Final answer:
The Kₐ value for HX is calculated using the concentration of H⁺ and X⁻ ions, which can be determined from the degree of dissociation and the equilibrium concentration of HX. In this case, the Kₐ value is found to be 0.01809.
Step-by-step explanation:
The acid dissociation constant (Kₐ) is a measure of the extent to which an acid dissociates into its component ions in water. In this case, the acid HX is 27% dissociated, which means that 27% of the initial concentration of HX has dissociated into H⁺ and X⁻ ions. The equilibrium concentration of HX is given as 0.25 M.
To calculate the Kₐ value, we first need to find the concentration of H⁺ ions and X⁻ ions. Since HX is 27% dissociated, the concentration of H⁺ ions is 27% of 0.25 M, which is 0.0675 M. Similarly, the concentration of X⁻ ions is also 0.0675 M.
The equation for the dissociation of HX is HX ⇌ H⁺ + X⁻. So the Kₐ value for HX can be calculated by taking the product of the concentrations of H⁺ and X⁻ ions and dividing it by the concentration of HX. Therefore, Kₐ = [H⁺][X⁻]/[HX] = (0.0675)(0.0675)/0.25 = 0.01809.