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Math Problems: Heat and Thermodynamics

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1. You have a 16 oz cup of coffee at 180 degrees F. That is way too hot to drink. So you want to cool the coffee off and decide to add some cold water. You add 2 ounces of cold water at 40 degrees F. How much will the water you added heat up? How much will the coffee that you poured the water into cool down?

2. An air bubble at the bottom of a lake has a volume of 15 cm3. The lake is 40 m deep and has a temperature of 4 ºC at the bottom. The bubble then rises to the surface where the temperature is 23 ºC. What is the volume of the bubble just before it reaches the surface?

3. You are sitting behind a curtain watching meters that measure pressure, volume, and temperature of some kind of heat engine. Pressure, volume, and temperature have reached an equilibrium state. Then someone behind the curtain tells you that they are going to add energy to the system. The energy is added and the equilibrium changes. Can you tell whether they did work on the system, heated the system, or a combination of both? Explain your answer.

4. In a refrigerator, heat is transferred from a colder area (the inside of the refrigerator) to a warmer area (the air outside of the refrigerator). Given what you know about internal energy, explain how this is possible.

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Solutions to math problems involving heat and thermodynamics are outlined in fine detail.

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Multiple choice questions on spontaneous reactions and maximum concentration

Calculate the maximum concentration (in M) of sulfide ions in a solution containing 0.181 M of lead ions. The Ksp for lead sulfide is 3.4 x 10-28.

a. 1.9 x 10-27
b. 9.4 x 10-28
c. 1.5 x 10-26
d. 3.0 x 10-25
e. 3.4 x 10-28

A reaction that is spontaneous ___________.

a. will proceed as written without outside intervention
b. will be very rapid as written
c. will occur very slowly
d. is also spontaneous in the reverse direction
e. has an equilibrium position that lies very far to the left

In a spontaneous process, __________.

a. the path between reactants and products is irreversible
b. the reverse process is also spontaneous
c. forward and reverse processes occur at the same rate
d. the reverse process occurs at a higher rate than the forward process
e. the path between reactants and products is reversible

Which of the following is a reversible process?

a. Melting of ice at 0°C and 1 atm
b.Freezing of water at -10°C and 1 atm
c.Evaporation of water at 25°C and 1 atm
d.Freezing of water at -25°C and 1 atm
e.Melting of ice at 25°C and 1 atm

Given the following table of thermodynamic data, determine the normal boiling point (in °C) of TiCl4.
Substance ΔHf° S°
TiCl4(g) -763.2 kJ/mol 354.9 J/mol-K
TiCl4(l) -804.2 221.9

a. 308.3
b. 41.0
c. 35.3
d. 273.3
e. 133.0

Which equation represents a reaction that is decreasing in entropy as the reaction proceeds?

a. H2O(l) H2O(g)
b. 2C(s) + O2(g) 2CO(g)
c. CaCO3(s) CaO(s) + CO2(g)
d. 2H2(g) + O2(g) 2H2O(l)
e. 2Na(s) + 2H2O(l) 2NaOH(aq) + H2(g)

For which one of the following reactions should the sign of ΔS be negative?

a. C(s) + O2(g) CO2(g)
b. H2O(l) H2O(g)
c. NH3Cl(s) HCl(g) + NH3(g)
d.2NaCl(s) + H2SO3(aq) 2HCl(g) + Na2SO4(s)
e.2SO2(g) + O2(g) 2SO3(g)

Consider a pure, crystalline solid being heated from absolute zero to some very high temperature. Which one of the following processes produces the greatest increase in the entropy of the substance?

a. Heating the liquid
b. Boiling the liquid
c. Heating the solid
d. Heating the gas
e. Melting the solid

Given the following table of thermodynamic data, determine the ΔS° (in J/mol-K) for the reaction:
C2H2(g) + 2 H2(g) C2H6(g).

Substance S°
C2H2(g) 200.8 J/mol-K
C2H4(g) 219.4
C2H6(g) 229.5
H2(g) 130.58

a. -111.98
b. -101.88
c. -232.46
d. +101.88
e. +111.98

Which species below has/have ΔG°f = 0?

a.Both Co(s) and H2(g)
b. HCo(PF3)4(g)
c. Co(s)
d. H2(g)
e. PF3(g)

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