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Enough of a monoprotic acid is dissolved in water to produce a 1.57 M solution. The pH of the resulting solution is 2.74. Calculate the [tex]K_a[/tex] for the acid.

Answer :

Final answer:

The equilibrium constant (K) for the acid is 1.16 x 10^(-5).

Explanation:

To calculate the equilibrium constant (K) for the acid, we need to determine the concentration of hydronium ions ([H3O+]) and the concentration of the acid ([HA]).

Given:

  • Concentration of the acid solution ([HA]) = 1.57 M
  • pH of the solution = 2.74

Step 1: Calculate the concentration of hydronium ions ([H3O+]) using the pH value.

The pH scale is logarithmic, so we can calculate the concentration of hydronium ions using the formula:

[H3O+] = 10^(-pH)

Substituting the given pH value:

[H3O+] = 10^(-2.74)

[H3O+] = 4.28 x 10^(-3) M

Step 2: Calculate the concentration of the conjugate base ([A-]).

Since the acid is monoprotic, the concentration of the conjugate base ([A-]) is equal to the concentration of hydronium ions ([H3O+]).

[A-] = [H3O+] = 4.28 x 10^(-3) M

Step 3: Calculate the equilibrium constant (K) using the formula:

K = [H3O+][A-] / [HA]

Substituting the values:

K = (4.28 x 10^(-3) M)(4.28 x 10^(-3) M) / (1.57 M)

K = 1.16 x 10^(-5)

Therefore, the equilibrium constant (K) for the acid is 1.16 x 10^(-5).

Learn more about calculating the equilibrium constant (k) for a monoprotic acid here:

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