#1. List two of the defining properties for each common state of matter.
#2. Changes in energy can cause changes in state. What does the energy correspond to?
#3. For what processes is the `DeltaH_"phase change"` positive? For what processes is it negative?
#4. Define the molality of a solution. What can you compare molality to?
#5. For what conditions is it appropriate to model a real gas as an ideal gas?
#6. In two lines or less, summarize the postulates of Kinetic Molecular theory.
#7. What does the energy of a gas depend on?
#8. FCC materials are ductile whereas BCC materials are not. Explain the mechanism behind this behavior.
#9. Explain what the vapor pressure of a liquid corresponds to. Additionally, explain why liquids, when left in open containers, will eventually evaporate despite being below the boiling temperature.
#10. What two variables is the phase dependent on?
#11. What is unique about the phase diagram of water?
#12. Using a phase diagram, explain what sublimation is.
#1. How many grams of KCl must be added to `400 "mL"` of water to depress the freezing point by 3°C? The `K_f` of water is `(1.86°C)/"m"` .
#2. A gas consisting of `3 "mol" CO_(2(g))`, `4 "mol" O_(2(g))`, and `0.5 "mol" N_(2(g))` is found to have a pressure of `2 "atm"`. What are the partial pressures of `CO_(2(g)),O_(2(g)), "and" N_(2(g))`?
#3. The vapor pressure of dry ice is `1 "atm"` at `-72°C` and `2 "atm"` at `-69°C`. Calculate the `DeltaH_"sublimation"` of dry ice.
#1. Solids: fixed volume and shape, incompressible. Liquids: fixed volume, changes shape to shape of container, incompressible, ability to flow. Gases: no fixed volume, changes shape to shape of container, compressible and expandable.
#2. The energy involved in changes of state corresponds to the breaking or forming of bonds.
#3. When `DeltaH_"phase change"` is positive, energy is being absorbed into the material and thus bonds are being broken. The changes of state where bonds are being broken are melting and vaporization. When the `DeltaH_"phase change"` is negative, energy is being released from the material and thus bonds are being formed. This corresponds to condensation and freezing.
#4. The molality of a solution is the `"moles solute"/"kg solvent"`. This is comparable to molarity, which is `"moles solute"/"L solvent"`. Both are measures of concentration.
#5. Under standard temperature and pressure, most gases behave ideally. In other cases, real gases can be modeled as ideal gases when the `V` is large and `n` is small. See the Van der Waals equation and think about what happens when `V ">>"nb` and `n` is small (the equation should simplify to the ideal gas law).
#6. Gases consist of small massless particles that do not interact with each other aside from during elastic collisions. The molecules travel in a straight line and bounce off the walls of the container.
#7. The energy of a gas only depends on the temperature of the gas according to `KE=3/2*k_B*T`.
#8. FCC materials contain large numbers of slip planes whereas BCC materials contain little. Slip planes will slide in response to a force, which allows for a material to change shape in response to force. This explains the ductility of FCC materials.
#9. The vapor pressure of a liquid corresponds to the pressure of the vapor that's in equilibrium with the liquid. Liquids will evaporate in open containers due to the nature of evaporation. At any temperature, molecules on the surface of a liquid are evaporating. In open containers, the gas molecules do not return to the liquid and thus, the liquid will simply continue evaporating.
#10. Phase is dependent on pressure and temperature.
#11. The phase diagram of water has a leftward slanting solid-liquid boundary. Most other substances have a straight or rightward slanting solid-liquid boundary. Water is able to melt by increasing pressure which usually doesn't happen.
#12. Sublimation is the change in state from solid to gas. On a phase diagram, this corresponds to the solid-gas boundary.
#1. Use the equation for freezing point depression:
`DeltaT=-iK_f*m`
We want our final answer in units of grams KCl. Expand out the equation to solve for the moles KCl, then convert to grams KCl using the molecular weight of KCl.
`DeltaT=-iK_f*("moles KCl"/"kg water")`
`(DeltaT*("kg water"))/(-iK_f)="moles KCl"`
We know `DeltaT, i, "and", K_f`. The kg of water can be calculated using the density of water, `((1 g)/"mL")`.
`(400 "mL water")((1 g)/"mL")((1 kg)/(1000 g))=0.4 "kg water"`
Solve for the number of moles KCl.
`((-3°C)(0.4 "kg water"))/(-2((1.86°C)/"m"))=0.323 "mol KCl"`
The molecular weight of KCl is `(74.6 g)/"mol"`
`(0.323 "mol KCl")((74.6 "g KCl")/"mol KCl")=24.1 "g KCl"`
Answer: `24.1 "g KCl"`
#2. Use Dalton's Law of Partial Pressure:
First, calculate the mole fraction of each gas.
`x_(CO_2)=(3/(3+4+0.5))=0.4`
`x_(O_2)=(4/(3+4+0.5))=0.53`
`x_(N_2)=(0.5/(3+4+0.5))=0.067`
Now, use the mathematical form of Dalton's Law of Partial Pressure: `P_i=x_iP_"total"`
`P_(CO_2)=(0.4)(2 "atm")=0.8 "atm"`
`P_(O_2)=(0.53)(2 "atm")=1.06 "atm"`
`P_(N_2)=(0.067)(2 "atm")=0.134 "atm"`
These partial pressures should all add up to form the total pressure:
`P_(CO_2)+P_(O_2)+P_(N_2)=0.8 "atm"+1.06 "atm"+0.134 "atm"=1.99 "atm"`
Accounting for rounding, the partial pressures added up are equal to the total pressure.
Answer: `P_(CO_2)=0.8 "atm", P_(O_2)=1.06 "atm", P_(N_2)=0.134 "atm"`
#3. Use the Clausius-Clapeyron equation. Rearrange the equation to solve for the `DeltaH_"sublimation"`:
`ln(P_2/P_1)=(-DeltaH_"sublimation")/R(1/T_2-1/T_1)`
`(-Rln(P_2/P_1))/(1/T_2-1/T_1)=DeltaH_"sublimation"`
Now, just plug in values. Let `P_1=1 "atm", P_2=2 "atm", T_1=201K, T_2=204K`
`(((-8.314 J)/("mol"*K))ln((2 "atm")/(1 "atm")))/(1/(204K)-1/(201K))=DeltaH_"sublimation"`
Answer: `(78.7 kJ)/"mol"`