I'm having trouble figuring out where to go with this question.
Calculate the degree of dissociation of $\ce{AlCl3}$ if molar conductivity of the solution is $31.3\ \mathrm{mS\ m^2\ mol^{-1}}$ and constant $\mathrm{K}$ is $\mathrm{108.96\ mS\ m^2\ mol^{-1}}$.
So the equations I think should be used are
for the dissociation constant
$$\alpha =\frac{\Lambda_m }{ \Lambda_m^0}$$
and
$$\Lambda_m = \Lambda_m^0 - K\sqrt{C}$$ where $\mathrm{K}$ is the positive constant for a given electrolyte.
But I don't know how to find C
The only relationship I've found that's related to molar conductance is $$\mathrm{C = k \frac{A}{L}}$$
where this $\mathrm{k}$ is the conductivity
$$\mathrm{k=\frac{1}{\rho}}$$
where $\rho$ is the specific resistance and $\mathrm{\frac{A}{L}}$ is the cell constant. I feel like at this point there's too many unknowns? What should I do?
Edit
Well, you can understand my frustration when the instructor updated his question last night, with the inclusion of the concentration in it. $\mathrm{C= 0.025}$