First, calculate for the mass of the aqueous solution by multiplying the given volume (in mL) by the density (in g/mL). In mathematical equation, that is,
m = ρV
where m is mass, ρ is density, and V is volume. Substituting the known values,
m = (1.03 g/mL)(250 mL) = 257.5 g
To get the concentration in ppm, divide the given mass of methanol by the mass of the solution. Note that the parts-per million (ppm) is equal to mass of solute in milligram(mg) divided by the mass of solution in kilogram (kg)
C (in ppm) = (1.56 x 10^-6 g)(1000 mg/1 g) / (257.5 g)(1 kg/1000 g)
Simplifying,
C (in ppm) = (1.56 x 10^-3 mg)/ 0.2575 kg
C (in ppm) = 0.00606 ppm
Answer: 0.00606 ppm