Use data from Appendix IIB to calculate ΔSrxn^∘ for each of the reactions. In each case, try to

Use data from Appendix IIB to calculate ΔSrxn^∘ for each of...

Use data from Appendix IIB to calculate $\Delta S_{\mathrm{rxn}}^{\circ}$ for each of the reactions. In each case, try to rationalize the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$ \begin{equation}\begin{array}{l}{\text { a. } 3 \mathrm\ {NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm\ {HNO}_{3}(a q)+\mathrm{NO}(g)} \\ {\text { b. } \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s)+3 \mathrm\ {CO}_{2}(g)} \\ {\text { c. } \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)} \\ {\text { d. } \mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm\ {H}_{2} \mathrm{O}(g)}\end{array}\end{equation}

Use data from Appendix IIB to calculate $\Delta S_{\mathrm{rxn}}^{\circ}$ for each of the reactions. In each case, try to rationalize the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$
\begin{equation}\begin{array}{l}{\text { a. } 3 \mathrm\ {NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm\ {HNO}_{3}(a q)+\mathrm{NO}(g)} \\ {\text { b. } \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s)+3 \mathrm\ {CO}_{2}(g)} \\ {\text { c. } \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)} \\ {\text { d. } \mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm\ {H}_{2} \mathrm{O}(g)}\end{array}\end{equation}

Key Concepts

Standard Entropy

Standard entropy is the entropy of a substance measured under standard conditions (usually 1 atm and 298 K). It is an intrinsic property that reflects the degree of randomness or disorder in a system. In thermodynamic calculations, standard entropy values are tabulated for various chemical species and are used as the basis for computing changes in entropy during a chemical reaction.

Standard Reaction Entropy

The standard reaction entropy (?S°_rxn) is the net change in entropy when a reaction proceeds under standard conditions. It is calculated by taking the difference between the sum of the standard entropy values of the products and that of the reactants, each multiplied by their respective stoichiometric coefficients. This concept is essential for predicting whether a reaction will lead to an increase or decrease in system disorder.

Phase Effects on Entropy

The physical state of a substance (solid, liquid, or gas) significantly influences its entropy. Gases generally have higher entropy due to the greater freedom of movement and higher disorder, compared to liquids and solids. Understanding these differences is crucial when calculating the overall entropy change in a reaction, as the conversion between phases can be a major factor in determining the sign of ?S°_rxn.

Stoichiometric Considerations

In calculating changes in reaction entropy, the stoichiometry of the reaction dictates the weighting of each substance's entropy contribution. This means that even small differences in stoichiometry, especially involving gaseous reactants or products, can greatly affect the overall entropy change. Rationalizing the sign of ?S°_rxn often involves examining whether the reaction produces more disordered (typically gaseous) species from less disordered ones, or vice versa.

Transcript

00:01 So this question is wanting us to calculate delta s of the reaction for each of these reactions, and then we'll try to rationalize why that entropy is the way it is, just logically.

00:15 And so to calculate delta s not, you can do s not of products minus s not of reactants.

00:31 And so you want to sum those up from each side, and also you want to include the number of moles for each of your molecules.

00:44 So, for example, for a, you have 3, no2, gas plus h2o liquid, going to 2, 203, aqueous, plus nogas.

01:12 And so what you're going to do is you're going to look up these tables.

01:16 These values from your appendix in your textbook.

01:22 And i've already looked at those values, so now we just plug in.

01:26 So delta s not is equal to 2 times 146 plus 210 .8.

01:42 So that's your products, minus your actants.

01:48 So you'll do 3 times 240 to count for your moles, plus 70.

01:59 And then when you finish your math, you'll get the answer to be minus 2, a 7 .5 joules per kelvin.

02:11 And so let's think about why this would be a negative change in entropy.

02:19 And so if you look at this equation, you're going from four, three moles of a gas to only one mole of a gas.

02:27 And so the gas is what is the most disorder, has the most entropy in this case.

02:34 So you're going from more of a molecule that has a lot of entropy to less of a molecule that has a similar amount of entropy.

02:43 So your entropy will decrease.

02:48 So do the same thing for b.

02:51 We have cr203 as a solid plus carbon monoxide, going to cr as a solid plus co2 as a gas.

03:12 So we'll look up our values in our textbook and then we'll get the delta s not equals so this is 23 .8 for any confusion minus your reactants which is 81 .2 plus 3 times 197 .7.

03:51 So always make sure you're accounting for your mold in your equation.

03:55 And so this will equal 16 .8 joules per kelvin.

04:03 And so this is a positive increase in entropy.

04:06 And the way you can rationalize that is you're going from three moles of a gas to three moles of a gas.

04:12 But instead of c carbon monoxide, you're having an extra oxygen to this gas molecule.

04:17 So you're giving it more ways to distribute its energy...

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