AP Chemistry
AP Chemistry 4: States of Matter Name __________________________
A. Gas State (10.2 to 10.9)
1. tend to be small, non-polar molecules
2. form homogenous mixtures
3. distributed throughout the entire container
(molecules typically occupy 0.1 % of the volume)
4. kinetic theory for gases (ideal gas)
a. molecules in continuous, chaotic motion, which is proportional to temperature
1. kinetic energy, Kmole = 1/2(MM)v2 = 3/2RT
a. R = 8.31 J/mol•K
b. MM (molar mass) in kg
c. T in kelvin (TK = ToC + 273)
2. root-mean-square speed, u = (3RT/MM)½
3. Graham’s law
a. rate r of effusion (leaking) or diffusion (spreading out) is proportional to speed
b. rA/rB = (MMB/MMA)½
c. time is inversely proportional to rate ∴ TB/TA = rA/rB
b. molecular volume is insignificant compared to container volume (approximation—see real gas)
c. collisions produce pressure w/o loss of total kinetic energy
d. Bonding between molecules is insignificant (approximation—see real gas)
5. gas laws
a. Ideal gas Law equation: PV = nRT
1. molecules generate pressure via collisions
a. pressure = force/area
b. 1 atm = 101 kPa = 760 mm Hg (torr)
c. measuring tools
1. barometer: atmospheric pressure
2. manometer: enclosed gas pressure
Pgas = Patm ± h (in mm Hg)
2. gas pressure is affected by:
a. n: each molecule exerts pressure ∴ more molecules exert more pressure: P ∝ n
b. T: hotter molecules move faster and collide with greater force ∴ generate more pressure: P ∝ T
c. V: molecules spread out which reduces collision per surface area ∴ generate less pressure: P ∝ 1/V
3. ideal gas law constant R (V in L, T in K)
a. 8.31 J/mol•K (P in kPa)
b. 0.0821 atm•L/mol•K (P in atm)
4. molar volume at STP = 22.4 L/mol
(standard T = 0oC, standard P = 1 atm)
5. derived equations
a. P1V1/T1 = P2V2/T2
b. MM = mRT/PV = dRT/P
b. Dalton’s law (P ∝ n)
1. Ptot = PA + PB
2. PA = XAPtot , where XA = molA/(molA + molB)
6. real gases
a. Van der Waals:(Preal + n2a/V2)(Vreal – nb) = nRT
b. "a" corrects for molecular bonding
1. "low" temperature (close to boiling point) molecules clump and collide less often, which generates less pressure ∴ Preal < Pideal
2. a is proportional to molecular polarity
c. "b" corrects for molecular volume
1. high pressure is generated by crowded molecules where the volume of empty space (Videal) is significantly less than 100 % of the total volume (Vreal)∴ Vreal > Videal
2. b is proportional to molar mass
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B. Phase Change (11.1 to 11.2, 11.4 to 11.6)
1. molecular-level comparison of gas, liquid, and solid states of a substance
[pic]
|Characteristic |Gas |Liquid |Solid |
|Energy |Highest |Middle |Lowest |
|Disorder |Greatest |Middle |Least |
|Occupied space |Whole |Bottom |Own |
|Compressibility |Yes |No |No |
|Flow rate |Fast |Middle |No |
|Diffusion |Rapid |Slow |No |
2. cohesive forces (van der Waals forces)
a. attraction between molecules
(covalent bonds hold atoms together in molecule)
b. dipole-dipole forces
1. polar molecules
2. δ+ of one molecule attracts δ− of a neighbor
3. strength ∝ to polarity, if all else is even
c. London dispersion forces
1. attraction between nuclei of one molecule's atoms for the electrons in a neighboring molecule causes temporary polarization throughout the liquid or solid (polarizability)
2. generalization
a. operates between all molecules (stronger than dipole-dipole for large molecules, i.e. large nonpolar > small polar)
b. only force for nonpolar (strength ∝ to mass: Xe > He, I2 > F2, C3H8 > CH4)
d. hydrogen bonding
1. super strong dipole-dipole force (stronger than dispersion forces)
2. H bonded to N, O or F
a. H ≈ +1 charge and N, O or F ≈ –1 charge because of extreme electronegative difference and small radius
b. bonding is ionic like (E ∝ Q1Q2/d)
3. explains unusual properties of water
a. each water molecule bonds to 4, which makes a 3-d structure with open cavities
b. high melting and boiling temperatures
c. low vapor pressure (low volatility)
3. cooling profile for water from 110oC to -10oC
| |A | | | | | |
|100oC | | | | | | |
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|0oC | | | |D E| | |
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| Heat Removed → (J) |
a. slope C-D < slope E-F ∴ more heat is removed when one mole H2O(l) is cooled 1oC compared to one mole H2O(s)
b. length B-C > length D-E ∴ more heat is removed when one mole H2O(g) → H2O(l) compared to one mole H2O(l) → H2O(s)
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c. calculations
|Step |Process |Formula |Constants |
|B-C |Condensation |Q = nΔHvap |ΔHvap = 40.7 kJ/mol |
| |(100oC) | | |
|C-D |Cooling liquid |Q = nClΔT |Cl = 75.3 J/mol•K |
|D-E |Freezing |Q = nΔHfus |ΔHfus = 6.01 kJ/mol |
| |(0oC) | | |
|E → |Cooling solid |Q = nCsΔT |Cs = 37.8 J/mol•K |
4. phase diagram
|Press| |
|ure | |
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| |Temperature |
a. point A: triple point (three phases at equilibrium)
1. below triple point: sublimation
2. above triple point: melting and vaporization
b. line A-B: equilibrium vapor-pressure curve for liquid (normal boiling point occurs at 1 atm pressure)
c. B: critical point, where there is no distinction between liquid and vapor (no liquid-vapor surface)
d. line A-C: equilibrium vapor-pressure curve for solid
e. line A-D: melting point of solid at various pressures
(normal freezing point occurs at 1 atm)
1. positive slope when solid is the densest phase (melting point increases with pressure)
2. negative slope when liquid is the densest phase (melting point decrease with pressure)
5. vapor
a. some surface molecules in the condensed phase have enough kinetic energy (speed) to escape surface (evaporate) below boiling point
b. as temperature increases more molecules have sufficient kinetic energy ∴ more vapor molecules
[pic]
c. cooling process (hottest evaporate first, leaving cooler molecules behind)
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d. equilibrium between liquid and vapor
1. evaporation rate = condensation rate in a closed container
2. concentration of vapor measured as Pvap
3. independent of container size until no liquid
4. Pvap increases at higher temperature because
a. more molecules are in vapor phase
b. vapor molecules exert greater pressure
e. boiling occurs when Pvap = Patm ∴ boiling point decreases with elevation (lower air pressure, Patm)
f. high Pvap indicates volatility—tendency to evaporate
C. Crystalline Solids (11.8)
1. ions, atoms or molecules fit into a regular geometric pattern (crystal lattice)
2. minimum energy state—maximum bond energy
3. intermolecular forces (attraction between δ+ and δ-) or bonds (covalent, ionic or metallic) hold particles together
4. 4 types of solids
a. metallic—metals only
1. attraction between cations and delocalized valence electrons (electron sea model)
[pic]
2. melting point: variable (∝ bond strength)
3. conductivity: free electrons ∴ yes
4. malleable: non-directional bond ∴ yes
5. water solubility: no molecular interactions ∴ no
6. examples: Cu, Ag, etc.
