For a weak acid HA, the ionization constant ($K_a$) is related to its concentration ($c$) and degree of dissociation ($\alpha$) by the formula: $K_a = \frac{c\alpha^2}{1-\alpha}$

Given the values: Concentration of acid, $c = 0.1\text{ mol L}^{-1} = 10^{-1}\text{ M}$ Percentage of dissociation = $1\%$ Degree of dissociation, $\alpha = \frac{1}{100} = 0.01 = 10^{-2}$

Since $\alpha$ ($0.01$) is very small compared to $1$, the term $(1 - \alpha)$ in the denominator can be approximated as $1$ . The formula simplifies to: $K_a \approx c\alpha^2$

Substituting the given values: $K_a = (10^{-1}) \times (10^{-2})^2$ $K_a = 10^{-1} \times 10^{-4}$ $K_a = 10^{-5}$

Thus, the ionization constant $K_a$ is $1 \times 10^{-5}$.