Demonstrate that the degree of ionization of a weak acid increases with dilution!
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Introduce $ \alpha $ into the second degree equation !
$x=[H_3O^+]$ $x^2+K_a\cdot x-K_a\cdot c_0=0$ $\alpha^2c_0^2+K_a\cdot\alpha\cdot c_0-K_a\cdot c_0=0$
Use the second-degree equation to extract $c_0$ !
$\alpha^2c_0+K_a\cdot\alpha-K_a=0$ $K_a(1-\alpha)=\alpha^2c_0$ $K_a\frac{1-\alpha}{\alpha^2}$ $=$ $c_0$
Discuss the fraction of the first member !
$K_a$ is a constant, so: If $ c_0 $ decreases (dilution), $ \alpha^2 $ increases and (or) $ 1-\alpha $ decreases, which means that $ \alpha $ must increase !
