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The acid dissociation constant, often represented as \( K_a \), is a crucial concept in chemistry. It reflects the strength of a weak acid in its ability to dissociate into ions in a solution. The higher the \( K_a \), the stronger the acid, as it indicates a greater degree of ionization.
For hydrocyanic acid (HCN), the given \( K_a \) is \( 4.9 \times 10^{-10} \). This small \( K_a \) value signifies that HCN is a weak acid. In other words, it does not dissociate completely in water. Understanding the \( K_a \) value helps predict how much of the acid will release hydrogen ions \( (H^+) \) when dissolved. This is fundamental when calculating the pH of weak acids.

An ICE Table (Initial, Change, Equilibrium Table) is a strategic tool in chemistry for solving equilibrium problems. It tracks the changes in concentration of each species in a chemical reaction.
In the case of HCN, the dissociation reaction is set up in the table as follows:

• Initial concentrations: \( [HCN] = 0.095 \, M \), \( [H^+] = 0 \, M \), \( [CN^-] = 0 \, M \).
• Change in concentration: As the reaction proceeds, HCN concentration decreases by \( x \), while \( H^+ \) and \( CN^- \) increase by \( x \).
• Equilibrium concentrations: \( [HCN] = 0.095 - x \), \( [H^+] = x \), \( [CN^-] = x \).

This setup allows us to easily plug into the \( K_a \) expression and solve for the unknowns.

The \( K_a \) expression is a formula used to relate the concentrations of the products and reactants involved in an acid's dissociation reaction at equilibrium. For hydrocyanic acid, this expression is:\[ K_a = \frac{[H^+][CN^-]}{[HCN]} \]This equation represents the ratio of the concentration of dissociated ions to the undissociated acid. Inserting the ICE table values results in:\[ K_a = \frac{x \cdot x}{0.095 - x} \]Because \( K_a \) for HCN is so small, we assume \( x \) (the amount of ionization) is very small compared to the initial concentration, allowing us to approximate \( 0.095 - x \approx 0.095 \). This simplification makes it easier to solve for \( x \), which represents the hydrogen ion concentration \([H^+]\).

Hydrocyanic acid (HCN) is a weak acid, meaning it does not completely dissociate in water. This is important when calculating pH because only a small fraction releases hydrogen ions into the solution.
Its weak nature is evident from the low \( K_a \) value \(4.9 \times 10^{-10}\), which implies a limited formation of \( H^+ \) and \( CN^- \) ions. When solving pH problems involving HCN, it's essential to use assumptions that simplify the math, such as neglecting \( x \) in the denominator of the expression \( 0.095 - x \approx 0.095 \).
This simplification leads us to find the concentration of \( H^+ \), which then allows for easy calculation of the pH using the formula: \( \text{pH} = -\log[H^+] \). With these calculations, students can better understand the behavior of hydrocyanic acid in aqueous solutions.