First slide

Ionization constants of weak acids, PH of weak acids

Question

For a weak acid ( $\large \alpha$ is very small)

Easy

A

K_a= C. ${\alpha ^2}$
B

$\alpha \, = \,\sqrt {\frac{{{K_a}}}{C}}$
C

[H⁺] = C. $\alpha$
D

all the above

Solution

Let us consider a weak acid 'HA' whose aqueous solution has a concentration of 'C'
                           HA   $\leftrightharpoons$ H⁺+ A¯
        At t = 0,      C             –        –
            t = t_eqC–Cα       Cα     Cα
${Ka} = \frac{{[C\alpha ][C\alpha ]}}{{C - C\alpha }} = \frac{{C{\alpha ^2}}}{{1 - \alpha }}\$
Since $\alpha \$ is small
K_a= C $\alpha \$ ²
$\alpha = \sqrt {\frac{{{K_a}}}{C}} \$
${\left[ {{H^ + }} \right]_{eq}}=C_\alpha$

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