(a) For what mass of molecule or particle is ???rms equal to 1.00 mm/s at 300 K? (b) If the particle is an ice crystal, how many molecules does it contain? The molar mass of water is 18.0 g/mol (c) Calculate the diameter of the particle if it is a spherical piece of ice. Would it be visible to the naked eye?
Solution 79P Problem (a) To find mass of molecule Step 1: v = 1 mm/s or 10 m/s rms T = 330K k = 1.381x10 23 J/K Step 2: 3kT m = vrms m = 3*1.38* 102*300 (10 )2 m = 1.24x10 14 Kg 14 Mass of the molecule is 1.24x10 Kg Problem (b) To find the number of molecules in ice crystals Step 1: mN A N = M N = 6.023x10 molecules/mol A M - Molar mass of water M = 18 g/mol Step 2: N = 1.2* 101*6.02* 103 1* 103 11 N = 4.15x10 molecules Number of molecules in the ice crystals is 4.15x10 molecules Problem (c) Step 1: To find the diameter of the spherical piece of ice D = 2R 33V D = 2x 4 Step 2: Volume V = Mass (density of ice = 917.6 kg/m ) Density 14 V = 1.916.7 V = 1.35x10 17m 3