Chapter 19 Second law of thermodynamics Probability of

Chapter 19 Second law of thermodynamics

Probability of finding all gas molecules in left bulb as a function of the total number of gas particles • • • # molecules Probability 1 ½ 2 ½x½=¼ 3 ½ x ½ = 1/(2)3 5 ½x½ x½x½x½ = 1/(2)5 • n ½ x ½ x… 1/(2)n

Entropy Generalizations • The solid state has the lowest entropy, the smallest volume and particles with the fewest positional options. • The gas state has the highest entropy. The particles are far apart with many positional options available. • Liquid is closer to solid than gas in these terms.

S symbol for entropy • ΔS symbol for change in entropy • ΔS Positive when entropy increases • ΔS Negative when entropy decreases

Entropy and Solutions • ΔH on mixing may be either positive or negative, but ΔS is always positive. ΔS is due to the decrease in the concentrations of Small Change in Volume the individual Decrease in Concentration components in the of Red Molecules change from a limited Decrease in Concentration volume in the pure of Blue Molecules state to a much larger Increase in Configurational Entropy volume in the mixture.

Other increases in ΔS

For each pair, which has the higher ΔS per mole at any given temp. ? • Solid CO 2 and gaseous CO 2 • N 2 gas at 1 atm and N 2 gas at 1. 0 x 10 -2 atm • 1 liter of Na. Cl 1 M and 1 liter of Fe. SO 4 1 M or a two liter mixture of equal volumes of both

Answers • gaseous CO 2 • N 2 gas at 1. 0 x 10 -2 atm • a two liter mixture of equal volumes of both

Predict the sign of ΔS • Solid sugar is added to water to form a solution • Iodine vapor condenses on a cold surface to form crystals • A sample of gas in a constant volume container is heated 25 °C

Answer • • Since ΔS = S final – S initial: ΔS = + ΔS = 0 since the volume is unchanged and the positional options for the molecules is the same. (Configurational Entropy)

The Second Law of Thermodynamics • In any spontaneous process there is an increase in the entropy of the universe. • Or, the entropy of the universe is increasing. "Now, in the second law of thermodynamics

The Second Law of Thermodynamics Therefore: • If ΔS univ = ΔS system + ΔS surround • Then if the sign of ΔS univ is positive, the entropy of the universe is increasing and the process is spontaneous in the direction in which it was written

A Tough one • In a living cell, large molecules are assembled from simple ones. Is this process consistent with the second law of thermodynamics?

Yes!! • ΔS univ = ΔS system + ΔS surround • Although the ΔS of the system is decreasing, disorder in the surrounding is increasing. As long as the total or ΔS of the universe is + , the process agrees with the 2 nd law.