For a $ 0.20 \; M $ solution of a weak acid an ionization degree of $ 0.12$ was measured. Calculate its $pK_a$!
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First calculate $x=[H_3O^+]$
$[H_3O^+]$ $=$ $\alpha\cdot c_0$ $=$ $0.12\cdot 0.20$ $=$ $0.024\; M$
Use the second degree equation to search $K_a$ !
$x^2+K_a\cdot x-K_a\cdot c_0=0$ $0.024^2+K_a\cdot 0.024-K_a\cdot 0.20=0$ $K_a\;=\;3.3\cdot 10^{-3}$