pH of acids, bases and salts

Exercise 11

    

Calculate the $pH$ of a sodium ethanoate solution ($pK_a$ $=$ $4.75$) with concentration $c$ = 0.637 $M$

Ethanoate: weak base $pK_b$ $=$ $14$ $-$ $pK_a$ $=$ $9.25$ $c_{sodium\;ethanoate}$ $=$ $c_{ethanoate}$ $=$ $c$ Given $z=[OH^-]$ The equation $z^2$ $+$ $K_bz$ $-$ $K_bc$ $=$ $0$ becomes: $z^2$ $+$ $10^{-9.25}z$ $-$ $10^{-9.25}$ 0.637 = 0 and produces: $z$ $=$ 1.9 10^-5 and so: $pOH$ $=$ $-log\; z$ = 4.72 $pH$ $=$ $14$ $-$ $pOH$ = 9.28