6/13/2009 10:13:00 PM [2/4/09] did lab [2/5/09] Mole-volume hypothesis Avogadro hypothesized that equal volumes of a gas at the same temperature and pressure contain equal number of particles o If PV = nRT (and P,V,T, are the same then n is the same) STP – 273 K, 1 atm, 1 mol o (1 atm)(V) = 1 mol (.0821)(273) V = 22.4 L o At STP 1 mol (NA particles) of any gas occupies a volume of 22.4 liters 22.4 molar liters o At STP volume of gas = (# mol) x (22.4 L/mol) Ex. how many moles of H2 are in 0.2 L? 8.92 x 10-3 mol H2 o At STP molar mass = density x molar volume (g/mol) = (g/l) (l/mol) The density of a compound containing C and O is 1.94 g/l at STP what is the molar mass? 44 g/mol (1.94*22.4) All the ways to convert moles Moles to particles o Multiply by NA Particles to moles o Divide by NA Mole to mass o Multiply by molar mass Mass to mole o Divide by molar mass Mole to volume of gas (Must be STP) o Multiply by 22.4 mol/l Volume of gas to mole (Must be STP) o Divide by 22.4 mol/l Q: what volume of SO2 will result from the complete burning (S + O2 = SO2) of pure sulfur in 8 L of Oxygen gas? 8 L / 22.4 L/mol = .36 mol O2 .36 mol S O2 * 22.4 = 8L Q: How many liters of N2 will react with 36 grams of H2 at STP, given N2 + 3H2 2NH3? 36 g / 2 g/ mol = 18 mol H2 x (1/3) = 6 mol N2 * 22.4 L/mol = 134.4 L Q: How many liters of carbon dioxide at STP are produced by combustion of 342 grams of octane (C8H18) according to the equation 2C8H18 + 25O2 16CO2 +18H2O? o 342/114 = 3 mol x (16/2) = 24 mol x 22.4 L/mol = 537.6 L Q: How many liters of oxygen gas at 755 mm Hg and 305 K form when 294 g of KClO3 completely react in 2KClO3 (s) 2KCl (s) + 3O2 (g)? 294 / 122.5 = 2.4 mol (3/2) = 3.6 mol O2 755/760 = .993 atm (.993)V = (3.6)(.0821)(305) o V = 90.78 L [2/6/09] Co (g) + 2H2 (g) CH2OH (g) What volume of H2 (in L) at 748 mmHg and 86 C is required to produce 25.8 g CH3OH? o 25.8/32 = .80625 mol x (2/1) = 1.6125 o 748/760 = .984 mmHg o 359 K o PV = nRT o (.984)(v) =(1.6125)(.0821)(359) V= 47.9 Mixture of gases Air – 78% nitrogen, 21% oxygen, .9% argon, .03% CO2 o Percent by volume o Each gas exerts partial pressure Partial pressure – pressure due to any individual component in a gas mixture Daltons law of partial pressure o Total pressure - sum of all partial pressures Ptotal = Pa + Pb + Pc + …] [2/9/09] continued PA= XAPtotal o XA = mol fraction of gas A XA = Moles of A / total # of moles of gas o PA = Partial pressure Ex. .75 mol nitrogen, .2 mol hydrogen, .005 mol fluorine. Total pressure 2.5 atm o .955 total mol Partial pressure of Nitrogen – 1.88 atm (.75/.955)*2.5 Hydrogen – .52 atm (.2/.955)*2.5 Fluorine – .013 atm (.005/.955)*2.5 Diffusion/Effusion Diffusion o Tendency of molecules to move toward areas of how concentration until the concentration Effusion o Gas escapes through a tiny hole in a container o * lower molar mass effuse faster Graham’s law of effusion o The rate of effusion is inversely proportional to the square root of gas’s molar mass RateA / rateB = √(molar mass B / molar mass A) o Ex. How much faster does Helium effuse than nitrogen? Rate He / Rate N2 = √(28/4) ≈ 2.7 Rate He is 2.7 times the rate of N2 o Rate is anything over time [2/10/09] When doing calculations remember diatomic atoms Partial pressure Pressure that one atom or molecule would exert if it alone was in a container o In problems you may need to use boyle’s law PV = PV ( to find new pressure of something) Total pressure = added partial pressures A certain gas effusion 4 times as fast as oxygen gas. What is the molar mass of this gas? Rate ? / rate O2 = 4 = √32 / x o X=2 H2 Real gases At high pressures or low temperatures gases do not behave ideally o Van Der Waals equation [P+a(n/v)2] x [v-nb] = nRT [2/11/09] ex. solve for pressure, 1 mol Cl2 , 5 L , 273 K using o Van der Waals A – 6.49, B - .0562 [P + 6.49(1/5)2] x [5 – 1.0562] = 1(.0821)(273) P = 4.27 atm o Ideal P(5) = 1(.0821)(273) P = 4.48 atm [2/12/09] Determine density of CH4. 