Problem 10 - Chemistry and Chemical Reactivity

Question

Nitrosyl bromide, NOBr, is formed from NO and Bre: $$2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})$$ Experiments show that this reaction is second order in NO and first order in \(\mathrm{Br}_{2}.\) (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) \( r = k [\mathrm{NO}]^2[\mathrm{Br}_2] \); (b) Rate increases by factor of 3; (c) Rate decreases to one-fourth.

Step 1: Write the Rate Equation

The rate of a reaction can be written in terms of the concentration of the reactants raised to the power of their respective orders. The reaction is second order in NO and first order in \( \mathrm{Br}_2 \). Thus, the rate equation can be written as \( r = k [\mathrm{NO}]^2[\mathrm{Br}_2] \), where \( k \) is the rate constant.

Step 2: Change in Reaction Rate with [Br2] Increase

The rate equation is \( r = k [\mathrm{NO}]^2[\mathrm{Br}_2] \). If the concentration of \( \mathrm{Br}_2 \) changes from \(0.0022 \mathrm{mol}/\mathrm{L}\) to \(0.0066 \mathrm{mol}/\mathrm{L}\), this is a 3-fold increase. Since the rate is directly proportional to \( [\mathrm{Br}_2] \), the initial reaction rate will also increase by a factor of 3.

Step 3: Change in Reaction Rate with [NO] Decrease

If the concentration of \( \mathrm{NO} \) is changed from \(0.0024 \mathrm{mol}/\mathrm{L}\) to \(0.0012 \mathrm{mol}/\mathrm{L}\), the concentration is halved. Since the rate of the reaction is proportional to \( [\mathrm{NO}]^2 \), the rate decreases by \( (\frac{1}{2})^2 = \frac{1}{4} \). This means the rate becomes one-fourth of its original value.

Key Concepts

Reaction Rate

The reaction rate tells us how quickly or slowly a chemical reaction occurs over time.
It measures the change in concentration of reactants or products per unit time. Understanding reaction rates is crucial because they determine the efficiency and speed of chemical processes. For example, in industrial settings, knowing the reaction rate helps optimize production rates, save costs, and enhance safety protocols.Several factors influence reaction rates:

• Concentration of reactants: Higher concentrations usually increase reaction rates because more reactant molecules are available to collide.
• Temperature: Increasing temperature generally speeds up reactions; molecules move faster, causing more frequent collisions.
• Presence of a catalyst: Catalysts provide an alternative pathway with a lower activation energy, increasing the rate without being consumed.

In our particular example, the rate is affected by the concentration of NO and \( \mathrm{Br}_2 \). Adjusting these concentrations changes the speed at which \( \mathrm{NOBr} \) is formed.

Rate Equation

The rate equation provides a mathematical relationship that describes how the rate of a reaction depends on the concentration of its reactants. It is specifically tailored to each reaction based on experimental data. In our example reaction with NO and \( \mathrm{Br}_2 \), the rate equation is formulated as:\[ r = k [\mathrm{NO}]^2[\mathrm{Br}_2] \]Here:

• \( r \) represents the rate of the reaction.
• \( k \) is the rate constant, which is unique for every reaction and determined experimentally.
• \( [\mathrm{NO}]^2 \) implies that the reaction is second order in NO.
• \( [\mathrm{Br}_2] \) indicates the reaction is first order in \( \mathrm{Br}_2 \).

The order of each reactant shows how its concentration affects the reaction rate.
In this case, doubling the concentration of NO increases the rate fourfold, due to its second-order dependence.

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate equation, and it provides insight into how reactant concentration affects reaction rates. This concept helps us understand the effect of changing concentrations in a chemical reaction.In our given reaction, the order is different for NO and \( \mathrm{Br}_2 \):

• Second order in NO means doubling the NO concentration results in a fourfold increase in the rate \(( \text{because } (2^2 = 4) )\).
• First order in \( \mathrm{Br}_2 \) implies a simple proportional relationship; tripling its concentration triples the rate.

Overall reaction order is obtained by summing individual orders. Here, the reaction is third-order \((2 + 1 = 3)\).
Knowing the reaction order helps predict how fast a reaction proceeds when conditions change and aids in the design of chemical processes.