b. covalent network—nonmetals w/o H or halogen
1. atoms covalently bond throughout w/o size limit (different than large molecule)
2. melting point: strong bonds ∴ high
3. conductivity: no free electrons ∴ no
4. malleability: bond highly directional ∴ brittle
5. water solubility: no molecular interactions ∴ no
6. three examples
a. diamond and graphite—C
1. allotropes (2 forms in the same state)
2. diamond: covalently bonded 3-d structure—good abrasive
3. graphite: covalent bonded planar sheets linked by dispersion forces
a. separate easily—good lubricant
b. electron flow—good conductivity
b. quartz—SiO2
1. 3-d structure similar to diamond
2. softens when heated until liquid
3. fast cooling = non-crystalline glass
c. molecular—nonmetals often with H and/or halogen
1. attraction between +δ of one molecule with
–δ of another
2. melting point: weak bonds ∴ low
3. conductivity: no free electrons ∴ no
4. malleability: non-directional ∴ yes
(H-bonding in H2O(s) is somewhat directional)
5. water solubility ("like dissolves like") ∴ yes/no
6. examples: H2O, C6H12O6, etc.
d. Ionic—metal plus nonmetals
1. attraction between cations and anions
2. melting point: strong bonds ∴ high
3. conductivity: no free electrons ∴ no
(fused or dissolved state is conducting)
4. malleability: bond highly directional ∴ brittle
5. water solubility: ion-dipole interaction ∴ yes
6. examples: NaCl, CaCO3, etc.
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D. Solubility (13.1 to 13.4)
1. dissolving process
a. one substance disperses uniformly throughout other
1. solvent: dissolving medium (usually majority)
a. water = aqueous solution
b. ethanol (C2H5OH) = tincture solution
2. solute: dissolved in a solvent (usually minority)
a. ionic or acid = electrolyte (forms ions)
b. number of free ions = i (van't Hoff factor)
c. polar molecules = nonelectrolyte
3. solvation: attraction between solute-solvent (hydration if solvent is water)
a. cation with δ− side of H2O (O side)
b. anion with δ+ side of H2O (H side)
b. saturated solution
1. undissolved solid Δ dissolved solid
2. solution rate = crystallization rate
3. maximum amount that dissolves = solubility
(liquids that mix in all proportions = miscible)
c. effect of temperature on solubility
1. solvent kinetic energy is used to break solute-solute bonds ∴ solute gains energy; solvent lose kinetic energy (cools)
2. energy is released when solute-solvent bonds form and turns into kinetic energy of solution particles (warms up)
3. ΔH = Esolute-solute – Esolute-solvent
a. when Esolute-solute > Esolute-solvent
1. +ΔH (solution cools = endothermic)
2. raising T increases solubility
b. when Esolute-solute < Esolute-solvent
1. –ΔH (solution warms = exothermic)
2. raising T decreases solubility
4. solubility graphs (g solute/100 g H2O)
[pic]
5. gas solubility generally decreases with increased temperature because solution depends on solute-solvent bonds, which weaken as temperature increases
d. effect of pressure upon solubility (gas only)
1. solubility increases proportionally to partial pressure above solution Mg = kPg (Mg = mol/L)
2. gas in solution Δ gas in air space ∴ more gas in air space force more into solution
3. only Pg, not Ptot, will increase solubility
2. expressing concentration
a. concentration units [ ]
1. mass percent: % = 102(msolute/mtotal)
ppm (106), ppb (109)
2. mole fraction: Xsolute = molsolute/moltotal
3. molarity: M = molsolute/Vsolution(L)
4. molality: m = molsolute/msolvent(kg)
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b. conversion of concentration units
|determine mass or moles of solute and solvent |
| |Unit |Assume |Conclusion | |
| |% |102 g solution |gsolute = % | |
| | | |gsolvent = 100 – % | |
| |X |1 mol solute + |nsolute = X | |
| | |solvent |nsolvent = 1 – X | |
| |M |1 L solution |nsolute = M | |
| | | |gsolvent = 1000d – (nsolute)MM | |
| |m |1 kg solvent |nsolute = m | |
| | | |msolvent = 1000 g | |
|convert numerator and/or denominator |
|mass Δ volume: m = (d)(V) |
|mass Δ moles: m = (n)(MM) |
3. Separation solute and solvent
a. filtration: separate solvent from insoluble solute
b. distillation
1. simple: separate solvent from soluble solid
2. fractional: separate solvent from soluble liquid
[pic]
E. Colligative Properties (13.5)
1. lower vapor pressure
a. solute particles reduce vapor pressure
b. nonvolatile-nonelectrolyte: Pvap = XsolventPosolvent
c. two volatile liquids: Pvap = XAPoA + XBPoB
2. higher boiling point and lower freezing point
a. lowered vapor pressure changes melting and boiling temperatures (extends liquid phase)
b. ΔTb = Kbmi, ΔTf = Kfmi
1. m = molality
2. i ≈ number of ions (van't Hoff factor)
3. Kb/Kf = molal boiling/freezing point constant
c. determination of molar mass of non-electrolyte solute by freezing pt. depression
|calculate molality: molality = ΔTf/Kf |
|calculate molsolute: molsolute = (molality)(msolvent/1000) |
|calculate molar mass: MM = msolute/molsolute |
3. osmotic pressure
a. semi-permeable membrane blocks solute
b. solvent flows from high [ ] to low [ ] ∴ osmosis
c. osmotic pressure (π) = pressure to stop flow
d. π = MRTi
(R = 8.31 when π in kPa or 0.0821 when π in atm)
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Experiments
1. Molar Mass of a Gas Lab—Measure the mass and volume of butane released from a lighter, determine the molar mass and compare it to the known molar mass.
