If the molar conductivity (Λ_m) of a 0.050 mol L⁻¹ solution of a monobasic weak acid is 90 S cm² mol⁻¹, its extent (degree) of dissociation will be:

[Assume Λ₊ = 349.6 S cm² mol⁻¹ and Λ₋ = 50.4 S cm² mol⁻¹]

The correct option is 0.225.

To find the extent (degree) of dissociation of the monobasic weak acid, we can follow these steps:

Step 1: Calculate the molar conductivity at infinite dilution (${\Lambda }_m^0$)
According to Kohlrausch's law of independent migration of ions, the molar conductivity of a weak acid at infinite dilution is the sum of the individual molar conductivities of its constituent cations and anions.

For a monobasic acid, the dissociation can be represented as:
$\text{HA}\rightleftharpoons {\text{H}}^{+}+{\text{A}}^{-}$

Therefore, the molar conductivity at infinite dilution is:
${\Lambda }_m^0={\Lambda }_{+}+{\Lambda }_{-}$

Substitute the given values into the equation:
${\Lambda }_m^0=349.6\text{S}{\text{cm}}^2{\text{mol}}^{-1}+50.4\text{S}{\text{cm}}^2{\text{mol}}^{-1}$

${\Lambda }_m^0=400.0\text{S}{\text{cm}}^2{\text{mol}}^{-1}$

Step 2: Calculate the degree of dissociation ($\alpha$)
The degree of dissociation is defined as the ratio of molar conductivity (${\Lambda }_m$) at a given concentration to the molar conductivity at infinite dilution (${\Lambda }_m^0$):

$\alpha =\frac{{\Lambda }_m}{{\Lambda }_m^0}$

Given that the molar conductivity (${\Lambda }_m$) at the concentration of 0.050 mol L⁻¹ is 90 S cm² mol⁻¹, we substitute the values:
$\alpha =\frac{90}{400}$

$\alpha =0.225$

Thus, the extent of dissociation of the weak acid is 0.225.