1. Use freezing point depression relation

The depression in freezing point is

$\Delta T_f = T_f^\circ - T_f$

Given:

$T_f^\circ = 156.0\,\text{K}, \qquad T_f = 155.1\,\text{K}$

So,

$\Delta T_f = 156.0 - 155.1 = 0.9\,\text{K}$

2. Find molality of the solution

Using

$\Delta T_f = K_f m$

Given $K_f = 2.00\,\text{K kg mol}^{-1}$,

$m = \frac{\Delta T_f}{K_f} = \frac{0.9}{2.00} = 0.45\,\text{mol kg}^{-1}$

3. Calculate mass of ethanol (solvent)

Volume of ethanol $= 62.5\,\text{cm}^3$

Density of ethanol $= 0.80\,\text{g cm}^{-3}$

$\text{mass of ethanol} = 62.5 \times 0.80 = 50.0\,\text{g}$

Convert into kg:

$50.0\,\text{g} = 0.0500\,\text{kg}$

4. Calculate moles of solute

Molality is defined as

$m = \frac{\text{moles of solute}}{\text{kg of solvent}}$

So,

$\text{moles of solute} = m \times \text{kg of solvent} = 0.45 \times 0.0500 = 0.0225\,\text{mol}$

5. Calculate molar mass of solute A

Given mass of solute $= 1.80\,\text{g}$

$M = \frac{\text{mass}}{\text{moles}} = \frac{1.80}{0.0225} = 80\,\text{g mol}^{-1}$

6. Final answer

$\boxed{80}$

g $\text{mol}^{-1}$