3.25 L, 5.8 atm, 25.5 C (5.8) (3.25) = n (.0821) (298.5) o .77 mol * 16 g/mol = 12.3 grams o 3.8 g/l Calculate molar mass of unknown gas Flask o 143.187 g , empty, 255 ml Filled o 267 torr, 25 C, 143.289 g 267/760 = .35 atm, 25+273 = 298 K, 143.289-143.187 = .102 PV = nRT (.35)(.255) = n(.0821)(298) n = .0037 o .102 /.0037 =27.5 g /mol Chapter 7 6/13/2009 10:13:00 PM [2/17/09] Isaac Newton discovered that light traveled in particles Later it was discovered that light travels in waves as well o Amplitude - maximum distance from equilibrium o Wavelength – distance from one point on a wave to an identical point on another wave Symbol – λ (lamda) o Crest – top point on a wave o Trough – bottom point on a wave o Frequency – number of waves to pass a point in one second o Measured in hertz 1 hertz = 1/sec (or s-1) Symbol - ν (nu) o C (speed of light) = λν Light changes color (pg. 285) as frequency grows greater (this is only in a small portion of all the frequencies) o C = λν C – 3 x 106 m λ – 510 x 10-9 m/s ν = 5.88 x 1014 hertz o if sun is shined on a prison a reflection of all the colors appear this happens with a rainbow (water drops reflect the lights) Dual nature of lights o Acts as waves + particles (light is unique that this happens) Particles made up of photons (little package of light) Atomic spectra o Pass electric current through a gas in a tube This energizes electrons of atoms The electrons absorb energy and move to higher energy levels (rings around nucleus) The electrons then lose energy + come back to original position and emit light [2/18/09] Ground state – lowest possible energy state of e- in atom E = quantum of energy o E = hν v (nu) – frequency of light emitted h = pianck’s constant = 6.63 x 10-34 JS Combined with C = λν E = hc / λ energy = (h) 6.63x 10-34 * (c) frequency / wavelength λ o energies unit is J*S Bohr model o Named after Neils Bohr o Said that e- can be found in orbits around the nucleus o Each orbit has a fixed amount of energy = energy level Ladder Atom Lowest ring Energy level closest to nucleus (lowest amount of energy) Person climbs from ring to ring e- travel from energy level to another To move from energy level to another e- amount must be gained or lost contain amount of energy Quantum of energy – amount of energy required for an electron to move from one energy level to another o Higher energy levels (further from nucleus) are closer together o Goes up, needs energy o Goes down, emit energy [2/19/09] 44. Calculate the energy of a photon of a electromagnetic radiation at o 100.2 MHZ E = hv 6.63 x 10-34 JS * 100,200,000 hz = 6.76 x 10-26 J o 1070 KHZ E = hv 6.63 x 10-34 JS * 1,070,000 = 7.09 x 10-28 J o 450 nm E = hc / λ [6.63 x 10-34 JS x (3x108 m/s)] /450 x10-9 m = 4.44 x 10-19 J Heisenberg uncertainty principle o Impossible to know both position and velocity of an electron at the same time Schrodinger o Came up with quantum mechanical model Atom: probability of find an electron within a certain region of space surrounding the nucleus represented as fuzzy cloud Cloud is denser where there is a greater probability of finding electrons o Atomic orbital’s – regions of space with highest probability of finding electrons in an energy level o Energy levels are represented by a principle quantum numbers: n = 1,2,3,4… Numbering from nucleus out Within each energy level are sublevels corresponds to orbital’s of different shapes describing where electrons are likely to be found Sublevels are represented by letters s , p , d , f Labeled by angular momentum numbers o If L is: 0=s 1=p 2=d 3=f S: spherical P: dumbbell shaped o Every P has three orbital’s one on – px, pz, py orbital’s On that axis o Every orbital’s holds on two electrons S – 2 electrons P – 6 electrons D – 10 electrons F – 14 electrons [2/23/09] Sublevels