How much ml of sulfur dioxide are in one cubic meter of air if the ppm (parts per million) of sulfur dioxide in one cubic meter of air is 0.010?

I am not sure if what I did is right

V SO2 = 3.814 mL

Explanation:

∴ V air = 1 m³ = 1000 L

∴ [SO2]air = 0.010 ppm mg/L

⇒ V SO2 = ?

mass SO2:

⇒ m SO2 = (0.010 mg/L) * (1000 L) = 10 mg = 0.01 g

mol SO2:

∴ molar mass SO2 = 64.066 g/mol

⇒ n SO2 = (0.01 g) * (mol/64.066 g) = 1.5609 E-4 mol

assuming ideal gas at STP:

∴ PV = RTn

⇒ V = RTn/P

∴ P = 1 atm

∴ T = 298 K

∴ R = 0.082 atm. L/K. mol

⇒ V = ((0.082 atm. L/K. mol) (298 K) (1.5609 E-4 mol)) / (1 atm)

⇒ V = 3.814 E-3 L = 3.814 mL