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Calculate the Ka for a 0.43M weak acid solution that has a pH equal to 3.50.2.33 x 10-73.21 x 10-51.05 x 10-74.43 x 10-6

Question

Calculate the Ka for a 0.43M weak acid solution that has a pH equal to 3.50.2.33 x 10-73.21 x 10-51.05 x 10-74.43 x 10-6

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Solution

To calculate the Ka for a weak acid solution, we first need to understand the relationship between pH, [H+], and Ka.

  1. The pH of a solution is a measure of the hydrogen ion concentration, [H+]. The relationship between pH and [H+] is given by the equation: pH = -log[H+].

  2. We can rearrange this equation to solve for [H+]: [H+] = 10^-pH.

  3. Substituting the given pH of 3.50 into this equation gives: [H+] = 10^-3.50 = 3.16 x 10^-4 M.

  4. For a weak acid, HA, the ionization in water is given by the equation: HA ⇌ H+ + A-. The equilibrium constant for this reaction, Ka, is given by the equation: Ka = [H+][A-]/[HA].

  5. Since the acid is weak, we can assume that the concentration of HA at equilibrium is approximately equal to the initial concentration of the acid. Therefore, [HA] ≈ 0.43 M.

  6. We can also assume that the concentration of H+ is equal to the concentration of A- at equilibrium, since each molecule of HA that ionizes produces one H+ ion and one A- ion. Therefore, [H+] = [A-] = 3.16 x 10^-4 M.

  7. Substituting these values into the equation for Ka gives: Ka = (3.16 x 10^-4)^2 / 0.43 = 2.33 x 10^-7.

So, the Ka for the weak acid solution is 2.33 x 10^-7.

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