pH of acids, bases and salts

Exercise 24

    

Acetylsalicylic acid (aspirin) is an analgesic drug (threshold of pain perception increased), antipyretic (temperature drop for fever), and anti-inflammatory (treatment of arthritis). The ingestion of large doses may cause bleeding of the stomach lining. Its acidity constant is $2.75\cdot10^{-5}$. A $350\;mg$ pill is dissolved in enough water to get $200\;ml$ of solution. What will the $pH$ of this solution?

Aspirin : weak acid $n$ $=$ $\frac{0.35}{180.157}$ $c$ $=$ $\frac{\frac{0.35}{180.157}}{0.2}$ $ =$ $ 0.0097 \frac{mol}{L}$ Given $y=[H_3O^+]$: The equation $y^2$ $+$ $K_a\;y$ $-$ $K_a\;c$ $=$ $0$ becomes: $y^2$ $+$ $2.75 10^{-5}y$ $-$ $2.75 10^{-5}\cdot 0.0097$ $ =0$ and produces $y=$ 4.02 10^-4 and so: $pH$ $=$ $ -log\; y $ $=$ 3.4