Answer
0.80 g
Work Step by Step
Given: Molality= 0.050 mol/kg and
Mass of the solvent=500. g = 0.500 kg
Recall: Molality=$\frac{moles\, of\,solute}{mass\, of\, solvent\,in\,kg}$
$\implies$ moles of methanol=
Molality$\times$ mass of solvent in kg
$=0.050\,mol/kg\times 0.500\,kg=0.025\,mol$
Mass of methanol needed =
number of moles$\times$ molar mass
$=0.025\,mol\times 32\,g/mol=0.80\,g$