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Chapter 17: Problem 54

Two crystalline forms of white phosphorus are known. Both forms contain \(\mathrm{P}_{4}\) molecules, but the molecules are packed together in different ways. The \(\alpha\) form is always obtained when the liquid freezes. However, below \(-76.9^{\circ} \mathrm{C},\) the \(\alpha\) form spontaneously converts to the \(\beta\) form: $$\mathrm{P}_{4}(s, \alpha) \longrightarrow \mathrm{P}_{4}(s, \beta)$$ a. Predict the signs of \(\Delta H\) and \(\Delta S\) for this process. b. Predict which form of phosphorus has the more ordered crystalline structure (has the smaller positional probability).

Short Answer

Expert verified
a. Since the α form spontaneously converts to the β form and releases energy, the process is exothermic, making ΔH negative. As spontaneous processes increase the total entropy, ΔS is positive. b. The α form has a more ordered crystalline structure as it has a smaller positional probability compared to the β form.

Step by step solution

01

Determine whether the process is exothermic or endothermic

The α form spontaneously converts to the β form. This suggests that the β form is more stable than the α form and the transformation process releases energy. Therefore, the process is exothermic, and we can expect the enthalpy change, ΔH, to be negative.
02

Determine whether the process increases or decreases entropy

Since the transformation process happens spontaneously, the entropy change, ΔS, should be positive. This is because spontaneous processes tend to increase the total entropy of the system and its surroundings. #b. Predicting the more ordered crystalline structure#
03

Analyze the change in positional probability

Because the β form is more stable and the system's entropy increases when it transforms from the α form to the β form, we can assume that the positional probability (how the molecules are randomly organized) is higher in the β form than in the α form.
04

Determine the more ordered crystalline structure

Since the positional probability of the β form is higher than the α form, the α form must have a more ordered crystalline structure. Therefore, the form of phosphorus with the smaller positional probability (more ordered) is the α form.

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Most popular questions from this chapter

Consider the reaction $$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)$$ a. Use \(\Delta G_{f}^{\circ}\) values in Appendix 4 to calculate $\Delta G^{\circ}$ for this reaction. b. Is this reaction spontaneous under standard conditions at 298 $\mathrm{K} ?$ c. The value of \(\Delta H^{\circ}\) for this reaction is 100 . kJ. At what temperatures is this reaction spontaneous at standard conditions? Assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

A reaction has \(K=1.9 \times 10^{-14}\) at \(25^{\circ} \mathrm{C}\) and $K=9.1 \times 10^{3}$ at \(227^{\circ} \mathrm{C}\) . Predict the signs for $\Delta G^{\circ}, \Delta H^{\circ},\( and \)\Delta S^{\circ}\( for this reaction at \)25^{\circ} \mathrm{C}\( . Assume \)\Delta H^{\circ}\( and \)\Delta S^{\circ}$ do not depend on temperature.

At 1 atm, liquid water is heated above \(100^{\circ} \mathrm{C}\) . For this process, which of the following choices (i-iv) is correct for $\Delta S_{\text { surr }} ? \Delta S ?\( \)\Delta S_{\text { univ }} ?$ Explain each answer. i. greater than zero ii. less than zero iii. equal to zero iv. cannot be determined

The synthesis of glucose directly from \(\mathrm{CO}_{2}\) and $\mathrm{H}_{2} \mathrm{O}$ and the synthesis of proteins directly from amino acids are both nonspontaneous processes under standard conditions. Yet it is necessary for these to occur for life to exist. In light of the second law of thermodynamics, how can life exist?

For mercury, the enthalpy of vaporization is 58.51 kJ/mol and the entropy of vaporization is 92.92 J/K ? mol. What is the normal boiling point of mercury?
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