Mass a butane lighter (m1). Fill a 50 mL graduated cylinder with water and place it upside down in a filled trough. Release butane into the graduated cylinder until the water levels in the cylinder and trough are the same. Record volume (V). Dry the lighter thoroughly and mass (m2). Record temperature (T), pressure (Plab) and vapor pressure (PH2O).
a. Record the collected data.
|m1 |m2 |V |T |Plab |PH2O |
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b. Complete the following calculations to determine the molar mass and percent difference from known value.
|P = Plab – PH2O |T |V |Δm = m1 – m2 |
|(atm) |(K) |(L) |(g) |
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|MM = mRT/PV |MM (C4H10) |% Δ |
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c. How would the following affect the molar mass value?
(1) The butane lighter was not thoroughly dried.
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(2) The vapor pressure of water was not subtracted from the room pressure.
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(3) The water level in the inverted graduated cylinder was higher than the level in the trough.
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2. Solute Concentration Lab (Wear Goggles)—Mass a measured volume of solution and the solute that remains after all the water is boiled away and use the mass values to determine the solution concentration in different units.
Mass an empty, clean 125 mL flask (m1). Add 25.0 mL solution to the flask and mass (m2). Place the flask on the hot plate until all the water has boiled away and the rim of the flask is dry. Mass the cooled flask plus solute (m3).
a. Record the masses in the chart below.
|m1 |m2 |m3 |
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b. Determine the following.
|mNaCl = m3 – m1 | |
|mH2O = m2 – m3 | |
|Volume of solution | |
c. Calculate the following.
|Mole NaCl | |
|Mole H2O | |
|mass % | |
|mole fraction | |
|molarity | |
|molality | |
3. Molar Mass of Solute Lab—Graph the data to determine freezing point and use the data to calculate molar mass.
Part 1: 5.00 g of BHT is cooled while recording temperature.
|Time (s) |0 |20 |40 |60 |80 |100 |120 |140 |
|ToC |74.0 |72.2 |69.8 |68.0 |66.8 |67.8 |69.0 |69.0 |
|Time (s) |160 |180 |200 |220 |240 |260 |280 |300 |
|ToC |68.8 |68.8 |69.0 |68.8 |69.0 |67.0 |65.2 |63.8 |
Part 2: 0.500 g of naphthalene (C10H8) is added to 5.00 g BHT. The mixture is cooled while recording temperature.
|Time (s) |0 |20 |40 |60 |80 |100 |120 |140 |
|ToC |70.0 |68.0 |65.8 |64.2 |61.8 |60.0 |58.8 |60.2 |
|Time (s) |160 |180 |200 |220 |240 |260 |280 |300 |
|ToC |59.8 |59.2 |58.8 |58.2 |57.6 |57.0 |55.2 |53.4 |
Part 3: 0.500 g of unknown is added to 5.00 g BHT. The mixture is cooled while recording temperature.
|Time (s) |0 |20 |40 |60 |80 |100 |120 |140 |
|ToC |72.0 |70.0 |68.2 |65.8 |64.0 |62.8 |64.0 |63.4 |
|Time (s) |160 |180 |200 |220 |240 |260 |280 |300 |
|ToC |63.0 |62.8 |62.2 |61.8 |61.4 |61.0 |59.0 |57.2 |
a. Graph the data from parts 1, 2 and 3 using three different colors. Draw a straight line following the cooling process and a second straight line following the freezing process for each graph. Record the intersection, Tf (freezing pt.).
|Temper| | | | | | | | |
|ature | | | | | | | | |
|(oC) | | | | | | | | |
| |Time (s) |
b. Complete the following chart.
|Naphthalene/BHT Mixture |
|Tf (BHT) |Tf (Solution) |ΔTf |
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|n = m/MM | |
|Molality m | |
|Kf = ΔTf/m | |
|Unknown/BHT Mixture |
|Tf (BHT) |Tf (Solution) |ΔTf |
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|m = ΔTf/Kf | |
|n = mBHTm | |
|MM = m/n | |
c. The unknown's molecular formula is CH3(CH2)14CH2OH. Determine the percent error for this experiment.
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Practice Problems
A. Gas State
1. What features of the kinetic theory of gases
a. describe all gas molecules?
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b. describe ideal gas molecules only?
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2. Consider one mole of Ne gas at 274 K. Determine
a. the total kinetic energy.
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b. the average speed.
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3. a. What alkane effuses at 1/5 the rate of He?
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b. How many times faster does C2H2 diffuse compared to the alkane?
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4. Consider the graph below.
