The molality is 0.50 mol/kg.
molality = #("moles of solute")/("kilograms of solvent")#
moles of NaOH = 10 g NaOH × 1mol NaOH40.00g NaOH = 0.25 mol NaOH
kilograms of H₂O = 500 g H₂O × 1kg H₂O1000g H₂O = 0.500 kg H₂O
molality = moles of solutekilograms of solvent=0.25mol0.500kg = 0.50 mol/kg