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Chapter 5: 5.3 (page 155)

Use the data at the back of this book to verify the values of 鈭�Hand 鈭�G quoted above for the lead-acid reaction 5.13.

Short Answer

Expert verified

The value of Gibbs free energy = -315.72 kJ.

Step by step solution

01

Given Information

T= 298 K and P=1 bar.

The information from the table

02

Explanation

Gibbs energy is given by

G= H-TS

where G= Gibbs energy, H= Enthalpy, T =temp and S =entropy.

Assume there is infinitesimal change in Gibbs energy , then

鈭�G=鈭�H-T鈭�S.............(1)

Now write equation for change in enthalpy for the given reaction

螖H=2螖HPbSO4+2螖HH2O-螖HPb-螖HPbO2+4螖HH+-2螖HSO42-

Now substitute the values from the given table, we get

螖H=2(-920.0kJ)+2(-285.83kJ)-0-(-277.4kJ)-4(0)-2(-909.27kJ)=-315.72kJ

Similarly write equation for change in Gibbs energy for the given reaction

螖G=(2螖GPbSO4+2螖GH2O-螖GPb-螖GPbO2+4螖GH+-2螖GSO42-)

Put the values from the table, we get

鈭�G=2(-813.0kJ)+2(-237.13kJ)-0-(-217.33kJ)-4(0)-2(-744.53kJ)

= -315.72 kJ.

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Most popular questions from this chapter

Ordinarily, the partial pressure of water vapour in the air is less than the equilibrium vapour pressure at the ambient temperature; this is why a cup of water will spontaneously evaporate. The ratio of the partial pressure of water vapour to the equilibrium vapour pressure is called the relative humidity. When the relative humidity is 100%, so that water vapour in the atmosphere would be in diffusive equilibrium with a cup of liquid water, we say that the air is saturated. The dew point is the temperature at which the relative humidity would be 100%, for a given partial pressure of water vapour.

(a) Use the vapour pressure equation (Problem 5.35) and the data in Figure 5.11 to plot a graph of the vapour pressure of water from 0掳C to 40掳C. Notice that the vapour pressure approximately doubles for every 10掳 increase in temperature.

(b) Suppose that the temperature on a certain summer day is 30掳 C. What is the dew point if the relative humidity is 90%? What if the relative humidity is 40%?

Problem 5.58. In this problem you will model the mixing energy of a mixture in a relatively simple way, in order to relate the existence of a solubility gap to molecular behaviour. Consider a mixture of A and B molecules that is ideal in every way but one: The potential energy due to the interaction of neighbouring molecules depends upon whether the molecules are like or unlike. Let n be the average number of nearest neighbours of any given molecule (perhaps 6 or 8 or 10). Let n be the average potential energy associated with the interaction between neighbouring molecules that are the same (4-A or B-B), and let uAB be the potential energy associated with the interaction of a neighbouring unlike pair (4-B). There are no interactions beyond the range of the nearest neighbours; the values of 渭oand渭ABare independent of the amounts of A and B; and the entropy of mixing is the same as for an ideal solution.

(a) Show that when the system is unmixed, the total potential energy due to neighbor-neighbor interactions is 12Nnu0. (Hint: Be sure to count each neighbouring pair only once.)

(b) Find a formula for the total potential energy when the system is mixed, in terms of x, the fraction of B.

(c) Subtract the results of parts (a) and (b) to obtain the change in energy upon mixing. Simplify the result as much as possible; you should obtain an expression proportional to x(1-x). Sketch this function vs. x, for both possible signs of uAB-u0.

(d) Show that the slope of the mixing energy function is finite at both end- points, unlike the slope of the mixing entropy function.

(e) For the case uAB>u0, plot a graph of the Gibbs free energy of this system

vs. x at several temperatures. Discuss the implications.

(f) Find an expression for the maximum temperature at which this system has

a solubility gap.

(g) Make a very rough estimate of uAB-u0for a liquid mixture that has a

solubility gap below 100掳C.

(h) Use a computer to plot the phase diagram (T vs. x) for this system.

Is heat capacity (C) extensive or intensive? What about specific heat (c) ? Explain briefly.

Assume that the air you exhale is at 35掳C, with a relative humidity of 90%. This air immediately mixes with environmental air at 5掳C and unknown relative humidity; during the mixing, a variety of intermediate temperatures and water vapour percentages temporarily occur. If you are able to "see your breath" due to the formation of cloud droplets during this mixing, what can you conclude about the relative humidity of your environment? (Refer to the vapour pressure graph drawn in Problem 5.42.)

Sketch a qualitatively accurate graph of G vs. T for a pure substance as it changes from solid to liquid to gas at fixed pressure. Think carefully about the slope of the graph. Mark the points of the phase transformations and discuss the features of the graph briefly.
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