Problem 2 - Chemistry and Chemical Reactivity

Question

Give the relative rates of disappearance of reactants and formation of products for each of the following reactions. (a) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})\) (b) \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\)

Step-by-Step Solution

Answer

(a) -\( \frac{1}{2} \frac{d[\mathrm{NO}]}{dt} = - \frac{d[\mathrm{Br}_{2}]}{dt} = \frac{1}{2} \frac{d[\mathrm{NOBr}]}{dt} \) (b) -\( \frac{d[\mathrm{N}_{2}]}{dt} = -\frac{1}{3} \frac{d[\mathrm{H}_{2}]}{dt} = \frac{1}{2} \frac{d[\mathrm{NH}_{3}]}{dt} \)

Step 1: Understanding Reaction (a)

Identify the reaction given: \(2 \mathrm{NO}(\mathrm{g}) + \mathrm{Br}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NOBr}(\mathrm{g})\). The stoichiometry coefficients are 2 for \(\mathrm{NO}\), 1 for \(\mathrm{Br}_{2}\), and 2 for \(\mathrm{NOBr}\).

Step 2: Write Relative Rate Expressions for Reaction (a)

Using the reaction stoichiometry: \[-\frac{1}{2}\frac{d[\mathrm{NO}]}{dt} = -\frac{d[\mathrm{Br}_{2}]}{dt} = \frac{1}{2}\frac{d[\mathrm{NOBr}]}{dt}\]. This equation relates the disappearance rate of NO and Br₂ to the appearance rate of NOBr.

Step 3: Understanding Reaction (b)

Identify the reaction given: \(\mathrm{N}_{2}(\mathrm{g}) + 3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\). Here the stoichiometry coefficients are 1 for \(\mathrm{N}_{2}\), 3 for \(\mathrm{H}_{2}\), and 2 for \(\mathrm{NH}_{3}\).

Step 4: Write Relative Rate Expressions for Reaction (b)

Using the reaction stoichiometry: \[-\frac{d[\mathrm{N}_{2}]}{dt} = -\frac{1}{3}\frac{d[\mathrm{H}_{2}]}{dt} = \frac{1}{2}\frac{d[\mathrm{NH}_{3}]}{dt}\]. This relates the rates of disappearance of N₂ and H₂ to the rate of formation of NH₃.

Key Concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that deals with the study of reaction rates. It focuses on understanding how fast chemical reactions occur and the various factors that influence these rates. For beginners, think of it as the speedometer of chemical reactions, showing how fast or slow different components of a reaction are used up or created.

• Reaction rate refers to the change in concentration of reactants or products per unit time.
• The faster a reaction, the quicker the reactants are consumed and products are formed.
• Kinetics helps in determining optimal conditions for industrial chemical processes to be efficient and economical.

Understanding the rate of chemical reactions is crucial for various applications such as pharmaceuticals, environmental studies, and energy production.

Stoichiometry

Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. It is like a chemical recipe, showing the proportion of ingredients needed to create a desired product without leaving leftovers.

• Simplifies the process of calculating amounts of substances involved in reactions.
• Essential for converting laboratory experiments to large-scale production.

In reactions like \( 2 \mathrm{NO} + \mathrm{Br_2} \rightarrow 2 \mathrm{NOBr} \), stoichiometry tells us that two molecules of NO react with one molecule of Br₂ to form two molecules of NOBr.
Stoichiometry uses the coefficients in a balanced equation to guide the calculations of moles and thus allows us to convert these values to grams if necessary.
This is extremely useful when preparing reactants in exact amounts to ensure there are no shortages or excesses.

Rate of Reaction Expressions

The rate of reaction expressions correlate the rate at which reactants are consumed and products are formed based on their stoichiometric coefficients.
These expressions are vital for dissecting the dynamics of a reaction. The general approach is to set the rate expressions based on the balanced chemical equation, which involves taking into account the stoichiometric coefficients.
In the reaction \( 2 \mathrm{NO} + \mathrm{Br_2} \rightarrow 2 \mathrm{NOBr} \), the rate expression looks like this:

• \[-\frac{1}{2}\frac{d[\mathrm{NO}]}{dt} = -\frac{d[\mathrm{Br}_2]}{dt} = \frac{1}{2}\frac{d[\mathrm{NOBr}]}{dt}\]

This means that for every two NO molecules disappearing, two NOBr molecules are formed.
The negative sign indicates the consumption of a reactant while the positive terms are for product formation.
The expression for Reaction (b) shows a similar pattern, considering the stoichiometry:

• \[-\frac{d[\mathrm{N}_2]}{dt} = -\frac{1}{3}\frac{d[\mathrm{H}_2]}{dt} = \frac{1}{2}\frac{d[\mathrm{NH}_3]}{dt}\]

These expressions help predict and control how quickly products are generated during chemical processes.

Chemical Reactions

Chemical reactions involve the transformation of substances, known as reactants, into one or more new substances, called products.
These transformations are represented by balanced chemical equations that show the specific details of the reaction process. Key components include:

• Reactants: Initial substances that undergo change.
• Products: New substances formed as a result of the reaction.
• Catalysts: Substances that can speed up the reaction without being consumed.

In the provided reactions, this involves reactants like NO, Br₂, N₂, and H₂ turning into products like NOBr and NH₃.
Chemical reactions are classified into various types such as synthesis, decomposition, single-replacement, and double-replacement reactions, each having distinct patterns and characteristics.
A deeper understanding of these processes allows us to manipulate and control chemical reactions in industrial, lab, and natural environments.