Using Appendix C, compare the standard entropies at 25^∘ C for the following pairs of substances

Using Appendix C, compare the standard entropies at 25^∘ C...

Using Appendix C, compare the standard entropies at $25^{\circ} \mathrm{C}$ for the following pairs of substances: (a) $\mathrm{CuO}(s)$ and $\mathrm{Cu}_{2} \mathrm{O}(s)$ (b) $1 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{4}(g)$ and $2 \mathrm{~mol} \mathrm{NO}_{2}(g)$, (c) $\mathrm{SiO}_{2}(s)$ and $\mathrm{CO}_{2}(g)$ (d) $\mathrm{CO}(g)$ and $\mathrm{CO}_{2}(g)$. For each pair, explain the difference in the entropy values.

Using Appendix C, compare the standard entropies at $25^{\circ} \mathrm{C}$ for the following pairs of substances:
(a) $\mathrm{CuO}(s)$ and $\mathrm{Cu}_{2} \mathrm{O}(s)$
(b) $1 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{4}(g)$ and $2 \mathrm{~mol} \mathrm{NO}_{2}(g)$,
(c) $\mathrm{SiO}_{2}(s)$ and $\mathrm{CO}_{2}(g)$
(d) $\mathrm{CO}(g)$ and $\mathrm{CO}_{2}(g)$. For each pair, explain the difference in the entropy values.

Key Concepts

Standard Entropy

Standard entropy refers to the measure of randomness or disorder in a substance under standard conditions. It is typically reported per mole and reflects the absolute number of microstates available to a substance at a given temperature and pressure, thereby providing insight into how energy is distributed among its particles.

Phase of Matter and Entropy

A substance's physical state (solid, liquid, or gas) greatly influences its entropy. Gases generally have much higher entropy than solids because the particles in a gas move more freely and occupy a larger volume, leading to a greater number of accessible microstates. Thus, when comparing substances in different phases, the state of matter is a primary factor in determining their relative entropies.

Molecular Complexity and Degrees of Freedom

The complexity of a molecule, including the number of atoms and its molecular structure, affects its entropy through the available degrees of freedom—translational, rotational, and vibrational. More complex or less symmetrical molecules can rotate and vibrate in a larger number of ways, leading to a higher entropy. Additionally, structural ordering in solids (such as crystalline arrangements) can restrict these motions and result in lower entropy values.

Quantity of Moles and Entropy

When comparing systems with different numbers of moles of gaseous substances, the total entropy is also influenced by the number of particles present. More moles of a gas offer more particles to contribute to the overall disorder, which typically results in a higher total entropy despite similar molecular compositions.

Transcript

00:01 Let's take a look at which of the two in these examples has the higher standard entropy.

00:08 In the first example, we have c -u -o as a solid versus c -u -2 -o as a solid.

00:16 Now, they're both solids, and as such, they're not going to be moving from place to place.

00:22 They will not have translational motion.

00:26 The atoms in the molecule are locked in place as a solid, so that they're not going to be moving from place to place.

00:31 There isn't going to be rotational motion.

00:34 So vibrational motion is going to be the only type that's going to account for entropy here.

00:40 And that vibrational motion is within bonds.

00:43 And so there are more bonds with cu2o than there is with cuo.

00:49 So we should anticipate that the cu2o should have the higher entropy.

00:54 When we go and take a look at what the values for the entropy are for each of these substances.

01:00 For cuo, it's 42 .59 joules per mole kelvin.

01:08 And for cu2o, it's 92 .36 joules per mole kelvin.

01:15 So those values confirm our explanation.

01:21 When we take a look at the next example, we have one mole of n204 versus two moles of n02.

01:27 The same number of atoms overall, but a different number of particles.

01:34 Remember, moles deals with number of particles.

01:36 And so two moles has twice the amount of particles...

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