The decomposition of NOBr is studied manometrically because the number of moles of gas changes; it cannot be studied colorimetrically because both \(\mathrm{NOBr}\) and \(\mathrm{Br}_{2}\) are reddish brown: $$ 2 \mathrm{NOBr}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) $$ Use the data below to answer the following: (a) Determine the average rate over the entire experiment. (b) Determine the average rate between 2.00 and \(4.00 \mathrm{~s}\). (c) Use graphical methods to estimate the initial reaction rate. (d) Use graphical methods to estimate the rate at \(7.00 \mathrm{~s}\). (e) At what time does the instantaneous rate equal the average rate over the entire experiment? $$ \begin{array}{cc} \text { Time (s) } & \text { [NOBr] (mol/L) } \\ \hline 0.00 & 0.0100 \\ 2.00 & 0.0071 \\ 4.00 & 0.0055 \\ 6.00 & 0.0045 \\ 8.00 & 0.0038 \\ 10.00 & 0.0033 \end{array} $$

Chemical kinetics is the branch of chemistry that explores the rates of chemical reactions. It examines how various factors like concentration, temperature, and catalysts influence the speed at which reactants turn into products. In this exercise, we're focusing on the decomposition of NOBr, a chemical reaction that breaks down a compound into simpler substances.

Understanding reaction rates is crucial in chemical kinetics. The rate of reaction tells us how fast or slow a chemical reaction occurs, and we can calculate it by monitoring changes in reactant or product concentrations over time. For the decomposition of NOBr, the rate is monitored manometrically because the number of gas moles changes during the reaction.

Key formulas and concepts in this exercise include using the average rate formula:

\(\text{Average Rate} = -\frac{\text{Change in concentration}}{\text{Change in time}} \),

and understanding how to measure rates both on average and at specific time intervals using graphical methods. These principles lay the groundwork for analyzing more complex reactions and predicting how they will behave under different conditions.

The rate of reaction is a measure of how quickly reactants are converted into products in a chemical reaction. For the decomposition of NOBr, we can determine the average rate over a given period and also at specific points in time.

To calculate the average rate over the entire experiment, we use the change in concentration of NOBr and divide it by the total time taken. The formula looks like this:

\(\text{Average Rate} = -\frac{\text{-0.0067 \text{ mol/L}}}{10.00 \text{ s}} = 0.00067 \text{ mol/L} \text{ s}^{-1}\).

We can also find the average rate between any two time points. Using the data from 2.00 to 4.00 seconds, for example, we calculate the rate similarly:

\(\text{Average Rate} = -\frac{-0.0016 \text{ mol/L}}{2.00 \text{ s}} = 0.0008 \text{ mol/L} \text{ s}^{-1}\).

Understanding the rate of reaction helps chemists control how quickly a desired product is formed. If a reaction is too slow, various techniques like increasing the temperature or adding catalysts can be used to speed it up. Conversely, cooling the reaction or removing catalysts can slow down reactions as needed.

Graphical methods are powerful tools in chemistry for interpreting data and understanding reaction dynamics. In this exercise, graphical methods help us estimate the initial reaction rate and the rate at specific times.

To estimate the initial rate of reaction, we plot the concentration of NOBr versus time on a graph. By drawing a tangent line at the very beginning of the reaction (t = 0.00 s), we can determine the slope of this line. The slope represents the initial rate of reaction.

Similarly, to estimate the rate at 7.00 seconds, we draw a tangent line at t = 7.00 seconds on the same graph. The slope of this tangent line tells us the reaction rate at that specific point in time. Graphs visually demonstrate how the concentration of reactants changes, making it easier to understand and calculate the rates of the reaction.

Additionally, the instantaneous rate at any point can be found by determining the slope of the tangent line at that point. This technique helps students grasp how reaction rates vary throughout the course of a reaction.

Decomposition reactions involve breaking down a compound into two or more simpler substances. The decomposition of NOBr given in this exercise is an example:

\({2 \text{NOBr}(g) \rightarrow 2 \text{NO}(g) + \text{Br}_{2}(g)}}\).

In decomposition reactions like this one, the total number of gas molecules changes, which is why it's studied manometrically. Manometric methods measure pressure changes due to the changing number of gas molecules.

In this reaction, each NOBr molecule splits into NO and Br2 gas molecules. Decomposition reactions are common in both laboratory and industrial processes, making it crucial to understand how to control and measure them.

Being able to calculate reaction rates and visualize them through graphical methods allows chemists to optimize these reactions for various applications, such as chemical manufacturing, environmental monitoring, and energy production.

Understanding decomposition reactions also helps in recognizing how complex molecules break down over time and transform into simpler, often more stable substances.