To determine the degree of dissociation (α) of a weak acid, we use the formula:

$ \alpha = \frac{\Lambda_{\mathrm{m}}}{\Lambda_{\mathrm{m}}^{\circ}} $

where:

$ \Lambda_{\mathrm{m}} $ is the molar conductivity of the solution, provided as $ 90 \, \mathrm{S} \, \mathrm{cm}^2 \, \mathrm{mol}^{-1} $.

$ \Lambda_{\mathrm{m}}^{\circ} $ is the limiting molar conductivity of the acid, calculated as the sum of the limiting molar conductivities of its ions.

Given:

$ \Lambda_{+}^{\circ} = 349.6 \, \mathrm{S} \, \mathrm{cm}^2 \, \mathrm{mol}^{-1} $ (cation)

$ \Lambda_{-}^{\circ} = 50.4 \, \mathrm{S} \, \mathrm{cm}^2 \, \mathrm{mol}^{-1} $ (anion)

First, calculate $ \Lambda_{\mathrm{m}}^{\circ} $:

$ \Lambda_{\mathrm{m}}^{\circ} = \Lambda_{+}^{\circ} + \Lambda_{-}^{\circ} = 349.6 + 50.4 = 400 \, \mathrm{S} \, \mathrm{cm}^2 \, \mathrm{mol}^{-1} $

Next, use the given values to find the degree of dissociation:

$ \alpha = \frac{90}{400} = 0.225 $

Therefore, the degree of dissociation of the acid is 0.225.