Answer
$$P_4$$
Work Step by Step
1. Convert the values to K and Pa:
$$T/K = 100 + 273.15 = 373.15$$ $$T = 373.15 \space K$$ $$p = 16.0 \space kPa= 16.0 \times 10^3 \space Pa = 16000 \space Pa$$
2. Calculate the molar volume.
$$pV_m = RT$$ $$V_m = \frac{RT}{p} = \frac{(8.31447 \space Pa \space m^3 \space K^{-1} \space mol^{-1})(373.15 \space K)}{16000 \space Pa}$$ $$V_m = 0.1939 \space m^3 \space mol^{-1}$$
3. Find the molar mass:
$$0.1939 \space m^3 \space mol^{-1} \times 0.6388 \space kg \space m^{-3} = 0.124 \space kg \space mol^{-1}$$ $$0.124 \times 10^3 \space g \space mol^{-1} = 124 \space g/mol$$
4. Calculate the number of Sulfur atoms:
$$1 \space Phosphorus \space atom = 31 \space g/mol$$ $$124 \space g/mol \times \frac{1 \space Phosphorus \space atom}{31 \space g/mol} = 4 \space Phosphorus \space atoms$$
