(a) What is the entropy of a perfect crystal at 0 K ? (b) Does entropy increase or decrease as t

step 1 Okay, to start with question A. So at zero Kelvin, a perfect crystal will have zero entropy. Thi

(a) What is the entropy of a perfect crystal at 0 K ? (b)...

(a) What is the entropy of a perfect crystal at 0 $\mathrm{K}$ ? (b) Does entropy increase or decrease as the temperature rises? (c) Why is $\Delta H_{\mathrm{f}}^{\circ}=0$ but $S^{\circ}>0$ for an element? (d) Why does Appendix $\mathrm{B}$ list $\Delta H_{\mathrm{f}}^{\circ}$ values but not $\Delta S_{\mathrm{f}}^{\circ}$ values?

(a) What is the entropy of a perfect crystal at 0 $\mathrm{K}$ ?
(b) Does entropy increase or decrease as the temperature rises?
(c) Why is $\Delta H_{\mathrm{f}}^{\circ}=0$ but $S^{\circ}>0$ for an element?
(d) Why does Appendix $\mathrm{B}$ list $\Delta H_{\mathrm{f}}^{\circ}$ values but not $\Delta S_{\mathrm{f}}^{\circ}$ values?

Key Concepts

Standard State Conventions in Thermodynamics

In thermodynamics, the standard enthalpy of formation (?H°f) of an element in its reference state is defined as zero for convenience, serving as a baseline for comparing reactions. However, the standard entropy (S°) of an element is not zero at temperatures above absolute zero because thermal motion introduces disorder, even in a pure element.

Tabulation of Thermodynamic Data

Standard enthalpies of formation are commonly listed in tables because they form the basis for calculating reaction energetics and are defined relative to specified reference states. In contrast, standard entropies are recorded as absolute values rather than as formation values, so tables typically do not include ?S°f values.

Third Law of Thermodynamics

This law states that the entropy of a perfect crystal at absolute zero (0 K) is zero because there is only one microstate available. It sets an absolute reference point for the determination of entropy values for other substances.

Entropy and Temperature Dependence

Entropy is a measure of the disorder or randomness in a system. As temperature rises, the thermal energy increases, which in turn increases the number of accessible microstates, leading to an increase in entropy.

Transcript

00:02 Okay, to start with question a.

00:06 So at zero kelvin, a perfect crystal will have zero entropy.

00:17 This is because entropy is a measurement of disorder.

00:20 So let's say right here, this is our crystal.

00:24 As you can see, pretend these are all little atoms all connected together.

00:29 At absolute zero, a perfect crystal, there will be no movement.

00:32 The atoms will be completely stationary, so there will be no disorder, and that's why we can say that entropy will be equal to s's for entropy.

00:46 It will be equal to zero.

00:50 And then moving on to b, so a good way to think about this is to kind of relate it back to a.

00:57 So again, entropy is equal to the amount of disorder in a system.

01:01 So the more disorder that will be the higher the entropy.

01:04 So if a perfect crystal at zero kelvin has no entropy that is actually stated in the third law of thermodynamics, we can say when we increase the temperature, we're going to also increase the kinetic energy of all of the molecules in the substance.

01:21 So let's say when we increase temp, we increase the kinetic energy of a substance or a molecule.

01:35 And this will cause an increase in disorder.

01:39 So let me say, oops, there we go.

01:44 Increases disorder, which increases entropy.

01:53 All right, so moving on to c.

01:55 So first, let's just define the delta h formation.

01:59 So the delta h of formation is the energy needed to create a compound from its constituent elements...