change in concentration (Δ[O3]) is calculated as the final concentration minus the initial concentration, for each interval. For 0-100 μs: Δ[O3] = [O3]_100 μs - [O3]_0 μs = \((9.93 \times 10^{-3}) - (1.13 \times 10^{-2})\) M For 200-300 μs: Δ[O3] = [O3]_300 μs - [O3]_200 μs = \((8.15 \times 10^{-3}) - (8.70 \times 10^{-3})\) M

Step 2: Calculate the average reaction rate

Region_interval For both time intervals, the average reaction rate can be calculated by dividing the change in concentration by the time interval in seconds. Since 1 μs is equivalent to \(10^{-6}\) seconds, we can convert the given time intervals to seconds. For 0-100 μs (converting to seconds: 0-100 × \(10^{-6}\) s): Average reaction rate = \(\frac{\Delta[\mathrm{O}_{3}]}{\Delta t}\) = \(\frac{(9.93 \times 10^{-3}) - (1.13 \times 10^{-2})}{100 \times 10^{-6}}\) M s\(^{-1}\) For 200-300 μs (converting to seconds: 200-300 × \(10^{-6}\) s): Average reaction rate = \(\frac{\Delta[\mathrm{O}_{3}]}{\Delta t}\) = \(\frac{(8.15 \times 10^{-3}) - (8.70 \times 10^{-3})}{100 \times 10^{-6}}\) M s\(^{-1}\) Now we can calculate the numerical values of the average reaction rates for both time intervals. For 0-100 μs: Average reaction rate = \(\frac{9.93 \times 10^{-3} - 1.13 \times 10^{-2}}{100 \times 10^{-6}}\) M s\(^{-1}\) = \(-20 \times 10^{3}\) M s\(^{-1}\) (the negative sign indicates that the concentration is decreasing). For 200-300 μs: Average reaction rate = \(\frac{8.15 \times 10^{-3} - 8.70 \times 10^{-3}}{100 \times 10^{-6}}\) M s\(^{-1}\) = \(-5.5 \times 10^{3}\) M s\(^{-1}\) (the negative sign indicates that the concentration is decreasing). So, the average reaction rates for the given time intervals are: - \(2.00 \times 10^4\) M s\(^{-1}\) between 0 and 100 μs - \(5.5 \times 10^3\) M s\(^{-1}\) between 200 and 300 μs.

Key Concepts

Nitrite Ion

Reacting with ozone, the nitrite ion \((\mathrm{NO}_{2}^{-})\) plays a crucial role in the chemical process occurring in this problem. In this reaction, the nitrite ion is transformed into a nitrate ion \((\mathrm{NO}_{3}^{-})\). This transformation represents a typical oxidation reaction, where the nitrite ion loses electrons and gains an oxygen, thus becoming a nitrate ion.

Nitrite ions are often found in various environmental reactions, especially in water systems, because they are common components in fertilizers and wastewater. These ions can participate in complex reactions with other atmospheric particles and contribute to the formation of compounds like ozone, which further affects their stability and behavior in the solution.

• Originates typically from the environment or fertilizers.
• Easily participates in redox reactions.
• Key player in atmospheric and water chemistry.

Ozone Reaction

The reaction involving ozone \((\mathrm{O}_{3})\) is a vital part of the exercise, as it helps underscore the kinetics of ozone depletion. Ozone acts as a powerful oxidizing agent, reacting readily with other chemicals such as nitrite ions. In this setup, the ozone is reduced, turning into oxygen \((\mathrm{O}_{2})\) during the process.

This reaction is not only relevant in the lab but also has practical implications in the study of ozone layer depletion and pollution. Ozone reactions are crucial in understanding how airborne chemicals interact and transform under different environmental conditions.

• Powerful oxidizing agent.
• Converts to oxygen during reactions.
• Important for environmental and atmospheric chemistry.

Concentration Change

The concept of concentration change is central to understanding the kinetics of this reaction. Concentration change here refers to the difference in concentration of ozone molecules over a specific time interval. Calculating this change helps determine how fast a reactant is used up or how fast a product is formed in a reaction.

In this exercise, the concentration of ozone decreases over time, indicating that it is being consumed as the reaction proceeds. The concentration change is calculated by subtracting the final concentration from the initial concentration within a given time interval.

• Reflects the rate of consumption or production in reactions.
• Essential for calculating reaction rates.
• Calculated as final minus initial concentration within a time period.

Kinetics Calculation

Kinetics calculations involve determining how quickly a chemical reaction occurs. In this context, it refers to calculating the average reaction rate. The average reaction rate can be calculated by dividing the change in concentration by the change in time. This calculation provides insight into the speed at which the reactants (ozone) are consumed in the reaction.

For the given exercise, the reaction rate varies between different time intervals, reflecting how the concentration of ozone changes over time. The negative sign in calculated reaction rates indicates a decrease in concentration, consistent with the consumption of ozone during the reaction.

• Average rate calculated as change in concentration over change in time.
• Helps understand the speed and dynamics of a reaction.
• Negative rates indicate consumption of reactants.