Calculate the pH using the K_sp and the K_a

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So far, this is the only problem of this type that I can find. Just gotta keep looking!!

Example #1: The K_sp of tin(II) iodide is 8.39 x 10¯⁶ and the K_a1 of Sn(H₂O)₆²⁺ is 4.0 x 10¯⁴. Predict the pH of a saturated solution of tin(II) iodide.

Solution:

1) Write the K_sp expression for tin(II) iodide:

SnI₂(s) ⇌ Sn²⁺(aq) + 2I¯(aq)

K_sp = [Sn²⁺] [I¯]²

2) Determine the molar concentration of Sn²⁺ in a saturated solution of tin(II) iodide:

8.39 x 10¯⁶ = (s) (2s)²

s = 0.0128 M

3) Write the dissociation equation for the first dissociation step of Sn(H₂O)₆²⁺:

Sn(H₂O)₆²⁺ + H₂O ⇌ H₃O⁺ + Sn(H₂O)₅OH⁺

The second dissociation step will be ignored.

4) Write the K_a1 expression:

K_a1 = $\frac{\mathrm{[H₃O⁺]\; [Sn(H₂O)₅OH⁺]}}{\mathrm{[Sn(H₂O)₆²⁺]}}$

5) Solve for the [H₃O⁺]:

4.0 x 10¯⁴ = $\frac{\mathrm{(x)\; (x)}}{\mathrm{0.0128}}$

x = 0.00226274 M

6) Calculate the pH:

pH = −log [H₃O⁺]

pH = −log 0.00226274

pH = 2.645

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