[pic]
a. A and B are He and O2, at 25oC, which is which? Explain
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b. A and B are at 100 K and 200K, which is which? Explain
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5. Determine the pressure of 1.22 atm in the following units.
|mm Hg |kPa |torr |
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6. If the atmospheric pressure is 749 mm Hg, what is the pressure of the enclosed gas in each case below?
[pic]
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7. A gas is confined inside a container with a movable piston held down by a fixed pressure.
[pic]
a. What affect would doubling the number of gas molecules at the same temperature have on the system? Explain.
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b. What affect would doubling the Kelvin temperature of the gas have on the system? Explain.
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c. What affect would doubling pressure by the piston at the same temperature have on the system? Explain.
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8. Complete the following table for an ideal gas:
|P |V |n |T |
|2.00 atm |1.00 L |1.500 mol | |
|30.3 kPa |1.250 L | |27oC |
|650 torr | |0.333 mol |350 K |
|atm |585 mL |0.250 mol |295 K |
9. Oxygen gas in a 10.0-L container has a pressure of 94.6 kPa and temperature of 25oC.
a. How many moles of oxygen gas are in the container?
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b. How many grams of oxygen gas are in the container?
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10. A sample of gas occupies 350 mL at 15oC and 750 torr. What temperature will the gas have at the same pressure if its volume increases to 450 mL?
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11. Determine the molar mass of an unknown gas given the data.
|Mass |Volume |Temperature |Pressure |
|4.93 g |1.00-L |400. K |1.05 atm |
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12. Calculate the density of ammonia, NH3, at STP.
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13. Consider the samples of gases.
[pic]
I II III
The samples are at the same temperature. Rank them with respect to the following (1 is highest).
| |I |II |III |
|Total Pressure | | | |
|Partial Pressure of He | | | |
|Density | | | |
|Average Kinetic energy per molecule | | | |
|Total Kinetic energy | | | |
14. Each bulb contains a gas at the pressure and volume shown and temperature of 25oC. Determine
[pic]
a. the number of moles of each gas.
|N2 | |
|Ne | |
|H2 | |
b. the total pressure after all stopcocks are opened.
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c. the partial pressure of each gas.
|N2 | |
|Ne | |
|H2 | |
15. 2.00 L of Hydrogen gas is collected over water at 30.0oC. The total pressure is 740 torr (PH2O = 32 torr).
a. What is the partial pressure of the hydrogen gas?
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b. How many moles of hydrogen gas are collected?
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16. A 20-L flask holds 0.20 mol O2 and 0.40 mol NO2 at 27oC.
a. What is the pressure of the mixture in kPa?
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b. What is the partial pressure of oxygen in kPa?
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17. Which gas, SO2 or CO2, should be least ideal at STP? Explain
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18. a. Why do gases under high pressure deviate from ideal behavior?
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b. Why do gases at temperatures near their boiling point deviate from ideal behavior?
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B. Phase Change
19. Which letter illustrates the types of molecular forces?
[pic]
|Dipole-Dipole | |Dispersion | |H-bond | |
20. For each pair, highlight the molecule with the higher boiling point and then justify your choice.
|Pair |Justification |
|H2O & H2S | |
|Ne & Kr | |
|Cl2 & SO2 | |
21. Explain the boiling points for the two isomers.
[pic]
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22. In addition to dispersion, what type of force would you expect between the following molecules?
|H2 |H2S |CHF3 |NH3 |
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23. Consider the heating profile for water in your notes.
a. What can you conclude about the value of Cl compared to Cs based on the slope of line C-D compared to E-F?
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b. What can you conclude about ΔHfus compared to ΔHvap based on the length of line B-C compared to D-E?
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24. Calculate the amount of heat needed to warm 2 mole of H2O between the given temperatures or phase change.
|-10oC → 0oC | |
|melt | |
|0oC → 100oC | |
|boil | |
|Total | |
25. Consider the phase diagram in your notes.
a. How does melting point change when pressure increases?
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b. How would the diagram differ for water?
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26. Answer the questions based on the phase diagram.
[pic]
|Normal melting point | |
|Normal boiling point | |
|Most dense phase | |
|Phase at 150 K, 0.2 atm | |
|Phase at 100 K, 0.8 atm | |
|Phase at 300 K, 1.0 atm | |
|Phase change: 50 K → 150 K at 0.2 atm | |
|Phase change: 1.0 atm → 0.2 atm at 300 K | |
|Phase change: 200 K → 300 K at 1.0 atm | |
27. Answer the questions based on the vapor pressure curve.
[pic]
|Vapor pressure at 30oC | |
|Temperature where pressure = 300 mm Hg | |
|Normal boiling point | |
28. Explain how pure water can boil at room temperature when placed in an evacuated bell jar.
| |
29. Explain why baking takes longer at high elevations.
| |
30. 0.010 moles of water is added to a 5.0-L container filled with dry air at 20oC (vapor pressure = 20 torr). The container is then sealed and equilibrium is established.
a. How many moles of water evaporate?
| |
b. What percentage of the water evaporates?
| |
31. Explain why water droplets form on a cold water bottle.
| |
C. Crystalline Solids
32. Use the electron-sea model of metals to explain
a. malleability.
| |
b. conductivity.
| |
33. What are allotropes?
| |
34. In what way is SiO2 like diamond; unlike diamond?
| |
35. What two factors affect ionic bond strength (lattice energy)?
| |
36. Complete the chart for each type of solid.
| |Metallic |Covalent |Molecular |Ionic |
| | |Network | | |
|Structural Unit | | | | |
|Bond name | | | | |
|Bond strength | | | | |
|Melting point | | | | |
|Solubility | | | | |
|Conductivity | | | | |
|Malleability | | | | |
|Example | | | | |
37. Explain the following observations. You must discuss both of the substances in your explanation.
a. SO2 melts at 201 K and SiO2 melts at 1,883 K.
| |
b. Cl2 boils at 238 K and HCl boils at 188 K.
| |
c. KCl melts at is 776oC and NaCl melts at 801oC.
| |
d. Si melts at 1,410oC and Cl2 melts at -101oC.
| |
D. Solubility
38. What is the approximate van't Hoff factor for the following?
|Na2O |CaCl2 |AlF3 |C6H12O6 |
| | | | |
39. Indicate whether the solute is likely to dissolve in water?
|NaCl |CH3OH |HC2H3O2 |C20H42 |
| | | | |
40. When KNO3 is added to water, the temperature of the solution decreases. Highlight the correct option.
a. lattice energy is (greater/less) than hydration energy.
b. KNO3 is more soluble in (warm/cold) water.
