Question

An acid HX is \(25 \%\) dissociated in water. If the equilibrium concentration of \(\mathrm{HX}\) is \(0.30 \mathrm{M}\), calculate the \(K_{\mathrm{a}}\) value for \(\mathrm{HX}\).

Short answer

The Ka value for HX is 0.025, which was calculated using the equilibrium concentrations of HX, H^+, and X^-.

Step-by-step solution

Calculate the dissociated concentration.

Since HX is 25% dissociated, we can find the concentrations of H^+ and X^- ions by multiplying 0.30 M by the percentage dissociation. Dissociated concentration = 0.25 × 0.30 M = 0.075 M Step 2: Calculate the remaining concentration of HX.

Calculate the remaining concentration of HX.

To calculate the remaining concentration of HX, subtract the dissociated concentration from the initial concentration. Remaining concentration of HX = Initial concentration - Dissociated concentration = 0.30 M - 0.075 M = 0.225 M Step 3: Write the equilibrium concentrations for each species.

Write the equilibrium concentrations for each species.

We have the following equilibrium concentrations: -[HX] = 0.225 M -[H^+] = 0.075 M -[X^-] = 0.075 M Step 4: Calculate the Ka value.

Calculate the Ka value.

Using the Ka expression and the equilibrium concentrations from step 3, we can calculate the Ka value for HX. \[K_a = \frac{[H^+][X^-]}{[HX]} = \frac{(0.075)(0.075)}{(0.225)}\] \[K_a = 0.025\] The Ka value for HX is 0.025.

Key concepts

Equilibrium Concentration

Understanding equilibrium concentration is vital in the study of chemical reactions, especially when dealing with acid-base reactions. Equilibrium concentration refers to the concentration of reactants and products in a reaction mixture at the state of equilibrium. This state is achieved when the rate of the forward reaction equals the rate of the reverse reaction, leading to constant concentrations over time, even though the reactions are still occurring.

For weak acids like HX in the given exercise, not all molecules dissociate in water. Instead, a dynamic equilibrium is established between the undissociated acid and the ions produced upon dissociation. To determine these concentrations at equilibrium, it's first necessary to know the initial concentration and the extent of dissociation, which can be represented as the percent dissociation. Given the initial concentration of HX is 0.30 M and it is 25% dissociated, we can calculate the equilibrium concentrations of HX, H⁺, and X^- ions.

For HX undergoing dissociation in water: HX ⇌ H⁺ + X^-,the equilibrium concentrations will be as follows:

• [HX] remaining undissociated is 0.225 M.
• Concentration of [H⁺] ions is 0.075 M.
• Concentration of [X^-] ions is 0.075 M.

These concentrations are utilized to calculate the acid dissociation constant (Ka) as seen in the exercise, reflecting the strength of the acid in question.

Percent Dissociation

Percent dissociation is an illustrative metric used to describe the strength of an acid or base in solution. It is the ratio of the amount of substance that has dissociated to form ions to the initial concentration of that substance, multiplied by 100 to yield a percentage.

In the context of the given exercise, the acid HX has a percent dissociation of 25%, which means that a quarter of the original acid amount has been converted to H⁺ and X^- ions in solution. The calculation for percent dissociation is rather straightforward, employing the equilibrium concentrations of the reacting species:

• Percent dissociation = (concentration of dissociated substance / initial concentration of substance) × 100

Through this concept, we can relate the observable degree of dissociation to the inherent properties of the acid or base such as its Ka value. A higher percent dissociation indicates a stronger acid or base, as more molecules are successful in releasing or accepting protons in solution.

Acid-Base Equilibrium

Acid-base equilibrium is a specific type of chemical equilibrium that pertains to the transfer of protons (H⁺) between a proton donor (acid) and a proton acceptor (base). The equilibrium lies at the heart of understanding the behavior of acids and bases in solution and is described by the acid dissociation constant, Ka, for weak acids or the base dissociation constant, Kb, for weak bases.

At the acid-base equilibrium, the rate at which the acid donates protons to the solvent water is equal to the rate at which the conjugate base (formed from the proton donation) recombines with the protons to reform the acid. This concept is essential when discussing the strength of acids and bases. Weak acids, such as HX in our exercise, do not completely dissociate in solution, leading to a dynamic equilibrium.

• For general weak acid HA: HA ⇌ H⁺ + A^-

The position of this equilibrium, dominated by the relative concentrations of the reactants and products, gives us the Ka value. A smaller Ka value indicates a weaker acid, which dissociates less, while a larger Ka value indicates a stronger acid. The calculation of Ka using equilibrium concentrations provides a quantifiable measure of the acid's tendency to lose its proton in a watery environment.