91Ó°ÊÓ

In chemistry, the dissociation equation represents the splitting of a compound into its constituent ions when dissolved in water. For acetic acid (\text{CH}_3\text{COOH}), it dissociates as follows:

\(\text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \)

This equation shows that acetic acid partially breaks down into acetate ions (\(\text{CH}_3\text{COO}^- \)) and hydrogen ions (\(\text{H}^+ \)) in an aqueous solution. The nature of acetic acid as a weak acid means it does not fully dissociate. Understanding this equation is crucial as it lays the foundation for calculating the degree of dissociation and further using it to find the dissociation constant expression.

Acetic acid, also known as ethanoic acid, is a common weak acid with the chemical formula \(\text{CH}_3\text{COOH} \). Found in vinegar, it has a distinctive sour taste and pungent smell. Unlike strong acids, which dissociate completely in water, acetic acid only partially dissociates. This attribute makes it essential to apply specific calculations, such as those involving the dissociation constant (\(\text{K}_a \)), when working with it.

For students, it's vital to differentiate between strong acids like hydrochloric acid (\(\text{HCl}\)), which dissociate entirely, and weak acids like acetic acid.

The degree of dissociation (\text{α}) is a measure of how much a weak acid dissociates in solution. It is defined as the ratio of the concentration of dissociated acid to the initial concentration of the acid.

In the context of acetic acid, if we start with an initial concentration of \(\text{CH}_3\text{COOH} \) (denoted as \([\text{CH}_3\text{COOH}]_0 = 0.01 \text{ M}\)), and part of it dissociates into ions, the degree of dissociation is calculated by:
\text{α} = \(\frac{[\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]_0} \).

In the given problem, \(\text{α} \) was found by relating the dissociation constant to the concentrations involved and solving for \(\text{α} \). This led to the value of \(\text{α} = 1.69 \times 10^{-3} \).

The dissociation constant (\text{K}_a) of an acid quantifies its strength in terms of its ability to donate protons to water, creating ions. For acetic acid, the expression is formulated as:

\(\text{K}_a = \frac{[\text{CH}_3\text{COO}^-][\text{H}^+]}{[\text{CH}_3\text{COOH}]}\)

This equation represents the equilibrium constant of the dissociation reaction. By substituting the known concentrations into this expression, students can calculate key parameters like the degree of dissociation or pH of the solution.

The initial concentration of acetic acid is crucial in determining the degree of dissociation and calculating the dissociation constant. In the problem, we start with an initial concentration of \(\text{CH}_3\text{COOH} = 0.01 M\) and consider the presence of \(\text{HCl} = 0.01 M\) as well.

This initial concentration helps set up the initial conditions before dissociation occurs and is crucial for setting up the equation to solve for the degree of dissociation. When \(\text{HCl}\) is added, it fully dissociates and alters the \(\text{H}^+\) ion concentration in the solution, which, in turn, affects the acid dissociation equilibrium calculations.