02042018

Question 1

Spontaneous processes

Answer 1

• A process that does occur under a specific set of conditions is called a spontaneous process
• e.g.
  1. Ice melting at rm temp
  2. Sodium metal reacting violently with water to produce NaOH and H2 gas
  3. A ball rolling downhill
  4. The rusting of iron at rm temp
  5. Water freezing at -10C
• Nonspontaneous e.g.
  1. Water freezing at rm temp
  2. NaOH reacting with H2 gas to produce sodium metal and water
  3. A ball rolling uphill
  4. The conversion of rust back to iron metal at rm temp
  5. Ice melting at -10C

Question 2

Spontaneous process

Answer 2

• A process that result sin a decrease in the energy of a system often is spontaneous:
  CH4 (g) + 2O2 (g) > CO2 (g) + 2H2O (l); change in H = -890.4kJ/mol
• The sign of change in H alone is insufficient to predict spontaneity in every circumstance:
  H2O (l) > H2O (s); T>0C; change in H = -6.01 kJ/mol

Question 3

Entropy: a qualitative description of entropy

Answer 3

• To predict spontaneity, both the enthrall and entropy must be known
• Entropy (S) of a system is a measure of how spread out or how dispersed the system’s energy is

Question 4

A quantitative description of entropy

Answer 4

• Spontaneity is favored by an increase in entropy
  S = k ln W
• k = Boltzmann constant (1.38*10^-23 J/K)
  W = number of different arrangements
• The number of arrangements possible is given by:
  W = X^N
• X = number of cells in a volume
  N = number of molecules
• The most probable state has the largest number of arrangements

Question 5

Entropy changes in a system: calculating change in S_sys

Answer 5

• The change in entropy for a system is the difference in entropy of the final state and the entropy of the initial state.
  Change in S_sys = S_final - S_initial
• Alternatively:
  Change in S_sys = nR ln(V_final / V_initial)

Question 6

Example: Determine the change in entropy for 1.0 mole of an ideal gas originally confined to one-half of a 5.0L container when the gas is allowed to expand to fill the entire container at constant temperature.

Answer 6

• Change in S_sys = nR ln(V_f / V_i)
  = 1.0mol * 8.314J/kmol * ln (5.0L / 2.5L) = 5.80 J/K
  > +ve value of S_sys > spontaneous process has S_sys value in +ve

Question 7

Standard entropy, S^o

Answer 7

• The standard entropy is the absolute entropy of a substance at 1atm.
• Temperature is not part of the standard state definition and must be specified.
• There are several important trends in entropy:
  1. S^o_liquid > S^o_solid
  2. S^o_gas > S^o_liquid
  3. S^o increases with molar mass
  4. S^o increases with molecular complexity
  5. S^o increase with the mobility of a phase (for an element with 2 or more allotropes)
• In addition to translational motion, molecules exhibit vibrations and rotations.
• For a chemical reaction:
  aA + bB > cC + dD
  > Change in S^o_rxn = [cS^o(C) + dS^o(D)]-[aS^o(A)+bS^o(B)]
  > Alternatively,
  Change in S^o_rxn = Sum of nS^o(products) - Sum of mS^o(reactants)

Question 8

Example: From the standard enthrall values, calculate the standard entropy changes for the following reaction at 25C.
CaCO3 (s) > CaO (s) + CO2 (g)

Answer 8

- Given / S^o J/Kmol
   [CaCO3(s)] / 92.9
   [CaO(s)] / 39.8
   [CO2(g)] / 213.6
- CaCO3 (s) > CaO (s) + CO2 (g)
   S^o_rxn = [S^o(CaO) + S^o(CO2)] - [S^o(CaCO3)]
= 39.8 + 213.6 - 92.9 = 160.5 J/Kmol

Question 9

Qualitatively predicting the sign of change in S^o_sys

Answer 9

• Several process that lead to an increase in entropy are:
  1. Melting
  2. Vaporization or sublimation
• The process of dissolving a substance can lead to either an increase or a decrease in entropy, depending on the nature of the solute.
• Table 14.3
  Dissolution equation / Change in S^o_soln (J/Kmol)
  NH4NO3 (s) > NH4+ (aq) + NO3- (aq) / 108.1
  AlCl3 (s) > Al3+ (aq) + 3Cl- (aq) / -253.2
  FeCl3 (s) > Fe3+ (aq) + 3Cl- (aq) / -266.1
  >* Molecular solutes (i.e. sugar): entropy increases
  > * Ionic compounds: entropy could decrease or increase

Question 10

Example: For each process, determine the sign of Change in S for the system:
A. Decomposition of CaCO3 (s) to give CaO (s) and CO2 (g)
B. Heating bromine vapor from 45C to 80C
C. Condensation of water vapor on a cold surface
D. Reaction of NH3 (g) and HCl (g) to give NH4Cl (s)
E. Dissolution of sugar in water

Answer 10

A. +ve
B. +ve
C. -ve
D. -ve
E. +ve

Question 11

Entropy changes in the universe

Answer 11

• Correctly predicting the spontaneity of a process requires us to consider entropy changes in both the system and the surroundings.
• An ice cube spontaneously melts in a room at 25C
  Perspective / Components / Change in S
  System / ice / positive
  Surroundings / everything else / negative
• A cup of hot water spontaneously cools to room temperature
  Perspective / Components / Change in S
  System / hot water / negative
  Surroundings / everything else / positive