Calculate the $pH$ of a 0.5 % ($d$ = 1.0039) sodium hydroxide solution named $S$
$OH^-$ treated as a strong base
If $d$ = 1.0039, then $\rho$ = 1.0039 $\frac{g}{mL}$
Let's take $1\;L$ of solution $S$:
$m_S=\rho \cdot V_S = \rho \cdot 1000 $ =
1003.9$\;g$
$m_{NaOH}$ =
$\frac{\%_{NaOH}\cdot m_S}{100} $ =
$\frac{0.5 \cdot1003.9}{100} $ =
5.02$\; g$
$n_{NaOH}=\frac{m_{NaOH}}{M_{NaOH}}$ =
$\frac{5.02}{40}$ =
0.125$ \;mol$
The number of moles of $NaOH$ is equal to the number of moles of $OH^-$ !
$[OH^-]$ $=$ $\frac{n_{OH^-}}{V_S}$ =
$\frac{0.125}{1}$ =
0.125 $\frac{mol}{L}$
$pH$ $=$ $14$ $+$ $log\;[OH^-]$ =
$14$ $+$ $log \;$0.125 =
13.099
