Use Appendix C to compare the standard entropies at 25^∘ C for the following pairs of substances

Use Appendix C to compare the standard entropies at 25^∘ C...

Use Appendix $\mathrm{C}$ to compare the standard entropies at $25^{\circ} \mathrm{C}$ for the following pairs of substances: (a) $\mathrm{Sc}(s)$ and $\mathrm{Sc}(g)$, $\mathrm{NH}_{3}(g)$ and $\mathrm{NH}_{3}(a q)$ (c) $1 \mathrm{~mol} \mathrm{P}_{4}(g)$ and $2 \mathrm{~mol} \mathrm{P}_{2}(g)$, (d) C(graphite) and C(diamond). In each case explain the difference in the entropy values.

Use Appendix $\mathrm{C}$ to compare the standard entropies at $25^{\circ} \mathrm{C}$ for the following pairs of substances:
(a) $\mathrm{Sc}(s)$ and $\mathrm{Sc}(g)$,
$\mathrm{NH}_{3}(g)$ and $\mathrm{NH}_{3}(a q)$
(c) $1 \mathrm{~mol} \mathrm{P}_{4}(g)$ and $2 \mathrm{~mol} \mathrm{P}_{2}(g)$,
(d) C(graphite) and C(diamond). In each case explain the difference in the entropy values.

Key Concepts

Allotropy and Structural Ordering in Solids

Different allotropes of the same element, such as graphite and diamond, differ in their crystal structures and bonding arrangements. These variations influence the degree of order and vibrational freedom within the solid lattice, leading to differences in entropy even though the chemical composition remains identical.

Solvation Effects

When a substance is dissolved in water, as in an aqueous solution, interactions between the solute and solvent can lead to significant ordering of water molecules around the solute ions or molecules. This ordering usually reduces the system's overall entropy compared to the pure substance in the gas phase, illustrating how solvation can impact entropy values.

Phase Effects on Entropy

The phase of a substance (solid, liquid, gas) dramatically influences its entropy. Gases typically have higher entropy than solids because their molecules or atoms exhibit more translational, rotational, and vibrational degrees of freedom. Thus, comparing a substance in the gas phase to one in the solid phase highlights the influence of physical state on molecular disorder.

Standard Molar Entropy

This concept refers to the absolute entropy of a substance per mole at a standard state (usually 1 atm pressure for gases and pure substances at a specified temperature like 25°C). It serves as a measure of the randomness or disorder inherent in a system and is essential for comparing the thermodynamic properties of different substances.

Molecular Complexity and Quantity Effects

Entropy increases with the number of particles and the complexity of molecular structure. An increased number of particles (or moles) corresponds to more microstates and greater overall randomness. Additionally, more complex molecules, due to their internal motions and structural possibilities, also contribute to higher entropy values.

Transcript

00:01 Let's take a look at the standard entropy of pairs of substances to determine which one has the higher entropy.

00:09 When we take a look at scandium, we have two examples of scandium.

00:12 One is a solid and one is a gas.

00:15 If we go and look up their entropies, we would find that the solid has an entropy of 34 .6 joules per mole kelvin, whereas the gaseous entropy is 174 .7 joules per mole kelvin.

00:40 And so as you can see, the gaseous one has the higher entropy, and that makes sense.

00:45 As a gas, the intermolecular forces are broken.

00:48 There's much more freedom for those molecules to move around.

00:53 When we compare nh3 gas to nh3 aqueous, we would, we can see that the entropy of the gas is 192 .5 joules per mole kelvin.

01:09 And for the aqueous, it's 11 .3 .3 joules per mole kelvin.

01:17 Now, nh3 is a covalent substance.

01:20 It's not going to break apart into ions.

01:23 So we still have, in both cases, both the gas and the aqueous solution, one particle of each.

01:31 As a gas, we have more freedom in that case, higher entropy.

01:38 When we take a look at one mole of p4 versus two moles of p2, you might say, well, we have the same number of atoms of each, but we have different total numbers of particles.

01:48 Two moles is twice the number of particles.

01:51 And when we take a look at the entropy for each, and we have one mole...

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