(Solved): 5. Arrhenius theory states that the degree of dissociation \( (\alpha) \) of a weak electrolyte is ...

5. Arrhenius theory states that the degree of dissociation \( (\alpha) \) of a weak electrolyte is equal to \( \Lambda_{\mathrm{m}} / \Lambda_{\mathrm{m}}{ }^{0} \). \( \Lambda_{\mathrm{m}} \) is the molar conductivity and \( \Lambda_{\mathrm{m}}{ }^{0} \) is the limiting molar conductivity of the weak electrolyte. Arrhenius's idea was expressed quantitatively by Friedrich Wilhelm Ostwald in terms of a dilution law. For a weak electrolyte, the relationship between the dissociation constant \( (\mathrm{K}) \) and the degree of dissociation is \[ \mathrm{K}=\mathrm{c \alpha}^{2} /(1-\alpha) \] where \( \mathrm{c} \) is the molar concentration of the weak electrolyte. The conductivity \( (\kappa) \) of \( \mathrm{CH}_{3} \mathrm{COOH} \) solution of various concentrations was obtained as follows. Determine the dissociation constant \( \left(\mathrm{K}_{\mathrm{a}}\right) \) for \( \mathrm{CH}_{3} \mathrm{COOH} \). (10 points)