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Chapter 19: Problem 49

The standard entropies at \(298 \mathrm{~K}\) for certain group 14 elements are: \(\mathrm{C}(s,\) diamond $)=2.43 \mathrm{~J} / \mathrm{mol}-\mathrm{K}, \mathrm{Si}(s)=18.81 \mathrm{~J} /$ $\mathrm{mol}-\mathrm{K}, \mathrm{Ge}(s)=31.09 \mathrm{~J} / \mathrm{mol}-\mathrm{K}, \quad\( a n d \)\quad \mathrm{Sn}(s)=51.818 \mathrm{~J} /$ mol-K. All but \(S\) n have the same (diamond) structure. How do you account for the trend in the \(S^{\circ}\) values?

Short Answer

Expert verified
The trend in the standard entropy values for the group 14 elements at 298 K can be attributed to the increase in atomic mass as we move down the group. This increasing atomic mass increases the number of vibrational modes, which in turn increases the entropy values of the elements.

Step by step solution

01

Recall the meaning of entropy

Entropy is a thermodynamic property that describes the measure of disorder in a system. In this case, it refers to the disorder of the elements in their solid-state lattice structures. A higher entropy value indicates a more disordered state.
02

Identify a possible factor

Since all the given elements have the same diamond structure, we must identify some other factors which can lead to the trend observed in entropy values. One possible factor for this trend is the increasing atomic mass of the elements in question.
03

Connect atomic mass to the entropy trend

As we go down the group 14 elements from carbon to silicon to germanium to tin, there is an increase in atomic mass. This increase in atomic mass causes an increase in the number of vibrational modes available in each element. A higher number of vibrational modes contribute to a higher entropy value.
04

Consider the fact that Sn does not have a diamond structure

Although Sn does not have a diamond structure, its increased entropy value can still be explained by the fact that it has an even higher atomic mass compared to the other elements. This increased atomic mass effectively contributes to the higher entropy value observed for Sn.
05

Conclusion

The trend in the standard entropy values for the group 14 elements at 298 K can be attributed to the increase in atomic mass as we move down the group. This increasing atomic mass increases the number of vibrational modes, which in turn increases the entropy values of the elements.

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Most popular questions from this chapter

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(C\) to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?\( (c) Calculate \)\Delta G\( at \)1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in \(H,\) we can know absolute values of $S .(\mathbf{b})\( If you heat a gas such as \)\mathrm{CO}_{2}$, you will increase its degrees of translational, rotational and vibrational motions. (c) \(\mathrm{CO}_{2}(g)\) and \(\mathrm{Ar}(g)\) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0,\) and \(w=0 .\) (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. \((\mathbf{c})\) What is the "driving force" for the expansion of the gas: enthalpy or entropy?

Predict the sign of \(\Delta S_{s y s}\) for each of the following processes: (a) Gaseous \(\mathrm{H}_{2}\) reacts with liquid palmitoleic acid \(\left(\mathrm{C}_{16} \mathrm{H}_{30} \mathrm{O}_{2},\right.\) unsaturated fatty acid) to form liquid palmitic acid $\left(\mathrm{C}_{16} \mathrm{H}_{32} \mathrm{O}_{2}\right.$ saturated fatty acid). (b) Liquid palmitic acid solidifies at \(1^{\circ} \mathrm{C}\) to solid palmitic acid. (c) Silver chloride precipitates upon mixing \(\mathrm{AgNO}_{3}(a q)\) and \(\mathrm{NaCl}(a q) .\) (d) Gaseous \(\mathrm{H}_{2}\) dissociates in an electric arc to form gaseous H atoms (used in atomic hydrogen welding).

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.
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