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Wize University Chemistry Textbook > Thermodynamics Part 2: (2nd Law-entropy, 3rd Law, Gibbs Free Energy, Spontaneity)

Entropy

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2nd Law of Thermodynamics

Entropy (S) is a measure of disorder or randomness in a system.




The 2nd Law of Thermodynamics states that disorder of the universe increases in a spontaneous process.

In other words, things naturally tend to go towards disorder and the universe is constantly getting more and more disordered!


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Entropy Equations

Entropy is defined as:

ΔSsurr=qsurrT\boxed{\Delta S_{surr}=\frac{q_{surr}}{T}}

ΔSsurr=entropy of the surroundings (in J/molK)
qsurr=heat in the surroundings (in J)
T=Temperature (in K)
Recall:
qsurr=−qsysq_{surr}=-q_{sys}
At constant pressure and temperature:
ΔHsys=qsys\Delta H_{sys}=q_{sys}


ΔSsurr=−ΔHsysT\boxed{\Delta S_{surr}=-\frac{\Delta H_{sys}}{T}}

The 2nd law of thermodynamics states that whenever a spontaneous event takes place in the universe, the total entropy of the universe increases:

∆Suniverse=∆Ssystem+∆Ssurroundings>0\boxed{∆S_{universe}=∆S_{system}+∆S_{surroundings}>0}

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Chemical Reactions

In the same way we can use standard heats of formation to calculate a reaction enthalpy at room temperature and pressure, we can use So (values will be provided to you in a table)

ΔSo=[(∑nSoproducts)−(∑nSoreactants)]\boxed{\Delta S^o=[(\sum nS^oproducts)-(\sum nS^oreactants)]}
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Factoring Affecting Entropy Changes

Entropy for Different Phases


Photo by Rice University / CC BY
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Entropy When a Higher Pressure is Applied to a Gas

If we have two gases, and apply a higher pressure to one of them, will the gas with the higher pressure applied have more or less entropy?

The gas with the higher pressure applied to it will have (more/less)
more
organized molecules and therefore there is (more/less)
less
disorder, meaning there is (more/less)
less
entropy!

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Entropy of a Solid Alone vs Dissolved in a Liquid


Example:

KCl(s) vs KCl(aq)

There is (more/less)
more
entropy when the solid is dissolved in a solvent.

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Entropy of a Gas Alone vs Dissolved in a Solvent

Example: Think of shaking a bottle of pop CO2(g) vs CO2(aq)

The gas would have (more/less)
less
more entropy when dissolved in the solvent.

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Entropy of Similar Substances in the Same Physical State

How would entropy change with increasing mass?

Entropy would (increase/decrease)
increase

Example:
H2(g) (MM=2g/mol) vs Ar(g) (MM=40g/mol) vs CO2(g) (MM=44g/mol)


How would entropy change as we increase the number of atoms in the molecule?

Entropy would (increase/decrease)
increase
Example:
CH4(g) vs C2H6(g) vs C10H22(g)

How would entropy be different if we compared the following two molecules?
Cyclopentane vs C5H12

Would entropy increase or decrease with increasing molecular freedom or flexibility?
Increase!


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Entropy in a Chemical Equation

Example:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

If we were asked if entropy increases or decreases in this equation, what would you consider?
  • look at the phases on the reactants side and products side of the equation
  • If the phases are all the same, you can also look at the number of moles on each side
  • Here there are two gases on the left, and one gas and one liquid on the right
  • Since there is a liquid on the right, that is less disordered so overall from reactants to products the reaction got less disordered!
Therefore, entropy
decreased!
We could also say that ΔS is
<
0

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Example: Qualitatively Estimating Entropy Changes

Determine if the entropy change will be positive or negative for the following reactions:

(NH4)2Cr2O7(s)→Cr2O3(s)+4H2O(l)+N2(g)(NH_4 )_2 Cr_2 O_7 (s) → Cr_2 O_3 (s) + 4H_2 O(l)+N_2 (g)
  • On the left side we only have a solid
  • On the right side we have a solid, a liquid, and a gas
  • Since there is a liquid and gas on the right side, we automatically know that there is more disorder on the right side
  • There are also more molecules on the right than the left
  • The entropy change is positive (entropy increases going to the right)

2H2(g)+O2(g)→2H2O(g)2H_2 (g)+O_2 (g)→2H_2 O(g)
  • Each reactant and product are in the gaseous phase
  • On the left side, there are 3 moles of gas
  • On the right side, there are 2 moles of gas
  • The entropy change is negative since there are less moles of gas on the products side of the reaction

PCl5(g)→PCl3(g)+Cl2(g) PCl_5 (g)→PCl_3 (g)+Cl_2 (g)
  • 1 mole of gas on the left side
  • 2 moles of gas on the right side
  • Since there are more moles of gas on the right side it means that there is more disorder on the right side
  • The entropy change is positive (entropy increases going to the right)

Using the following data, calculate the standard entropy of the reaction shown below. Enter your answer in units of J / (mol*K)

2 Al(s)+3 ZnO(s)→Al2O3(s)+3Zn(s)2\ Al_{(s)}+3\ ZnO_{(s)}\rightarrow Al_2O_{3(s)}+3Zn_{(s)}


So(Al(s))=28.3 J mol−1K−1S^o(Al_{(s)})=28.3\ J\ mol^{-1}K^{-1}

So(Zn(s))=41.6 J mol−1K−1S^o(Zn_{(s)})=41.6\ J\ mol^{-1}K^{-1}

So(ZnO(s))=43.9 J mol−1K−1S^o(ZnO_{(s)})=43.9\ J\ mol^{-1}K^{-1}

So(Al2O3(s))=51.0 J mol−1K−1S^o(Al_2O_{3(s)})=51.0\ J\ mol^{-1}K^{-1}




Using the ΔH0 of fusion for water 6.03 kJ/mol and the ΔS0 of fusion for water 22.1 J K-1 mol-1, calculate the ΔSuniv for ice melting at -10oC, 0oC and 10oC. Remember: the universe transfers heat in a reversible way.


Extra Practice
Entropy Change of a Reaction
Using the following data, calculate the standard entropy change of the reaction shown below.
2Al(s)+3ZnO(s)→Al2O3(s)+Zn(s)2Al_{(s)}+3ZnO_{(s)}\to Al_2O_{3(s)}+Zn_{(s)}
So(Al(s))=28.3J/mol.KS^o(Al_{(s)})=28.3J/mol.K
If we increase the temperature of water more NaCl will dissolve but less O2 will dissolve. Which if the following answers best explains why.
Gibbs Free Energy: Entropy
Which ONE of the following pairs has the member with the greatest molar entropy listed first?
Gibbs Free Energy: Entropy
In terms of entropy, what happens when hydrogen and oxygen spontaneously react in gas phase to form water, according to the equation, 2 H2 (g) + O2 (g) ⇌ 2 H2O (g)?
phase change
The greater the degree of randomness in a system the greater is its:
Which of these processes would not result in an increase in entropy?
Gibbs Free Energy: Entropy
Which one of the following statements is INCORRECT?
Entropy
Which of the following statements is most clearly false regarding the entropy of a system?