For a weak acid like acetic acid, the concentration of hydrogen ions ($H^+$) at equilibrium is given by the product of its initial concentration ($c$) and its degree of ionization ($\alpha$) .

Given: Concentration, $c = 0.01\text{ M} = 10^{-2}\text{ M}$ Degree of ionization, $\alpha = 1\% = \frac{1}{100} = 10^{-2}$

$[H^+] = c\alpha = 10^{-2} \times 10^{-2} = 10^{-4}\text{ M}$

The pH of the solution is calculated as: $\text{pH} = -\log[H^+]$ $\text{pH} = -\log(10^{-4}) = 4$

Therefore, the pH of the given acetic acid solution is $4$.