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19 Chemical Thermodynamics Solutions to Exercises (c) When equal volumes of two miscible liquids are mixed, the volume of the sample and therefore the number of possible arrangements increases. This produces more microstates and an increase in entropy. 19.39 (a) The entropy of a pure crystalline substance at absolute zero is zero. (b) In translational motion, the entire molecule moves in a single direction; in rotational motion, the molecule rotates or spins around a fixed axis. Vibrational motion is reciprocating motion. The bonds within a molecule stretch and bend, but the average position of the atoms does not change. (c) H CI H translational H H H H CI vibrational rotational 19.40 (a) In order for the entropy of a system to be zero, the system must be a pure crystalline (exactly ordered in three dimensions) solid, and the temperature must be absolute zero. (b) Since has more than one atom, the thermal energy can be distributed as translational, vibrational, or rotational motion. Z translational rotational C symmetric asymmetric bend stretch stretch vibrational (c) At a given temperature, has more microstates and thus greater entropy than Ar(g). Because is a triatomic molecule, it has multiple rotational and vibrational microstates not available to monatomic Ar(g). 19.41 Analyze/Plan. Consider the factors that lead to higher entropy: more mol gas in products than reactants, increase in volume of sample and, therefore, number of possible arrangements, more motional freedom of molecules, etc. Solve. (a) Ar(g) (gases have higher entropy due primarily to much larger volume) (b) He(g) at 1.5 atm (larger volume and more motional freedom) (c) 1 mol of Ne(g) in 15.0 L (larger volume provides more motional freedom) (d) CO₂(g) (more motional freedom) 19.42 (a) 1 mol of at 300°C, 0.01 atm has more massive atoms in a comparable system at the same temperature.) 585