$pH$ of acids, bases and salts

Exercise 6

    

Using the table of acid-base couples, calculate the pH of a 5 %  (d = 1.023) trichloracetic acid solution.

Weak acid If $d$ = 1.023, then $\rho$ = 1.023 $\frac{g}{mL}$ Let's take $1\;L$ of solution $S$: $m_S$ $=$ $\rho \cdot V_S$ $ =$ $ \rho \cdot 1000 $ = 1023$\; g$ $m_{}$ = $\frac{\%_{}\cdot m_S}{100} $ = $\frac{5 \cdot1023}{100} $ = 51.15$\; g$ $n_{}=\frac{m_{}}{M_{}}$ = $\frac{51.15}{163.38}$ = 0.313$\; mol$ $c_{}$ = $\frac{n_{}}{V_S}$ = $\frac{0.313}{1}$ = 0.313 $\frac{mol}{L}$ Given $y=[H_3O^+]$ The equation $y^2$ $+$ $K_a\;y$ $-$ $K_a\;c$ $=$ $0$ becomes: $y^2$ $+$ $10^{-3.86}y$ $-$ $10^{-3.86} 0.313$ $=$ $0$ and produces: $y$ $=$ 6.51 10^-3 and so: $pH$ $=$ $ -log\; y$ $ =$ 2.186