WEBVTT
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As an example, let's calculate the entropy change of the following reaction.
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This reaction is the formation reaction of aluminum oxide at standard condition.
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The enthalpy of formation is -16 hundreds 74 kJ/mole. To calculate entropy of the formation reaction,
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let's take the reversible path with the same reaction at zero K. This is the formation reaction at zero K.
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The entropy of formation at zero K is delta S3.
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The reversible path is involved in cooling of reactants aluminum and oxygen,
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the entropy of cooling is delta S1 and S2 for Al and O2, respectively.
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The heating of the product Al2O3 completes the reversible path, and the related entropy change is delta S4.
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So the entropy change of the original reaction is the summation of the entropy changes
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in the reversible path. Delta S1 and S2 is the simple cooling of Al and O2. Delta S4 is the heating of Al2O3.
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Delta 3 is the entropy change of the reaction at zero K. Then, let's calculate each of them.
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For materials that do not undergo phase change in the temperature range of interest such as
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solid aluminum and solid Al2O3, the entropy change can be simply calculated from the heap capacity Cp.
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So delta S1, the cooling of Al from room temperature to zero K is 2 times integration of Cp Aluminum
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over T dT from 298 to 0 K. And delta S4, the heating of Al2O3 from zero K to room temperature is
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integration of Cp over T dT from zero to 298 K.
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Delta S3, the reaction entropy at zero K is zero by the 3rd law. Now, delta S2 remains.
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It is the entropy change involved in cooling of O2 gas from room temperature to zero K.
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In cooling O2 gas to zero K, we have to consider phase transitions. O2 might be solid at 0 K
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and gas at 298 K, thus it experiences two phase transitions upon cooling from gas at 298 K to 0 K.
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So when we plot entropy versus temperature, it looks like this.
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In the single phase regime, such as gas O2, liquid O2, and solid O2, the entropy increases gradually
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with temperature and the slop is Cp over T. So the slop of solid O2 regime is Cp of solid O2 over T.
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Likewise the slope in liquid O2 regime is Cp of liquid O2 over T, and that of gas O2 is Cp of gas O2 over T.
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Then between each phases it experience phase change reaction.
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First, gas to liquid, the condensation reaction at boiling point Tb
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and then liquid to solid, the freezing reaction at melting point Tm.
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The entropy change during the first condensation reaction is denoted as delta S condensation,
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and that of freezing is delta S freezing O2.
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The total entropy change is like this. 1.5 is the mole number in the formation reaction.
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In the parenthesis, the first part is single phase cooling of O2 gas
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from room temperature to the boiling point.
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So the entropy change of cooling O2 gas is Cp of gas O2 over T dT.
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Then gas O2 experience condensation, and the involved entropy change is delta S, condensation.
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Next liquid O2 cools down from boiling point to melting point. Then it freeze to solid O2.
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Finally, solid O2 cools down from melting point to zero K.
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For the entropy change of phase transition reaction, it is simply related to the latent heats.
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Entropy change of condensation is the heat of condensation,
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that is the enthalpy of condensation divided by temperature, here the boiling pts.
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Likewise, the entropy of freezing is enthalpy of freezing over melting point.
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For most materials, the entropy change of evaporation is 21 cal per mole K,
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so entropy change of condensation is -21 cal per mole K.
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Entropy change of fusion is about 2 cal per mole K.
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Sometimes different from this value but usually it is in the range of 0.2 to 5.