41. Determine the missing value for the following solutes using the solubility graphs in the notes.
|Solute |mass solute |mass water |Temperature |
| |90 g |100 g |50oC |
|K2Cr2O7 | |100 g |90oC |
|NaCl |70 g | |30oC |
|KClO3 |15 g |50 g | |
42. What is the concentration of CO2 (k = 3.1 x 10-2 mol/L•atm) that is bottled with a partial pressure of 4.0 atm?
| |
43. What is the concentration of N2 (k = 6.8 x 10-4 mol/L-atm) in a diver's blood if he breaths air at 2.5 atm that is 78 % N2.
| |
44. A solution is made up of 123 g NaOH and 289 g water. The total volume is 300. mL. Determine
|mole NaOH | |
|mole H2O | |
|mass % | |
|mole fraction | |
|molarity | |
|molality | |
45. Determine the density of 12.0 M HCl is 37.0 % HCl by mass.
a. What is the mass of HCl in one liter of solution?
| |
b. What is the mass of one liter of solution?
| |
c. What is the density of 12 M HCl in g/mL?
| |
46. Name the separation technique for the following.
|Separate salt from water | |
|Separate sand from water | |
|Separate alcohol from water | |
E. Colligative Properties
47. 0.25 mol solute is added to 1.0 mol benzene (VP = 450 torr).
a. What is the mole fraction of benzene in the solution?
| |
b. What is the vapor pressure of the solution?
| |
48. What is the vapor pressure when PH2O = 2.4 kPa, when
a. 0.50 mol C6H12O6 is in 5.5 mol H2O.
| |
b. 0.50 mol C2H5OH (PC2H5OH = 9 kPa) is in 5.5 mol H2O.
| |
49. 7.90 g of dichlorobenzene (C6H4Cl2) is added to 50.0 g of benzene. (benzene: Kf = 5.12oC/m, Tf = 5.50oC)
a. How many moles of dichlorobenzene are in the solution?
| |
b. What is the molality of the solution?
| |
c. What is the change in freezing point of the solution?
| |
d. What is the freezing point of the solution?
| |
50. 5.00 g of ethylene glycol in 100 mL of water (Kf = 1.86 oC/m) freezes at –1.50oC. Determine
a. the molality of the solution.
| |
b. the moles of ethylene glycol are in the solution.
| |
c. the molecular mass of ethylene glycol.
| |
51. What is the freezing point of a solution made from 5.00 g of glucose (C6H12O6) in 25 mL of water (Kf = 1.86 oC/m)?
| |
52. 100 mL of solution contains 0.0020 mol solute at 25oC.
a. What is the molarity of the solution?
| |
b. What is the osmotic pressure in kPa of the solution?
| |
53. What is the concentration of solute particles in a solution with an osmotic pressure of 73.4 atm and temperature of 25oC?
| |
54. How do the colligative properties change (↑, ↓) when non-volatile solute is added to solvent?
|Vapor P. | |Freezing pt. | |Boiling pt. | |Osmotic P. | |
Summary
Gas State
Gases at room temperatures tend to be molecular with low molar mass. Air, a mixture composed mainly of N2 and O2. Some liquids and solids can also exist in the gaseous state, where they are known as vapor. Gases' volume can change because they are compressible and they mix in all proportions because their component molecules are far apart.
The gas state is characterized by four variables: pressure (P), volume (V), temperature (T), and quantity (n). Volume is measured in liters, temperature in kelvins, and quantity of gas in moles. Pressure is the force per unit area. In chemistry, pressure is measured in atmospheres (atm), torr (named after Torricelli), millimeter of mercury (mm Hg) and kilopascals (kPa). One atmosphere of pressure equals 101 kPa = 760 torr = 760 mm Hg. A barometer is used to measure atmospheric pressure and a manometer is used to measure the pressure of enclosed gases.
The ideal-gas law equation is PV = nRT, where V is in L, n is in moles and T is in K. The term R is the gas constant, which is 0.0821 when P is in atm or 8.31 when P is in kPa. The conditions of 273 K and 1 atm are known as the standard temperature and pressure and abbreviated as STP, where the molar volume of all gases is 22.4 L/mol. Additional equations using molar mass (MM) are MM = mRT/PV and MM = dRT/P.
In gas mixtures the total pressure (Ptot) is the sum of the partial pressures (PA) that gas A would exert if it were present alone under the same conditions: Ptot = PA + PB ... and the pressure of gas A is proportional to its mole fraction (XA): PA = XAPtot. In calculating the quantity of a gas collected over water, correction must be made for the partial pressure of water vapor.
The kinetic-molecular theory accounts for the properties of an ideal gas in terms of a set of statements about the nature of gases: Molecules are in continuous, chaotic motion; the volume of gas molecules is negligible compared to the volume of their container; the gas molecules have no attraction for one another; their collisions are elastic; and the molecule's kinetic energy is proportional to the absolute temperature: K = 3/2RT.
Molecules of a gas do not all have the same kinetic energy at a given instant. Their speeds are distributed over a wide range; the distribution varies with the molar mass of the gas and with temperature. The root-mean-square speed, u = (3RT/MM)½.
Effusion (rate of escape through a tiny hole into a vacuum) and diffusion (rate spreading of one gas through are related to molar mass by Graham's law: rA/rB = (MMB/MMA)½.
