91Ó°ÊÓ

The rate low for the hydrolysis of thioacetamide, \(\mathrm{CH}_{3} \mathrm{CSNH}_{2}\), CC(=S)NCOCC(N)=O Is rate \(=\mathrm{k}\left[\mathrm{H}^{+}\right][\mathrm{TA}]\), where \(\mathrm{TA}\) is thioacetamide. In which of the following solutions, will the rate of hydrolysis of thioacetamide (TA) is least at \(25^{\circ} \mathrm{C}\) ? (a) \(0.1 \mathrm{M}\) in \(\mathrm{TA}\) and \(0.20 \mathrm{M}\) in \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) (b) \(0.1 \mathrm{M}\) in \(\mathrm{TA}\) and \(0.20 \mathrm{M}\) in \(\mathrm{HNO}_{3}\) (c) \(0.1 \mathrm{M}\) in \(\mathrm{TA}\) and \(0.20 \mathrm{M}\) in \(\mathrm{HCO}_{2}^{3} \mathrm{H}\) (d) \(0.15 \mathrm{M}\) in TA and \(0.15 \mathrm{M}\) in \(\mathrm{HCl}\)

Step by step solution

01

Understanding the Rate Law

The rate law for the hydrolysis of thioacetamide (TA) is given by \( \text{rate} = k[\mathrm{H}^+][\mathrm{TA}] \). This indicates that the rate of reaction is directly proportional to the concentration of hydrogen ions \( [\mathrm{H}^+] \) and the concentration of thioacetamide \( [\mathrm{TA}] \). To find the solution where the hydrolysis rate is the least, we need to find the conditions with the lowest product of these concentrations.

02

Analyze Each Solution

For each solution, determine the product \([\mathrm{H}^+][\mathrm{TA}]\):- **Option (a)**: \( [\mathrm{TA}] = 0.1 \; \text{M}, [\mathrm{H}^+] \) from acetic acid. Acetic acid is a weak acid, thus its contribution to \([\mathrm{H}^+]\) will be relatively small.- **Option (b)**: \( [\mathrm{TA}] = 0.1 \; \text{M}, [\mathrm{H}^+] = 0.2 \; \text{M} \) from nitric acid, a strong acid that fully dissociates.- **Option (c)**: \( [\mathrm{TA}] = 0.1 \; \text{M}, [\mathrm{H}^+] \) from formic acid. As a weak acid, it also contributes moderately to \([\mathrm{H}^+]\).- **Option (d)**: \( [\mathrm{TA}] = 0.15 \; \text{M}, [\mathrm{H}^+] = 0.15 \; \text{M} \) from hydrochloric acid, another strong acid.

03

Compare Hydrogen Ion Contributions

Both \(\mathrm{HNO}_3\) and \(\mathrm{HCl}\) are strong acids, so they contribute significantly to \([\mathrm{H}^+]\). Acetic and formic acid are weak acids, and hence contribute less to \([\mathrm{H}^+]\). Since the rate depends on the product \([\mathrm{H}^+][\mathrm{TA}]\), solutions with lower \([\mathrm{H}^+]\) will have a lower reaction rate.

04

Determine the Lowest Rate Condition

Since acetic acid is the weakest acid among the given acids, option (a) with acetic acid will have the smallest contribution to \([\mathrm{H}^+]\), making the overall product \([\mathrm{H}^+][\mathrm{TA}]\) and thus the rate the smallest.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rate Law

The rate law for a chemical reaction is a mathematical expression that links the speed of the reaction to the concentration of the reactants. In the case of the hydrolysis of thioacetamide, the rate law is given by \( \text{rate} = k[\mathrm{H}^+][\mathrm{TA}] \). Here, \( k \) is the rate constant, \( [\mathrm{H}^+] \) represents the concentration of hydrogen ions, and \( [\mathrm{TA}] \) is the concentration of thioacetamide.
This formula tells us that the reaction rate increases with higher concentrations of both \( \mathrm{H}^+ \) ions and \( \mathrm{TA} \).

• If either \( [\mathrm{H}^+] \) or \( [\mathrm{TA}] \) increases, the rate of the reaction will increase proportionally, assuming the rate constant \( k \) remains unchanged.
• In this context, understanding the balance between these concentrations helps determine the conditions for the slowest reaction rate, which is crucial for applications where controlling reaction speed is necessary.

The overall rate of reaction thus depends on the combined effect of the concentrations of the reactants involved.

Thioacetamide Hydrolysis

Thioacetamide (TA) hydrolysis is a chemical reaction where thioacetamide reacts with water, resulting in the breakdown of molecules.
This process is influenced greatly by the chemical environment, especially factors such as temperature and the presence of catalysts or specific ions.
Hydrolysis reactions involving thioacetamide are particularly sensitive to the acidity of the solution. This is because the concentration of hydrogen ions (\( \mathrm{H}^+ \)) plays a direct role in the reaction rate.

• When thioacetamide is subjected to acidic conditions, the reaction tends to proceed faster due to increased availability of \( \mathrm{H}^+ \) ions driving the reaction forward.
• This makes understanding and controlling the pH of the environment crucial for manipulating the hydrolysis reaction rate, which can have various practical applications in different industries.

Hence, researchers and chemists often aim to optimize these conditions to ensure the desired rate of hydrolysis.

Acid Strength Effects

Acid strength refers to an acid's ability to donate protons (\( \mathrm{H}^+ \)) in a solution. Strong acids dissociate completely in water, releasing \(\mathrm{H}^+ \) ions, whereas weak acids only partially dissociate. The effect of acid strength on reaction kinetics is vital in understanding thioacetamide hydrolysis.
In the provided examples:

• Strong acids like nitric acid (\(\mathrm{HNO}_3\)) and hydrochloric acid (\(\mathrm{HCl}\)) provide more \(\mathrm{H}^+ \) ions compared to weak acids like acetic acid (\(\mathrm{CH}_3\mathrm{CO}_2\mathrm{H}\)).
• This leads to an increased reaction rate in the presence of strong acids due to the higher concentration of \(\mathrm{H}^+ \) available to facilitate the hydrolysis.
• Weak acids, contributing less \(\mathrm{H}^+ \), result in a slower reaction rate, as noted in the exercise example with acetic acid providing the least \(\mathrm{H}^+ \) contribution, thus slowing down the TA hydrolysis.

Understanding these effects allows for better prediction and control of chemical reactions where precise conditions are necessary.

Hydrogen Ion Concentration

The concentration of hydrogen ions (\( [\mathrm{H}^+] \)) is a key player in many chemical reactions, affecting the overall reaction rate. In aqueous solutions, these ions determine the acidity of the environment, which is quantified using the pH scale.
Higher concentrations of \( \mathrm{H}^+ \) ions lower the pH, indicating a more acidic solution, which can accelerate certain reactions.

• In the case of thioacetamide hydrolysis, a higher \( [\mathrm{H}^+] \) leads to a faster reaction rate, as seen with strong acids, which provide ample \( \mathrm{H}^+ \).
• Conversely, lower \( [\mathrm{H}^+] \) results in a slower reaction, offering more control for processes requiring minimal reaction rates.

Thus, manipulating \( \mathrm{H}^+ \) concentration is a strategic approach in chemical synthesis and industrial applications where specific reaction speeds are desired.