Answer
$$16.4 \space g/mol$$
Work Step by Step
1. Convert the volume to $dm^3$:
$$1 \space dm^3 = 1000 \space cm^3$$ $$250 \space cm^3 \times \frac{1 \space dm^3}{1000 \space cm^3} = 0.250 \space dm^3$$
2. Calculate the molar volume.
$$pV_m = RT$$ $$V_m = \frac{RT}{p} = \frac{(62.364 \space Torr \space dm^3 \space K^{-1} \space mol^{-1})(298 \space K)}{152 \space Torr}$$ $$V_m = 122.27 \space dm^3 \space mol^{-1}$$
3. Find the amount of moles:
$$n = \frac{0.250 \space dm^3}{122.27\space dm^3 \space mol^{-1}} = 0.002045 \space mol$$
4. Calculate the molar mass of that compound:
$$M = \frac{mass}{n} = \frac{33.5 \space mg}{0.002045 \space mol} = 16400 \space mg/mol $$ $$16400 \times 10^{-3} \space g/mol$$ $$16.4 \space g/mol$$