Departures from ideal behavior increase in magnitude as pressure increases and as temperature decreases. Real gases depart from ideal behavior because the molecules possess finite volume and because the molecules experience attractive forces for one another. The van der Waals equation is an equation that modifies the ideal-gas law equation to account for molecular volume and intermolecular forces.
Phase Change
Substances that are gases or liquids at room temperature are usually composed of molecules. In gases the intermolecular attractive forces are negligible compared to the kinetic energies of the molecules; thus, the molecules are widely separated and undergo constant, chaotic motion. In liquids the intermolecular forces are strong enough to keep the molecules in close proximity; nevertheless, the molecules are free to move with respect to one another. In solids the inter-particle attractive forces are strong enough to restrain molecular motion and to force the particles to occupy specific locations in a three-dimensional arrangement.
Three types of intermolecular forces exist between neutral molecules: dipole-dipole forces, London dispersion forces, and hydrogen bonding. London dispersion forces operate between all molecules. The relative strengths of the dipole-dipole and dispersion forces depend on the polarity, size, and shape of the molecule. Dipole-dipole forces increase in strength with increasing polarity. Dispersion forces increase in strength with increasing molecular mass, although molecular shape is also an important factor. Hydrogen bonding occurs in compounds containing N, O or F bonded to H. Hydrogen bonds are stronger than dipole-dipole or dispersion forces.
The stronger the intermolecular force, the greater is the viscosity, or resistance to flow, of a liquid. The surface tension of a liquid also increases as intermolecular forces increase in strength. Surface tension is a measure of the tendency of a liquid to maintain a minimum surface area. The adhesion of a liquid to the walls of a narrow tube and the cohesion of the liquid account for capillary action and the formation of a meniscus at the surface of a liquid.
A substance may exist in more than one state of matter, or phase. Phase changes are transformations from one state to another. Changes of a solid to liquid, melting, solid to gas, sublimation, and liquid to gas, vaporization, absorb energy. The reverse processes release energy. A gas cannot be liquefied by application of pressure if the temperature is above its critical temperature. The pressure required to liquefy a gas at its critical temperature is called the critical pressure.
The vapor pressure is the partial pressure of the vapor when it is in dynamic equilibrium with the liquid. At equilibrium the rate of evaporation, transfer of molecules from the liquid to the vapor, equals the rate of condensation, transfer from the vapor to the liquid. The higher the vapor pressure of a liquid, the more readily it evaporates and the more volatile it is. Vapor pressure increases nonlinearly with temperature. Boiling occurs when the vapor pressure equals the atmospheric pressure. The normal boiling point occurs at 1 atm pressure.
The equilibria between the solid, liquid, and gas phases of a substance as a function of temperature and pressure are displayed on a phase diagram. Equilibria between any two phases are indicated by a line. The line through the melting point usually slopes slightly to the right as pressure increases, because the solid is usually more dense than the liquid. The melting point at 1 atm is the normal melting point. The point on the diagram at which all three phases coexist in equilibrium is called the triple point.
Crystalline Solids
In a crystalline solid, particles are arranged in a regularly repeating pattern. An amorphous solid or glass is one whose particles show no such order.
The properties of solids depend both on the type of particles and on the attractive forces between them. Molecular solids, which consist of atoms or molecules held together by intermolecular forces, are soft and low melting. Covalent network solids, which consist of atoms held together by covalent bonds that extend throughout the solid, are hard and high melting. Ionic solids are hard and brittle and have high melting points. Metallic solids, which consist of metal cations held together by a sea of electrons, exhibit a wide range of properties.
Solubility
Solutions form when one substance disperses uniformly throughout another. The dissolving medium of the solution (usually in the greater amount) is called the solvent. The substance dissolved in a solvent (usually the smaller amount) is called the solute. The attractive interaction of solvent molecules with solute is called solvation. When the solvent is water, the interaction is called hydration. The dissolution of ionic substances in water is promoted by hydration of the separated ions by the polar water molecules. The overall change in energy upon solution formation may be either positive endothermic or negative exothermic, depending on the relative value of lattice energy (positive) and hydration energy (negative).
The equilibrium between a saturated solution and undissolved solute is dynamic; the process of solution and the reverse process, crystallization, occur simultaneously. In a solution in equilibrium with undissolved solute, the two processes occur at equal rates, giving a saturated solution. The amount of solute needed to form a saturated solution at any particular temperature is the solubility of that solute at that temperature.
The solubility of one substance in another depends on the tendency of systems to become more random, by becoming more dispersed in space, and on the relative intermolecular solute-solute and solvent-solvent energies compared with solute-solvent interactions. Polar and ionic solutes tend to dissolve in polar solvents such as water and alcohol, and nonpolar solutes tend to dissolve in nonpolar solvents ("like dissolves like"). Liquids that mix in all proportions are miscible; those that do not dissolve significantly in one another are immiscible. Hydrogen-bonding interactions between solute and solvent often play an important role in determining solubility; for example, ethanol and water, whose molecules form hydrogen bonds with each other, are miscible. The solubilities of gases in a liquid are generally proportional to the pressure of the gas over the solution, as expressed by Henry's law: Sg = kPg. The solubilities of most solid solutes in water increase as the temperature increases. In contrast, the solubilities of gases in water generally decrease with increasing temperature.
Concentrations of solutions can be expressed quantitatively by several different measures, including
mass percent: % = 102(msolute/mtotal)
mole fraction: Xsolute = molsolute/moltotal
molarity: M = molsolute/Vsolution(L)
molality: m = molsolute/msolvent(kg)
Conversions between concentration units is possible if molar mass of solute and solvent are known and/or the density of the solution is known.
