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Chapter 19: Problem 23

The normal boiling point of the element mercury (Hg) is $356.7{ }^{\circ} \mathrm{C},\( and its molar enthalpy of vaporization is \)\Delta H_{\text {vap }}=59.11 \mathrm{~kJ} / \mathrm{mol} .$ (a) When Hg boils at its nor- mal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when \(2.00 \mathrm{~mol}\) of \(\mathrm{Hg}\) is vaporized at \(356.7^{\circ} \mathrm{C}\).

Short Answer

Expert verified
(a) When Hg boils at its normal boiling point, its entropy increases due to the higher amount of disorder in the vapor state compared to the liquid state. (b) The value of ΔS when 2.00 mol of Hg is vaporized at 356.7°C is 0.18776 kJ/K.

Step by step solution

01

Determine if the entropy increases or decreases when Hg boils at its normal boiling point.

We know that when a substance boils, it changes from liquid to vapor. Since the vapor state has a higher amount of disorder compared to the liquid state, the entropy increases during boiling.
02

Convert the temperature from Celsius to Kelvin.

Given that the normal boiling point of mercury is 356.7°C, we need to convert it to Kelvin before we can use it in our calculations: T = 356.7 + 273.15 = 629.85 K
03

Calculate the change in entropy ΔS.

Using the relationship between enthalpy of vaporization, temperature, and entropy changes: ΔH_vap = TΔS We are given ΔH_vap = 59.11 kJ/mol and have calculated T = 629.85 K. Now we can solve for ΔS: ΔS = ΔH_vap / T = 59.11 kJ/mol / 629.85 K = 0.09388 kJ/(mol·K)
04

Calculate the change in entropy for 2.00 mol of Hg.

Now that we have the change in entropy per mole, we can calculate the total entropy change for 2.00 mol of Hg: ΔS_total = ΔS * n = 0.09388 kJ/(mol·K) * 2.00 mol = 0.18776 kJ/K So, the value of ΔS when 2.00 mol of Hg is vaporized at 356.7°C is 0.18776 kJ/K.

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Most popular questions from this chapter

(a) Is the standard free-energy change, \(\Delta G^{\circ}\), always larger than \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?\) (c) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily has a low activation barrier?

The reaction $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$ is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for \(\Delta S^{\circ}\). Did your classmate make a mistake in the calculation? Explain.

For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) \(1 \mathrm{~mol}\) of \(\mathrm{O}_{2}(g)\) at \(300^{\circ} \mathrm{C}, 1.013 \mathrm{kPa},\) or \(1 \mathrm{~mol}\) of \(\mathrm{O}_{3}(g)\) at \(300^{\circ} \mathrm{C}, 1.013 \mathrm{kPa} ;\) (b) \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at $100^{\circ} \mathrm{C}, 101.3 \mathrm{kPa}\(, or \)1 \mathrm{~mol}\( of \)\mathrm{H}_{2} \mathrm{O}(l)$ at $100^{\circ} \mathrm{C}, 101.3 \mathrm{kPa} ;(\mathbf{c}) 0.5 \mathrm{~mol}\( of \)\mathrm{N}_{2}(g)\( at \)298 \mathrm{~K}, 20-\mathrm{L}$. vol- ume, or \(0.5 \mathrm{~mol} \mathrm{CH}_{4}(g)\) at $298 \mathrm{~K}, 20-\mathrm{L}$ volume; (d) \(100 \mathrm{~g}\) \(\mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or $100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\( at \)30^{\circ} \mathrm{C}$

Which of the following processes are spontaneous and which are nonspontaneous: (a) mixing of water and ethanol, \((\mathbf{b})\) dissolution of sugar in a cup of hot coffee, (c) formation of oxygen atoms from \(\mathrm{O}_{2}\) molecules at \(\mathrm{STP}\), (d) rusting of iron, (e) formation of glucose from \(\mathrm{CO}_{2}\) and $\mathrm{H}_{2} \mathrm{O}\( at \)\mathrm{STP} ?$

The potassium-ion concentration in blood plasma is about $5.0 \times 10^{-3} \mathrm{M}$, whereas the concentration in muscle-cell fluid is much greater \((0.15 \mathrm{M})\). The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to \(\mathrm{K}^{+}\). (a) What is \(\Delta G\) for the transfer of \(1 \mathrm{~mol}\) of \(\mathrm{K}^{+}\) from blood plasma to the cellular fluid at body temperature \(37^{\circ} \mathrm{C} ?\) (b) What is the minimum amount of work that must be used to transfer this \(\mathrm{K}^{+} ?\)
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