6.2 Single-Component Systems
6.1.Determine the number of components in the following
systems: (a)an iceberg of pure H 2 O; (b)bronze, an alloy of
copper and tin; (c)Wood’s metal, an alloy of bismuth, lead,
tin, and cadmium (it is used in sprinkler systems for fire con-
trol); (d)vodka, a mixture of water and ethyl alcohol; (e)a
mixture of sand and sugar.
6.2.Coffee is an extract of a roasted bean, made with hot wa-
ter. It has many components. Some companies market instant
coffee, which is made by freeze-drying brewed coffee. Explain
from a components perspective why instant coffee rarely has
the quality of freshly brewed coffee.
6.3.How many different single-component systems can be
made from metallic iron and chlorine gas? Assume that the
components are chemically stable.
6.4.Explain how solid and liquid phases of a substance can
exist in the same closed, adiabatic system at equilibrium. Under
what conditions can solid and gas phases exist at equilibrium?
6.5.Liquid water at room temperature is placed in a syringe,
which is then sealed. The plunger of the syringe is drawn back,
and at some point bubbles of H 2 O vapor are formed. Explain
why we can state that the water is boiling.
6.6.If a system is not adiabatic, then heat leaves or enters the
system. What is the immediate response of a system (a)in liq-
uid-gas equilibrium if heat is removed? (b)in solid-gas equi-
librium if heat is added? (c)in liquid-solid equilibrium if heat
is removed? (d)composed entirely of solid phase if heat is
removed?
6.7.How many values of the normal boiling point does any
pure substance have? Explain your answer.
6.8.Write equation 6.2 in a different, yet algebraically equiv-
alent way. Explain why this is an equivalent expression.
6.3 Phase Transitions
6.9.Identify and explain the sign on transHin equation 6.5
if it is used for (a)a solid-to-gas phase transition (sublima-
tion), (b)a gas-to-liquid phase transition (condensation).
6.10.Calculate the amount of heat necessary to change
100.0 g of ice at 15.0°C to steam at 110°C. You will need
the values of the heat capacity for ice, water, and steam, and
fusHand vapHfor H 2 O from Tables 2.1 and 2.3. Is this process
exothermic or endothermic?
6.11.Citrus farmers sometimes spray water on the fruit trees
when a frost is expected. Use equations 6.4 to explain why.
6.12.What is the numerical change in chemical potential of
1 mole of carbon dioxide, CO 2 , as it changes temperature?
Assume that we are considering the infinitesimal change in
chemical potential as the temperature changes infinitesimally
starting at 25°C. Hint:See equation 4.40.
6.13.What is Sfor the isothermal conversion of liquid ben-
zene, C 6 H 6 , to gaseous benzene at its boiling point of 80.1°C?
Is it consistent with Trouton’s rule?
6.14.Estimate the melting point of nickel, Ni, if its fusHis
17.61 kJ/mol and its fusSis 10.21 J/molK. (Compare this to
a measured melting point of 1455°C.)
6.15.Estimate the boiling point of platinum, Pt, if its vapH
is 510.4 kJ/mol and its vapS124.7 J/molK. (Compare this
to a measured melting point of 3827 100°C.)
6.16.In ice skating, the blade of the skate is thought to ex-
ert enough pressure to melt ice, so that the skater glides
smoothly on a thin film of water. What thermodynamic prin-
ciple is involved here? Can you perform a rough calculation to
determine whether this is indeed the active mechanism in ice
skating? Would skating work if it were performed on other
solids and this were the mechanism involved?6.4 & 6.5 The Clapeyron and Clausius-
Clapeyron Equations
6.17.The integration of equation 6.11 to get 6.12 uses what
assumption?
6.18.Does the expression dphase1dphase2in the deriva-
tion of the Clapeyron equation imply that only a closed sys-
tem is being considered? Why or why not?
6.19.Sulfur, in its cyclic molecular form having the formula
S 8 , is an unusual element in that the solid form has two easily
accessible solid phases. The rhombic crystal solid is stable
at temperatures lower than 95.5°C, and has a density of
2.07 g/cm^3. The monoclinic phase, stable at temperatures
higher than 95.5°C and less than the melting point of sulfur,
has a density of 1.96 g/cm^3. Use equation 6.10 to estimate
the pressure necessary to make rhombic sulfur the stable phase
at 100°C if the entropy of transition is 1.00 J/molK. Assume
that transSdoes not change with changing conditions.
6.20.Refer to exercise 6.19. How applicable is transSat stan-
dardpressure to the extreme condition of pressure necessary
for the stated phase transition? How accurate do you think
your answer to exercise 6.19 is?
6.21.State whether or not the Clausius-Clapeyron equation
is strictly applicable to the following phase transitions.
(a)Sublimation of ice in your freezer
(b)Condensation of steam into water
(c)Freezing of cyclohexane at 6.5°C
(d)Conversion of ice VI to ice VII (see Figure 6.6)
(e)Conversion of diatomic oxygen, O 2 (g), to triatomic
ozone, O 3 (g)
(f)Formation of diamonds under pressure
(g)Formation of metallic solid hydrogen, H 2 , from liquid
hydrogen. (The transformation to metallic hydrogen occurs
under megabars of pressure and may be part of gas giant
planets like Jupiter and Saturn.)
(h)Evaporation of mercury liquid, Hg (), from a broken ther-
mometer.Exercises for Chapter 6 163EXERCISES FOR CHAPTER 6