A more rigorous theory of $pH$
Mathematical treatment
Exercise 5
Find a system of N equations with N unknowns for the following aqueous solutions:
a) $0.5\; M$ perchloric acid
a)
(1) E.n.
$[H_3O^+]$ $=$ $ [ClO_4^-]$ $+$ $ [OH^-]$
(2) C.m.
$[ClO_4^-]$ $=$ $ 0.5$
(3) P.i.e.
$[H_3O^+] [OH^-]$ $=$ $ 10^{-14}$
b) $1.045\;\%$ $(d=1.010)$ sodium hydroxide
b)
(1) E.n.
$[Na^+]$ $+$ $ [H_3O^+]$ $ =$ $ [OH^-]$
(2) C.m.
$[Na^+]$ $=$ $ 2.639 10^{-1}$
(3) P.i.e.
$[H_3O^+] [OH^-]$ $=$ $ 10^{-14}$
c) $0.1\; M$ ammonia
c)
(1) E.n.
$[NH_4^+]$ $+$ $ [H_3O^+]$ $=$ $ [OH^-]$
(2) C.m.
$[NH_4^+]$ $+$ $ [NH_3]$ $=$ $ 0.1$
(3) P.i.e.
$[H_3O^+] [OH^-]$ $=$ $ 10^{-14}$
(4) Ka.
$\frac{[NH_3][H_3O^+]}{[NH_4^+]}$ $=$ $ 10^{-9.20}$
d) $0.98\; \frac{g}{L}$ sodium cyanide
d)
(1) E.n.
$[Na^+]$ $+$ $ [H_3O^+]$ $=$ $ [OH^-]$ $+$ $ [CN^-]$
(2) C.m.
$[Na^+]$ $=$ $ 2.00 \cdot 10^{-2} $
(3) C.m.
$[HCN]$ $+$ $ [CN^-]$ $=$ $ 2.00 \cdot 10^{-2}$
(4) P.i.e.
$[H_3O^+] [OH^-]$ $=$ $ 10^{-14}$
(5) Ka.
$\frac{[CN^-][H_3O^+]}{[HCN]}$ $=$ $ 10^{-9.31}$
