(a) Use the value of the van der Waals constant b for CH₄(g), given in Table 6.5, to estimate the radius of the CH₄ molecule. (See Exercise 89.) How does your estimate of the radius compare with the value r = 228 pm, obtained experimentally from an analysis of the structure of solid methane? 

(b) The density of CH₄(g) is 66.02 g mL^-1 at 100 bar and 325 K. What is the value of the compressibility factor at this temperature and pressure?

Exercise 89

Use the value of the van der Waals constant b for He(g) given in Table 6.5, to estimate the radius, r, of a single helium atom. Give your answer in picometers.

Table 6.5

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TABLE 6.5 van der Waals Constants and Compressibility Factors (at 10 bar and 300 K) for Various Gases van der Waals Constants Gas H₂ He Ideal gas N₂ CO 0₂ CH4 NF3 CO₂ N₂O C₂H6 NH3 SF6 C3H8 SO₂ a, bar L² mol-² 0.2452 0.0346 0 1.370 1.472 1.382 2.303 3.58 3.658 3.852 5.580 4.225 5.580 9.39 7.857 b, L mol-¹ 0.0265 0.0238 0 0.0387 0.0395 0.0319 0.0431 0.0545 0.0429 0.0444 0.0651 0.0371 0.0651 0.0905 0.0879 Compressibility Factor 1.006 1.005 1 0.998 0.997 0.994 0.983 0.965 0.950 0.945 0.922 0.887 0.880 a a