Final answer:
The Ka value for HSO₄⁻ can be determined using the given pH value of the solution. By calculating the concentration of H₃O⁺ ions using the pH, we can use the ionization equation for HSO₄⁻ to represent the equilibrium. Using the values substituted into the expression for Ka, we can calculate the Ka value to be approximately 6.3096 x 10^(-3).
Step-by-step explanation:
The Ka value represents the acidity or strength of an acid. To determine the Ka value for HSO₄⁻, we need to use the given information about the pH of the solution. The pH is calculated using the concentration of H₃O⁺ ions, which is related to the concentration of the acid. We can use the formula: pH = -log[H₃O⁺] to find the concentration of H₃O⁺. From the given pH of 1.43, we can find [H₃O⁺] = 10^(-pH).
Next, we use the ionization equation for HSO₄⁻ to represent the equilibrium:
HSO₄⁻ (aq) ⇌ H₃O⁺ (aq) + SO₄²⁻ (aq)
We can assume that the concentration of SO₄²⁻ is negligible compared to the initial concentration of HSO₄⁻. So, we can represent the concentration of HSO₄⁻ using [HSO₄⁻] and the concentration of H₃O⁺ using [H₃O⁺], which we calculated earlier. The expression for Ka is: Ka = [H₃O⁺][SO₄²⁻]/[HSO₄⁻]. We can substitute the values and solve for Ka.
By substituting the values, we get:
Ka = [H₃O⁺] * [SO₄²⁻]/[HSO₄⁻] = [H₃O⁺] * [SO₄²⁻]/[HSO₄⁻] = 10^(-1.43)*[SO₄²⁻]/0.15 = 6.3096 x 10^(-3)*[SO₄²⁻]/0.15
Since we know the concentration of HSO₄⁻ is 0.15 M, we can use this value to calculate the [SO₄²⁻].
0.15 = [HSO₄⁻]-[H₃O⁺]. We can assume that [H₃O⁺] is negligible compared to [HSO₄⁻]. So, we can say that [HSO₄⁻] = 0.15 M.
By substituting this value, we get:
Ka = 6.3096 x 10^(-3)*[SO₄²⁻]/0.15 = 6.3096 x 10^(-3)*[SO₄²⁻]/0.15 = 6.3096 x 10^(-3)*0.15/0.15 ≈ 6.3096 x 10^(-3)
Therefore, the value of Ka for HSO₄⁻ is approximately 6.3096 x 10^(-3), so the correct answer is a) (1.2 × 10⁻³).