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How do you find the pH of a solution with a known pKa and Molarity?

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Do you know the formula:

$$K_\text{a} = \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}$$

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You will need to find a concentration first, however, on the equation.

$$\ce{HA <=> H+ + A-}$$

And solve for the dissociated hydrogen ion, say $x$.

$$K_\text{a} = \frac{[x][x]}{[\ce{HA}]-x} = \frac{x^2}{[\ce{HA}]-x}$$

The logic is: if $x$ of $\ce{HA}$ dissociated, then we would get $x$ of $\ce{H}$, $x$ of $\ce{A}$ and $[\ce{HA}]-x$ left of $[\ce{HA}]$.

Does this make sense?

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  • $\begingroup$ the expresssion you wrote is for $K_a=10^{-pK_a}$. The p subscript means $-log[...]$ $\endgroup$ – Ashish Gaurav Mar 30 '13 at 4:59

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