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Weak Acid and Base Equilibria

AP Chemistry· difficulty 4/5

For H2SO3H_2SO_3: Ka1=1.5×10−2K_{a1} = 1.5\times 10^{-2}, Ka2=6.3×10−8K_{a2} = 6.3\times 10^{-8}. Estimate the pH of 0.20 M H2SO3H_2SO_3.

  • A

    pH≈7.00pH \approx 7.00

  • B

    pH≈0.70pH \approx 0.70

  • C

    pH≈1.30pH \approx 1.30

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  • D

    pH≈4.20pH \approx 4.20

Explanation

First dissociation dominates. Ka1K_{a1} not small; solve x2/(0.20−x)x^2/(0.20-x) = 0.015. x2+0.015x−0.003x^2 + 0.015x - 0.003 = 0; xx = (−0.015+0.000225+0.012-0.015 + \sqrt{0.000225 + 0.012})/2 = (−0.015+0.1106-0.015 + 0.1106)/2 = 0.0478. pH = −log⁡(0.0478)-\log(0.0478) = 1.32 ≈\approx 1.30.

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