Answer
$$S_8$$
Work Step by Step
1. Convert the values to K and Pa:
$$T/K = 500 + 273.15 = 773.15$$ $$T = 773.15 \space K$$ $$p = 93.2 \space kPa= 93.2 \times 10^3 \space Pa = 93200 \space Pa$$
2. Calculate the molar volume.
$$pV_m = RT$$ $$V_m = \frac{RT}{p} = \frac{(8.31447 \space Pa \space m^3 \space K^{-1} \space mol^{-1})(773.15 \space K)}{93200 \space Pa}$$ $$V_m = 0.06897 \space m^3 \space mol^{-1}$$
3. Find the molar mass:
$$0.06897 \space m^3 \space mol^{-1} \times 3.710 \space kg \space m^{-3} = 0.256 \space kg \space mol^{-1}$$ $$0.256 \times 10^3 \space g \space mol^{-1} = 256 \space g/mol$$
4. Calculate the number of Sulfur atoms:
$$1 \space Sulfur \space atom = 32 \space g/mol$$ $$256 \space g/mol \times \frac{1 \space Sulfur \space atom}{32 \space g/mol} = 8 \space Sulfur \space atoms$$
