The molar mass of potassium benzoate trihydrate (C6H5COOK.3H2O) is 294.24 g/mol. To prepare one liter of a 0.125 molar solution of potassium benzoate trihydrate, we need to calculate the number of moles of potassium benzoate trihydrate required and then convert that to mass.

Number of moles of potassium benzoate trihydrate = concentration x volume

Number of moles of potassium benzoate trihydrate = 0.125 mol/L x 1 L = 0.125 mol

Mass of potassium benzoate trihydrate = number of moles x molar mass

Mass of potassium benzoate trihydrate = 0.125 mol x 294.24 g/mol = 36.78 g

Therefore, 36.78 g of potassium benzoate trihydrate is needed to prepare one liter of a 0.125 molar solution of potassium benzoate.