Problem 10 - Chemistry and Chemical Reactivity

Question

Nitrosyl bromide, NOBr, is formed from NO and \(\mathrm{Br}_{2}:\) $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NOBr}(\mathrm{g}) $$ Experiments show that this reaction is second-order in NO and first-order in Bra. (a) Write the rate equation for the reaction. (b) How does the initial reaction rate change if the concentration of \(\mathrm{Br}_{2}\) is changed from \(0.0022 \mathrm{mol} / \mathrm{L}\) to \(0.0066 \mathrm{mol} / \mathrm{L} ?\) (c) What is the change in the initial rate if the concentration of NO is changed from \(0.0024 \mathrm{mol} / \mathrm{L}\) to \(0.0012 \mathrm{mol} / \mathrm{L} ?\)

Step-by-Step Solution

Answer

(a) Rate = k[NO]²[Br₂]. (b) Rate increases by 3 times. (c) Rate decreases to 25%.

Step 1: Determine the Rate Equation

The given reaction is: \[ 2 \mathrm{NO}(\mathrm{g}) + \mathrm{Br}_2(\mathrm{g}) \rightarrow 2 \mathrm{NOBr}(\mathrm{g}) \]The problem states the reaction is second-order in NO and first-order in Br₂. The rate law, therefore, is:\[ \text{Rate} = k [\mathrm{NO}]^2 [\mathrm{Br}_2] \] where \( k \) is the rate constant.

Step 2: Analyze the Impact of Changing Br₂ Concentration

We need to examine how the change in concentration of \( \mathrm{Br}_2 \) affects the rate. The initial concentration is \( 0.0022 \mathrm{mol/L} \), updated to \( 0.0066 \mathrm{mol/L} \). Since the reaction is first-order in \( \mathrm{Br}_2 \), the rate changes proportionally to this change:\[ \frac{0.0066}{0.0022} = 3 \]Thus, the reaction rate increases by a factor of 3.

Step 3: Analyze the Impact of Changing NO Concentration

Now we examine how the change in the concentration of \( \mathrm{NO} \) affects the rate. The initial concentration is \( 0.0024 \mathrm{mol/L} \), reduced to \( 0.0012 \mathrm{mol/L} \). Since the reaction is second-order in \( \mathrm{NO} \), the rate changes with the square of the concentration change:\[ \left(\frac{0.0012}{0.0024}\right)^2 = \left(0.5\right)^2 = 0.25 \]The initial reaction rate is decreased to 25% of its original value, or by a factor of 0.25.

Key Concepts

Reaction Order

The reaction order is a key concept in understanding how different reactants influence the rate of a chemical reaction. In a rate equation, each reactant has an order which reflects how its concentration changes the reaction rate. Reaction orders are usually determined experimentally and can be zero, first, second, or even fractional. They help us understand the connection between concentrations and the rate of a reaction.

In the given chemical reaction, Nitrosyl bromide (NOBr) forms from nitrogen monoxide (NO) and bromine (\(Br_2\)). The step-by-step solution classifies the reaction as second-order in NO and first-order in \(Br_2\).

This means that the concentration of NO squared directly affects the rate, while the concentration of \(Br_2\) affects the rate linearly. This dual dependency showcases how the rate can vary significantly based on these concentrations, illustrating why understanding reaction order is vital for predicting reaction behaviors.

Rate Equation

The rate equation, also known as the rate law, is a mathematical expression that links the reaction rate to the concentration of reactants. It is written as follows:
\[ \text{Rate} = k [\text{Reactant}_1]^{m} [\text{Reactant}_2]^{n} \]
Here, \( k \) is the rate constant, and \( m \) and \( n \) are the reaction orders of the respective reactants.

For the given reaction between NO and \(Br_2\), the rate equation is written as:
\[ \text{Rate} = k [\text{NO}]^2 [\text{Br}_2] \]
This equation indicates that doubling the concentration of NO will quadruple the rate, due to its second-order nature, while doubling \(Br_2\) will double the rate. The rate equation provides a powerful tool for predicting how the rates will change with varying reactant concentrations.

Rate Constant

The rate constant, denoted as \( k \), is a crucial factor in the rate equation that helps determine the overall speed of a reaction. Unlike reaction order, the rate constant is independent of concentration and only varies with changes in temperature and the presence of a catalyst. This means it is a unique value for each reaction under specific conditions.

The value of \( k \) provides insights into the reaction kinetics and its speed; larger \( k \) values correspond to faster reactions, while smaller \( k \) values point to slower ones. This rate constant, combined with the concentrations of the reactants raised to their respective orders, gives a clear mathematical description of the reaction rate. Understanding \( k \) allows chemists to predict and manipulate the outcomes of chemical reactions.

Concentration Effect on Reaction Rate

The concentration of reactants plays a pivotal role in determining the reaction rate. Understanding how changes in concentration affect the reaction is a fundamental aspect of chemical kinetics.

In the reaction involving NO and \(Br_2\), the initial rate changes dramatically with concentration variations:

• For \(Br_2\), the reaction is first-order, meaning its effect on the rate is direct. If the concentration of \(Br_2\) increases from 0.0022 to 0.0066 mol/L, the rate triples due to the linear relationship.
• For NO, being second-order, the rate changes with the square of its concentration change. Halving NO from 0.0024 to 0.0012 mol/L results in the rate dropping to 25% of its original value, highlighting the exponential effect of reactant concentration on the rate.

Overall, these dependencies underline how slight modifications in reactant levels can greatly affect the speed and efficiency of chemical reactions. Learning about these effects allows chemists to control and optimize reactions in various scientific and industrial applications.