Question

An acid \(\mathrm{HX}\) 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 the acid HX is 0.025.

Step-by-step solution

Write the dissociation reaction for the acid

For a generic acid, HX, the dissociation reaction in water is : HX (aq) <=> H+ (aq) + X- (aq)

Determine the initial, change, and equilibrium concentrations of all species in the reaction using the percent dissociation and ICE table

Given that the acid is 25% dissociated, and the total concentration of HX is 0.3 M, we can determine the concentrations of all species in the reaction: Percent dissociation = (dissociated HX / initial HX) * 100 25% = (dissociated HX / 0.3 M) * 100 We can determine the dissociated HX: dissociated HX = 0.25 * 0.3 M = 0.075 M Since HX dissociates into H+ and X-, each dissociated HX contributes to an equal amount of both ions. Therefore, the initial concentrations of H+ and X- are 0 and 0, respectively. Now we can set up the ICE table: ``` Initial Change Equilibrium HX 0.3 M -0.075 M 0.225 M H+ 0 +0.075 M 0.075 M X- 0 +0.075 M 0.075 M ```

Write the Ka expression and solve for Ka

We can now write the Ka expression for the reaction. Ka is the equilibrium constant for acids and is defined as the product of the concentrations of the products divided by the concentration of the reactants: \(K_a = \dfrac{[H^+][X^-]}{[HX]}\) Plugging in the equilibrium concentrations from the ICE table: \(K_a = \dfrac{(0.075)(0.075)}{0.225}\) Finally, calculate Ka: \(K_a = \dfrac{0.005625}{0.225} = 0.025 \) So, the Ka value for the acid HX is 0.025.

Key concepts

Equilibrium Concentration

Understanding equilibrium concentration in a chemical reaction is crucial because it helps us decode the balance of chemical species involved.
For the given problem, we start with

• HX at an initial concentration of 0.30 M.
• At equilibrium, after considering the 25\(\%\) dissociation, we find HX is now 0.225 M.

This change occurs as some of the HX dissociates into H+ and X-. When we talk about equilibrium, it means that all chemical reactions have reached a state where the concentrations of reactants and products remain constant over time.
This does not mean the reactions stop, but the rate of conversion between products and reactants is equal, allowing stable concentrations of each species involved.

Percent Dissociation

Percent dissociation is a measure of how much of the acid molecule has dissociated into ions in solution. It is a way to understand how strong or weak an acid is.
For HX, we know it is 25\(\%\) dissociated in water. This tells us that under the given conditions, 25\(\%\) of the initial acid molecules

• have released hydrogen ions (H+).
• formed their corresponding conjugate base (X-).

This percentage helps us calculate how much of the acid has turned into ions.
In our exercise, the calculation showed that 0.075 M of the initial 0.30 M dissociates. Percent dissociation is vital for determining the strength and reactivity of the acid, as a higher percentage often indicates a stronger acid.

ICE Table

An ICE table, representing Initial, Change, and Equilibrium stages, is a simple yet powerful tool for analyzing reactions. For our example, the ICE table is used to break down concentration changes as the reaction progresses:

• Initial State: Start with initial concentrations: HX = 0.3 M, H+ = 0, X- = 0
• Change: Due to dissociation, HX decreases by 0.075 M, while H+ and X- increase by the same amount as seen in the table.
• Equilibrium State: Showing concentrations after reaction reaches balance: HX = 0.225 M, H+ = 0.075 M, X- = 0.075 M

This systematic approach helps visualize what happens to each species involved in a reaction right from the start to the point where no further changes occur. Once known, these values feed into the equilibrium constant expression for calculating \( K_a \), confirming the dissociation characteristics of the acid.