Question

Compare the rate of reaction: (a) \(\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}+\underset{1 \mathrm{M}}{\mathrm{H}_{2} \mathrm{O}} \longrightarrow\) (b) \(\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}+\underset{2 \mathrm{M}}{\mathrm{H}_{2} \mathrm{O}} \longrightarrow\) (c) \(\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}+\underset{1 \mathrm{M}}{\mathrm{H}_{2} \mathrm{O}} \longrightarrow\) (A) \(r_{\mathrm{a}}>r_{\mathrm{b}}>r_{\mathrm{c}}\) (B) \(r_{\mathrm{c}}>r_{\mathrm{b}}>r_{\mathrm{a}}\) (C) \(r_{\mathrm{a}}=r_{\mathrm{c}}r_{\mathrm{b}}=r_{\mathrm{c}}\)

Short answer

The short answer is: (C) \(r_{\mathrm{a}}=r_{\mathrm{c}}<r_{\mathrm{b}}\)

Step-by-step solution

Identify the concentration of reactants for each reaction

For each reaction, note the concentration of water (H2O) involved: (a) Reaction with \(\underset{1M}{\mathrm{H}_{2} \mathrm{O}}\) (b) Reaction with \(\underset{2M}{\mathrm{H}_{2} \mathrm{O}}\) (c) Reaction with \(\underset{1M}{\mathrm{H}_{2} \mathrm{O}}\)

Determine the rate expression for the reactions

The rate of reaction can be expressed as: \(r = k[\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}][\mathrm{H}_{2} \mathrm{O}]\), where k is the rate constant, and square brackets denote the concentration of the reactants.

Compare the rate of reactions (a), (b), and (c) based on the concentration of reactants

From the given rate expression, we can compare the rate of the reactions (a), (b), and (c): Reaction (a): \(r_a = k[\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}][1]\) Reaction (b): \(r_b = k[\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}][2]\) Reaction (c): \(r_c = k[\mathrm{Ph}_{3} \mathrm{C}-\mathrm{Cl}][1]\) Comparing the rates: \(r_a = r_c\) and \(r_b > r_a,r_c\) since reaction (b) has a higher concentration of Water (H2O).

Identify the correct option for the comparison of the rate of reactions

Based on the comparison of the rate of reactions, the correct option is: (C) \(r_{\mathrm{a}}=r_{\mathrm{c}}<r_{\mathrm{b}}\)

Key concepts

Concentration Effect

In chemical reactions, the concentration of reactants plays a pivotal role in determining the rate at which a reaction proceeds. This is due to the frequency of particle collisions; higher concentrations mean that particles are more likely to collide and react. Chemical reactions where higher concentrations lead to faster rates can be easily analyzed and predicted.
For the reactions given in the exercise, it is clear that the concentration of water (M\([H_2O]\)) influences the rate of reaction.

• In reactions (a) and (c), the concentration is 1M, which implies a certain rate of reaction.
• However, in reaction (b), the concentration is 2M, meaning water is available in higher quantity, causing more frequent collisions and thus, a faster reaction rate.

Simply put, an increase in concentration results in an increase in the number of effective collisions per unit time, accelerating the reaction speed.

Rate Expression

The rate of a chemical reaction can be quantitatively expressed using a rate equation. This rate expression is vital for understanding how changes in reaction conditions impact the reaction rate.

The general rate equation is given by:
\[ r = k[ ext{Reactant}_1][ ext{Reactant}_2]... \]
Here, \(r\) is the rate of reaction, \(k\) is the rate constant (a value that depends on factors like temperature but not concentration), and the brackets denote the concentration of the reactants involved in the reaction.

In the exercise provided, the rate expression is:
\[ r = k[ ext{Ph}_3 ext{C-Cl}][ ext{H}_2 ext{O}] \]
This equation highlights the direct influence that the concentration of water, M\([H_2O]\), has on the rate, as seen with reactions (a), (b), and (c). Specifically, reaction (b) with a 2M concentration of water shows faster kinetics under this rate expression compared to reactions (a) and (c) at 1M.

Organic Chemistry Reaction Rates

In organic chemistry, understanding reaction rates is essential for comprehending how substances transform into one another. Many organic reactions occur slowly compared to other types of chemical reactions because they involve complex molecular changes. This slow nature raises the importance of optimizing conditions such as concentration, which can significantly impact the speed of organic processes.

For instance, the reactions from the exercise involve the breakdown of a Ph\(_3\)C-Cl bond in the presence of water. The concentration of the reactants, particularly water, affects these reaction speeds as organic reactions usually involve multiple steps.

• Here, increasing the water concentration enhances the likelihood of a nucleophilic attack on the Ph\(_3\)C-Cl bond, thus accelerating the reaction as in (b).
• This understanding allows chemists to manipulate and control reaction conditions for more efficient synthesis.

In essence, mastering reaction rate concepts helps chemists predict and improve the reaction efficiency and yields, advancing the field of organic chemistry.