Colligative Properties
A physical property of a solution that depends on the concentration of solute particles present, regardless of the nature of the solute, is a colligative property. Colligative properties include vapor-pressure lowering, freezing-point lowering, boiling-point elevation, and osmotic pressure. The lowering of vapor pressure, Pvap = XsolventPosolvent. A solution containing a nonvolatile solute possesses a higher boiling point than the pure solvent. The molal boiling-point constant, Kb, represents the increase in boiling point for a 1 m solution of solute particles as compared with the pure solvent. Similarly, the molal freezing-point constant, Kf, measures the lowering of the freezing point of a solution for a 1 m solution of solute particles. The temperature changes are given by the equations ΔTb = Kbm and ΔTf = Kfm. When NaCI dissolves in water, two moles of solute particles are formed for each mole of dissolved salt. The boiling point or freezing point is thus elevated or depressed, respectively, approximately twice as much as that of a nonelectrolyte solution of the same concentration. The multiplier is called the van't Hoff factor i. Similar considerations apply to other strong electrolytes. Osmosis is the movement of solvent molecules through a semipermeable membrane from a less concentrated to a more concentrated solution. This net movement of solvent generates an osmotic pressure π which can be measured in units of gas pressure, such as atm. The osmotic pressure of a solution as compared with pure solvent is proportional to the solution molarity: π = MRT.
Practice Multiple Choice
Briefly explain why the answer is correct in the space provided.
Questions 1-2 The molecules have the normal boiling points.
|Molecule |HF |HCl |HBr |HI |
|Boiling Point, oC |+19 |-85 |-67 |-35 |
1. The relatively high boiling point of HF can be correctly explained by which of the following?
(A) HF gas is more ideal.
(B) HF molecules have a smaller dipole moment.
(C) HF is much less soluble in water.
(D) HF molecules tend to form hydrogen bonds.
| | |
2. The increasing boiling points for HCl, HBr and HI can be best explained because of the increase in
(A) dispersion force (B) dipole moment
(C) valence electrons (D) hydrogen bonding
| | |
3. A sample of an ideal gas is cooled from 50oC to 25oC in a sealed container of constant volume. Which of the following values for the gas will decrease?
I. The average kinetic energy of the molecules
II. The average distance between the molecules
III. The average speed of the molecules
(A) I only (B) II only (C) III only (D) I and III
| | |
Questions 4-7 refer to the phase diagram of a pure substance.
[pic]
4. Which phase is most dense?
(A) solid (B) liquid
(C) gas (D) can't determine
| | |
5. Which occurs when the temperature increases from 0°C to 40°C at a constant pressure of 0.5 atm?
(A) Sublimation (B) Condensation
(C) Freezing (D) Fusion
| | |
6. Which occurs when the pressure increases from 0.5 to 1.5 atm at a constant temperature of 60°C?
(A) Sublimation (B) Condensation
(C) Freezing (D) Fusion
| | |
7. The normal boiling point of the substance is closest to
(A) 20oC (B) 40oC (C) 70oC (D) 100oC
| | |
Questions 8-9The graph shows the temperature of a pure solid substance as it is heated at a constant rate to a gas.
[pic]
8. Pure liquid exists at time
(A) t1 (B) t2 (C) t3 (D) t4
| | |
9. Which of the following best describes what happens to the substance between t4 and t5?
(A) The molecules are leaving the liquid phase.
(B) The solid and liquid phases coexist in equilibrium.
(C) The vapor pressure of the substance is decreasing.
(D) The average intermolecular distance is decreasing.
| | |
10. Which actions would be likely to change the boiling point of a sample of a pure liquid in an open container?
(A) Placing it in a smaller container
(B) Increasing moles of the liquid in the container
(C) Moving the container to a higher altitude
(D) Increase the setting on the hot plate
| | |
11. Gas in a closed rigid container is heated until its absolute temperature is doubled, which is also doubled?
(A) The density of the gas
(B) The pressure of the gas
(C) The average speed of the gas molecules
(D) The number of molecules per liter
| | |
12. A 2.00-L of gas at 27oC is heated until its volume is 5.00 L. If the pressure is constant, the final temperature is
(A) 68oC (B) 120oC (C) 477oC (D) 677oC
| | |
13. Under the same conditions, which of the following gases effuse at approximately half the rate of NH3?
(A) O2 (B) He (C) CO2 (D) Cl2
| | |
14. What is the partial pressure (in atm) of N2 in a gaseous mixture, which contains 7.0 moles N2, 2.5 moles O2, and 0.50 mole He at a total pressure of 0.90 atm.
(A) 0.13 (B) 0.27 (C) 0.63 (D) 0.90
| | |
Questions 15-16 refer to the following gases at 0°C and 1 atm.
(A) Ne (B) Xe (C) O2 (D) CO
15. Has an average atomic or molecular speed closest to that of N2 molecules at 0°C and 1 atm
| | |
16. Has the greatest density
| | |
17. A 2-L container will hold about 4 g of which of the following gases at 0oC and 1 atm?
(A) SO2 (B) N2 (C) CO2 (D) C4H8
| | |
18. Which is the same for the structural isomers C2H5OH and CH3OCH3? (Assume ideal behavior.)
(A) Gaseous densities at STP
(B) Vapor pressures at the same temperature
(C) Boiling points
(D) Melting points
| | |
19. As the temperature is raised from 20oC to 40oC, the average kinetic energy of Ne atoms changes by a factor of
(A) ½ (B) (313/293)½
(C) 313/293 (D) 2
| | |
20. The system shown above is at equilibrium at 28°C. At this temperature, the vapor pressure of water is 28 mm Hg.
[pic]
The partial pressure (in mm Hg) of O2(g) in the system is
(A) 28 (B) 56 (C) 133 (D) 161
| | |
21. The partial pressure of toluene is 22 mm Hg and that of benzene is 75 mm Hg in a mixture of these two gases. What is the mole fraction of benzene in the gas mixture?
