Review entropy: a measure of the extent to which energy is dispersed throughout a system; a quantitative (numerical) measure of disorder at the nanoscale; given the symbol S.
In brief, processes that increase entropy (ΔS > 0) create more disorder and are favored, while processes that decrease entropy (ΔS < 0) create more order and are not favored.
Examples: 1. Things fall apart over time. (constant energy input is required to maintain things)
2. Water spills from a glass, but spilled water does not move back into the glass.
3. Thermal energy disperses from hot objects to cold objects, not from cold to hot.
4. A gas will expand to fill its container, not concentrate itself in one part of the container.
Chemistry 103 Spring 2011
Energy disperses (spreads out) over a larger number of particles. Ex: exothermic reaction, hot object losing thermal energy to cold object.
Energy disperses over a larger space (volume) by particles moving to occupy more space. Ex: water spilling, gas expanding.
Consider gas, liquid, and solid, Fig. 17.2, p. 618.
2 Chemistry 103 Spring 2011
Example: Predict whether the entropy increases, decreases, or stays about the same for the process: 2 CO2(g) 2 CO(g) + O2(g).
Practice: Predict whether ΔS > 0, ΔS < 0, or ΔS ≈ 0 for: NaCl(s) NaCl(aq)
Guidelines on pp. 617-618 summarize some important factors when considering entropy.
3 Chemistry 103 Spring 2011
Measuring and calculating entropy
At absolute zero 0 K (-273.15 °C), all substances have zero entropy (S = 0).
At 0 K, no motion occurs, and no energy dispersal occurs. Instead, a perfect crystal exists with particles locked into lattice positions (no wiggling, no vibrations) and with S = 0. This idea is known as the third law of thermodynamics.
To measure entropy, measure the energy dispersed at a specific temperature. Typically, use a calorimeter (Chapter 6) to measure thermal energy transferred (q) at a specific temperature.
4 Chemistry 103 Spring 2011
Mathematically, keep the temperature value essentially constant by assuming only very small changes in the conditions of the process.
ΔS = qrev / T
qrev = thermal energy transferred for a reversible process. A reversible process means a small change in conditions, such as the temperature, will reverse the direction of the process. Ex: If T is barely above 0 °C, then ice melts. If T is barely below 0 °C, then water freezes.
Example: Determine the entropy change for melting 1.00 mol of ice in a calorimeter containing water barely above 0 °C.
5 Chemistry 103 Spring 2011
Example: P-S Practice 17.1, p. 616. Calculate the entropy change of a thermal reservoir (calorimeter) with a temperature of 45.3 0 °C when a chemical reaction transfers 30.8 kJ to it.
Why can we calculate the entropy change of the ice in the previous example, but cannot calculate the entropy change of the chemicals here?
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We calculate the entropy of any substance at any temperature by integration (calculus) of the equation ΔS = qrev / T over the range from 0 K (where S = 0) up to the desired temperature T.
The result is a table of standard molar entropy (S°) values, similar to standard molar enthalpy values of formation (ΔHf°) from Chapter 6.
Table 17.1, p. 617, and Appendix J, A.35.
6 Chemistry 103 Spring 2011
S° = enthalpy value for one mole of substance at standard conditions (25 °C, 1 atm).
ΔHf° = enthalpy value to form one mole of substance at standard conditions (25 °C, 1 atm).
Similar to Hess’s Law calculations (Chapter 6) for enthalpy changes (ΔH°rxn), we can calculate entropy changes (ΔS°rxn) for a process.
ΔS°rxn = ΣnS°products - ΣnS°reactants
Example: Calculate the entropy change for
MgCO3(s) MgO(s) + CO2(g).
7 Chemistry 103 Spring 2011
Practice: Calculate the entropy change for
2 CO2(g) 2 CO(g) + O2(g)
NaCl(s) NaCl(aq)
8 Chemistry 103 Spring 2011
Why doesn’t entropy control everything?
1. NaCl(s) NaCl(aq) Ksp = “very large”
Entropy favors products. “Equilibrium constant” shows products favored.
-9 2. CaCO3(s) CaCO3(aq) Ksp = 8.7 x 10
Entropy favors products. Equilibrium constant shows reactants favored.
Why the difference?
Remember that physical and chemical processes also have an enthalpy change (ΔH, energy change at constant pressure), and you already know whether ΔH favors products or reactants.
Next time we will look at combining enthalpy and entropy changes into a single quantity called free energy, ΔG, a form of potential energy that predicts if a process favors products or reactants.
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