$pH$ of acids, bases and salts

Exercise 5

    

Using the table of acid-base couples, calculate the pH of a nitrous acid solution with concentration c = 0.178 M

Weak acid Let's take $y=[H_3O^+]$ The equation $y^2$ $+$ $K_a\;y$ $-$ $K_a\;c$ $=$ $0$ becomes: $y^2$ $+$ $10^{-3.3}y$ $-$ $10^{-3.3} 0.178$ $=$ $0$ and produces: $y$ $=$ 9.2 10^-3 and so: $pH$ $=$ $ -log\; y$ $ =$ 2.04