(A) 0.23 (B) 0.29 (C) 0.50 (D) 0.77
| | |
22. In which of the processes are covalent bonds broken?
(A) I2(s) → I2(g) (B) CO2(s) → CO2(g)
(C) NaCl(s) → NaCl(l) (D) C(diamond) → C(g)
| | |
23. Of the following compounds, which is the most ionic?
(A) SiCl4 (B) BrCl (C) PCl3 (D) CaCl2
| | |
24. Which of the following oxides is a gas at 25°C and 1 atm?
(A) Rb2O (B) N2O (C) Na2O2 (D) SiO2
| | |
25. Which of the following has the highest melting point?
(A) S8 (B) I2 (C) SiO2 (D) SO2
| | |
26. Under which conditions is O2(g) the most soluble in H2O?
(A) 5.0 atm, 80oC (B) 5.0 atm, 20oC
(C) 1.0 atm, 80oC (D) 1.0 atm, 20oC
| | |
27. Which is lower for a solution of a volatile solute compared to the pure solvent?
(A) normal boiling point (B) vapor pressure
(C) normal freezing point (D) osmotic pressure
| | |
Questions 28-30 Refer to 0.20 M solutions of the following salts.
(A) NaBr (B) KI (C) MgCl2 (D) C6H12O6
28. Has the lowest freezing point
| | |
29. Has the lowest conductivity
| | |
30. Has the lowest boiling point
| | |
31. The mole fraction of ethanol in a 6 molal aqueous solution is
(A) 0.006 (B) 0.1 (C) 0.08 (D) 0.2
| | |
32. What additional information is needed to determine the molality of a 1.0-M glucose (C6H12O6) solution?
(A) Volume (B) Temperature
(C) Solubility of glucose (D) Density of the solution
| | |
33. The mole fraction of toluene (MM = 90) in a benzene (MM= 80) solution is 0.2. What is the molality of the solution?
(A) 0.2 (B) 0.5 (C) 2 (D) 3
| | |
Practice Free Response
1. a. 3.327 g of an unknown gas occupies 1.00-L at 25oC and 103 kPa. What is the molar mass of the gas?
| |
b. What is the density of this gas at STP (standard temperature—0oC, and pressure—1 atm)?
| |
c. Which noble gas would have twice the effusion rate?
| |
2. N2 with V = 200. mL, P = 99.7 kPa, and T = 27.0oC is mixed with O2 and transferred to a 750.-mL container at 27.0oC. The total pressure of the mixture is 90.4 kPa, at 27.0oC.
a. Calculate the moles of N2.
| |
b. Calculate the total moles of gas.
| |
c. Calculate the partial pressure of each gas.
| |
3. Explain why methane gas does not behave as an ideal gas at low temperatures and high pressures.
| |
4. 10 g of water is added to a 10.0-L container filled with dry air at 20oC (PH2O = 20 torr). The container is sealed.
a. How many grams of the water will evaporate?
| |
b. Would the amount of water that evaporates increase (↑), remain the same (=) or decrease (↓) for the following changes?
| |↑ |= |↓ |
|Use a 5.0 L container | | | |
|Use humid air | | | |
|Raise the temperature to 25oC | | | |
|Add 20.0 g of water | | | |
5. Consider the following solids.
a. Rank the solids from highest melting point (1) to lowest.
|CH4 |H2O |MgO |Na |NaCl |SiO2 |
| | | | | | |
b. Justify your relative ranking of CH4 and H2O.
| |
c. Justify your relative ranking of MgO and NaCl.
| |
6. Explain the following observations.
a. NH3 boils at 240 K, whereas NF3 boils at 144 K.
| |
b. At 25°C and 1 atm, F2 is a gas, whereas I2 is a solid.
| |
7. Hydrogen gas is produced when aluminum foil is added to a solution of hydrochloric acid.
a. The hydrogen is collected over water at 25oC and a total pressure of 756 torr. What is the mole fraction of H2(g) in the wet gas? (PH2O) at 25oC = 23.8 torr.
| |
b. If 255 mL of wet gas is collected, what is the yield of hydrogen in grams?
| |
c. What is the density of the wet gas?
| |
8. When CaCl2 is added to water, the temperature of the solution decreases.
a. Justify which bond is stronger; hydration bonds between ions and water or ionic bonds between ions?
| |
b. Justify why you expect CaCl2 to be more or less soluble in warm water compared to cold water?
| |
9. What is the solubility of CO2 in an opened soft drink at 25oC where the partial pressure of CO2 is 3.0 x 10-4 atm? (kCO2 = 3.1 x 10-2 mol/L•atm).
| |
10. The freezing point decreases by 3.8oC when 0.500 g of an unknown is dissolved in 5.00 g of BHT (Kf = 9.3oC/m). What is the molar mass of the unknown?
| |
11. Explain the following observations. Your responses must include specific information about all substances.
a. When table salt (NaCI) and sugar (C12H22O11) are dissolved in water, it is observed that
(1) both solutions have higher boiling points than pure water
| |
(2) the boiling point of 0.10 M NaCI(aq) is higher than that of 0.10 M C12H22O11(aq).
| |
b. Ammonia, NH3, is very soluble in water, whereas phosphine, PH3, is only moderately soluble in water.
| |
12. Consider camphor, C10H16O, a substance obtained from the Formosa camphor tree. It has considerable use in the polymer and drug industry. A solution of camphor is prepared by mixing 30.0 g of camphor with 1.25 L of ethanol, C2H5OH (d = 0.789 g/mL). Assume no change in volume when the solution is prepared.
a. What is the mass percent of camphor in the solution?
| |
b. What is the molarity of the solution?
| |
c. What is the molality of the solution?
| |
d. The vapor pressure of pure ethanol at 25oC is 59.0 mm Hg. What is the vapor pressure of ethanol in the solution at this temperature?
| |
e. What is the osmotic pressure of the solution at 25oC?
| |
f. What is the boiling point of the solution? The normal boiling point of ethanol is 78.26oC (Kb = 1.22oC/m).
| |
g. The molar mass of cortisone acetate is determined by dissolving 2.50 g in 50.0 g camphor (Kf = 40.0oC/m). The freezing point of the mixture is 173.44oC; that of pure camphor is 178.40oC. What is the molar mass of cortisone acetate?
| |
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