8.1: Heating Curves and Phase Changes (Problems)

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PROBLEM \(\PageIndex{1}\)

From the phase diagram for water, determine the state of water at:

35 °C and 85 kPa
−15 °C and 40 kPa
−15 °C and 0.1 kPa
75 °C and 3 kPa
40 °C and 0.1 kPa
60 °C and 50 kPa

Answer a: Liquid

Answer b: solid

Answer c: solid

Answer d: gas

Answer e: gas

Answer f: liquid

PROBLEM \(\PageIndex{2}\)

Evaporation of sweat requires energy and thus take excess heat away from the body. Some of the water that you drink may eventually be converted into sweat and evaporate. If you drink a 20-ounce bottle of water that had been in the refrigerator at 3.8 °C, how much heat is needed to convert all of that water into sweat and then to vapor?? (Note: Your body temperature is 36.6 °C. For the purpose of solving this problem, assume that the thermal properties of sweat are the same as for water.)

Answer

20 ounces water= 567 g \( \dfrac{567 g}{18.0 g/mole} \) = 31.5 moles

Heating 567 g from 3.8 °C to 100 °C q₁= m Cp \( \Delta \)T = 567g x 4.18 J/g-°C x 96.2°C = 228 kJ

Vaporizing step q₂= n \( \Delta H_vap \) = 31.5 moles x 30.67 kJ/mole =1281 kJ

Cooling the vapor from 100 °C to 38.6 °C q₃= m Cp \( \Delta \)T =567g x 1.84 x (-61.4) = -64 kJ

q_Total= q₁+ q₂+ q₃ = 228kJ + 1281kJ -64kJ = 1445 kJ

PROBLEM \(\PageIndex{3}\)

How much heat is required to convert 422 g of liquid H₂O at 23.5 °C into steam at 150 °C?

Answer: 1130 kJ
Click here to see a video of the solution

PROBLEM \(\PageIndex{4}\)

Titanium tetrachloride, TiCl₄, has a melting point of −23.2 °C and has a ΔH_fusion = 9.37 kJ/mol.

How much energy is required to melt 263.1 g TiCl₄?
For TiCl₄, which will likely have the larger magnitude: ΔH_fusion or ΔH_vaporization? Explain your reasoning.

Answer a: 13.0 kJ

Answer b: It is likely that the heat of vaporization will have a larger magnitude since in the case of vaporization the intermolecular interactions have to be completely overcome, while melting weakens or destroys only some of them.

PROBLEM \(\PageIndex{5}\)

What phase changes will take place when water is subjected to varying pressure at a constant temperature of 0.005 °C? At 40 °C? At −40 °C?

Answer

At 0.005 °C vapor to solid to liquid. The triple point is at +0.01 °C and the freezing point is ever so slightly lower at 0.00 °C. So if one raises the pressure at a constant 0.005 °C one passes just to the left of the triple point and the vapor will first solidify at 0.612 KPa and then the solid will melt and become a liquid between the 0.00 °C melting point and 0.612 kPa

At 40 °C vapor to liquid.

At - 40 °C vapor to solid

PROBLEM \(\PageIndex{6}\)

From the phase diagram for carbon dioxide, determine the state of CO₂ at:

20 °C and 1000 kPa
10 °C and 2000 kPa
10 °C and 100 kPa
−40 °C and 500 kPa
−80 °C and 1500 kPa
−80 °C and 10 kPa

Answer a: liquid

Answer b: liquid

Answer c: liquid

Answer d: liquid

Answer e: solid

Answer f: solid

PROBLEM \(\PageIndex{7}\)

Determine the phase changes that carbon dioxide undergoes as the pressure changes if the temperature is held at −50 °C? If the temperature is held at −40 °C? At 20 °C?

Answer

−50 °C: gas to liquid to solid

−40 °C: gas to liquid to solid

20 °C: gas to liquid to solid

PROBLEM \(\PageIndex{8}\)

Dry ice, CO₂(s), does not melt at atmospheric pressure. It sublimes at a temperature of −78 °C. What is the lowest pressure at which CO₂(s) will melt to give CO₂(l)? At approximately what temperature will this occur?

Answer: Dry ice, CO₂(s), will melt to give CO₂(l) at 5.11 atm at −56.6 °C, the triple point of carbon dioxide.

PROBLEM \(\PageIndex{9}\)

Elemental carbon has one gas phase, one liquid phase, and three different solid phases, as shown in the phase diagram:

Screen Shot 2019-01-02 at 1.13.44 PM.png

On the phase diagram, label the gas and liquid regions.
Graphite is the most stable phase of carbon at normal conditions. On the phase diagram, label the graphite phase.
If graphite at normal conditions is heated to 2500 K while the pressure is increased to 10¹⁰ Pa, it is converted into diamond. Label the diamond phase.
Circle each triple point on the phase diagram.
In what phase does carbon exist at 5000 K and 10⁸ Pa?
If the temperature of a sample of carbon increases from 3000 K to 5000 K at a constant pressure of 10⁶ Pa, which phase transition occurs, if any?

Answer a

Answer b

Answer c

Answer d

Answer e: liquid

Answer f: sublimation

Contributors and Attributions

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).
Adelaide Clark, Oregon Institute of Technology

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