Question

Nitrosyl bromide decomposes to nitrogen oxide and bromine. Use the following data to determine the order of the decomposition of nitrosyl bromide. $$ \begin{array}{cccccc} \hline \text { Time (s) } & 0 & 6 & 12 & 18 & 24 \\ {[\mathrm{NOBr}]} & 0.0286 & 0.0253 & 0.0229 & 0.0208 & 0.0190 \\ \hline \end{array} $$

Short answer

Based on this step-by-step solution, create a short answer question: Question: Determine the order of the decomposition of nitrosyl bromide using the given data: initial concentration of 0.0286 M and final concentration of 0.0190 M. Answer: Compare the observed concentrations vs time plots for 0th, 1st, and 2nd order integrated rate laws and choose the best fit to find the order of the decomposition of nitrosyl bromide.

Step-by-step solution

Find the initial and final concentrations of nitrosyl bromide

The initial concentration of nitrosyl bromide is given as 0.0286 M, and the final concentration is given as 0.0190 M.

Create a table for integrated rate laws of different orders

Create a table that has columns for time (in seconds), observed concentrations of NOBr, 0th order integrated rate law values, 1st order integrated rate law values, and 2nd order integrated rate law values.

Create plots for different orders of integrated rate laws and compare with given data

Plot the observed concentrations versus time, and calculate the plot values for 0th, 1st, and 2nd order integrated rate laws. Compare the plots with the given data to determine the best fit.

Determine the best fit integrated rate law and find the order corresponding to it

Based on the comparison made in Step 3, determine the best fit integrated rate law, which gives the minimum deviation from the given data. The order of the reaction is the one that corresponds to the best-fit integrated rate law.

Key concepts

Chemical Kinetics

Chemical kinetics is the study of the speed at which chemical reactions occur and the factors that affect this speed. This field is critical in determining how quickly reactants are converted into products, which has implications in various industries, such as pharmaceuticals, where reaction rates can affect the stability and potency of drugs.

For the decomposition of nitrosyl bromide (NOBr) into nitrogen oxide and bromine, understanding the kinetics is essential for predicting the concentration of reactants and products at any given time. In the original exercise, the time taken for NOBr to decompose and the corresponding concentrations over different time intervals are given. This data is the starting point for analyzing the reaction's kinetics.

To analyze the reaction kinetics, students would first measure the initial and final concentrations of NOBr at specific time intervals. Then, by using integrated rate laws, which will be discussed further, they determine the reaction's order to understand how the concentration of NOBr decreases over time. Essentially, chemical kinetics provides a framework for analyzing how rapidly a chemical reaction proceeds.

Integrated Rate Laws

Integrated rate laws are equations that describe the concentration of a reactant as a function of time for a given reaction order. These laws are integral to understanding how different reactions proceed over time and are derived from the differential rate laws, which relate the rate of a reaction to the concentration of the reactants at any given moment.

In the context of our problem, integrated rate laws of 0th, 1st, and 2nd order are considered. A 0th order rate law implies that the reaction rate is constant and does not depend on the concentration of the reactants. A 1st order rate law shows that the reaction rate is directly proportional to the concentration of the reactant. Lastly, a 2nd order rate law indicates that the reaction rate is proportional to the square of the concentration of the reactant.

To determine which order law is appropriate, students construct plots of concentration versus time for each reaction order and compare these plots to the observed experimental data. The rate law that provides the best fit to the data reflects the true reaction order. This practical application of integrated rate laws reinforces our understanding by connecting theoretical concepts to empirical data.

Reaction Order

The reaction order is a term used to describe the dependence of the rate of a chemical reaction on the concentration of the reactants. It's essentially an exponent in the rate equation that indicates how the rate is affected when the concentration of one reactant is modified.

For the decomposition of NOBr, determining the reaction order is crucial as it dictates the relationship between the concentration of NOBr and the rate at which it decomposes. In the exercise, the aim is to use experimental data to deduce whether the reaction follows a 0th, 1st, or 2nd order kinetics. Each order of reaction suggests a unique integrated rate law and therefore a unique way in which the concentrations decrease over time.

To ascertain the order of reaction for NOBr decomposition, students were guided to plot the experimental concentration data against time and compare it against the predicted outcomes of the different order rate laws. The order that aligns best with the observed data, often through the linearity of the plot, is likely the true reaction order. For instance, if a plot of concentration versus time yields a straight line for a 1st order reaction, it suggests that the decomposition of NOBr is indeed 1st order.