L – angular momentum o Angular momentum numbers relate to sublevels which have different amounts of orbitals with each hold two electrons L sublevel Electrons 0 S 1 orbital - 2 1 P 3 orbitals - 6 2 D 5 orbitals - 10 3 F 7 orbitals - 14 o Principle energy # of sublevels Types of sublevels # of electrons 1 1S (1st energy 2 levels n=1 level- s sublevel) n=2 2 2S , 2P 2+6 =8 n=3 3 3S, 3P, 3D 2+6+10 =18 n=4 4 4S, 4P, 4D, 4F 2+5+10+14= 32 o 2n2 = the maximum number of electrons a energy level can hold o Magnetic quantum number (Ml) – l is a L Specific orientation of orbital’s L Ml S 0 0 P 1 -1,0,1 D 2 -2,-1,0,1,2 F 3 -3,-2,-1,0,1,2,3 P. 315 o Q 58: Chart above o Q:59 A) N = 2, l = 1, Ml = -1 which works B) n = 3, l = 2, Ml = 0 which works C) n = 3, l = 3, Ml = 2 which doesn’t work o Q:60 1s – works 2p – works 4s – works 2d – does not work Ml magnetic quantum numbers – ranges from –l to l L angular momentum # ranges from 0 to (n-1) Absorption / emission When it moves up it absorbes energy Come back down, emit energy o 315: 64 n = 3 n = 1 - emits n = 2 n = 4 - absorbs Chapter 8.2-8.9 6/13/2009 10:13:00 PM [2/23/09] Electron configurations – way in which electrons are arranged in orbitals around the nucleus Rules for writing electron configurations o 1. Aufbau principle Electrons occupy orbital’s of lowest energy first 1s,2s,2p,3s,3p,(*)4s,3d,4p,5s,4d,5p,6s,5d,4f,6p *doesn’t make sense anymore Picture – pg 325 o 2. Pauli exclusion principle To occupy the same orbital, 2 electrons must have opposite spins This is represented by a box which has an up arrow and then a down arrow o 3. Hund’s rule electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible ex. [2/25/09] Elements Orbital diagram Electron configuration H 1s1 (exponents represents electrons) He 1s2 Li 1s22s1 C 1s22s22p2 O 1s22s22p4 Na 1s22s22p63s1 1s22s22p63s23p64s23d2 Ti [2/26/09] Figuring out an electron configuration based periodic table SPD o Right two columns are S block o Middle columns (transition elements) are D block o Columns to the left of middle (left six) are P block o Inner transition elements are f Block Period number (for S + P) = principle quantum number o Ex. Ca 1s22s22p63s23p64s2 Period number (for D) = n – 1 o The block next to 4s would be 3d o Ex. Fe = 1s22s22p63s23p64s23d6 (its 3d not 4d since its in the d block) Period number (for f) = n - 2 Other problems o Ex. As 1s22s22p63s23p64s23d104p3 o Ex. Rb 1s22s22p63s23p64s23d104p65s1 If you don’t want to write the entire formula you can write a noble gas and what comes after that o Ex. [Kr]5s1 Can only be done when specified, otherwise must write entire thing Exception to Aufbau principle o All elements below Cr and below Cu (Mo, W, Unh, Cu, Ag, Au) Since these two electrons are close to being half full or filled the electron in the s before jumps to the d, so that both will be half full or filled Ex. Cr 1s22s22p63s23p64s13d5 Ex. Cu 1s22s22p63s23p64s13d10 Or Cu [Ar]4s3d10 Close Electrons Core o Electrons in inner energy levels Valence o Electrons in outermost principle energy level Example if the highest energy level is 4s1 then there is one o If it has four valance and it’s a metal it will lose electrons Other things if 1,2, or 3 it will lose, if 5,6,7 it will gain If 8 nothing will happen [2/27/09] Electron configuration for Mg2+ 1s22s22p6 O2- 1s22s22p6 o If are given any ion that figure out if it will lose or gain electrons and then write the electron configuration Periodic table Atomic radius o One half of the distance between the nuclei of 2 atoms of same element when atoms are joined Measured in picometers (pm) – x 10-12 If you go down a group the atomic size increases o Since energy levels are added If you go across a period the atomic size decreases o Since a proton is added as well as a proton and there is a greater charge between the proton and the electron [3/3/09] Periodic trends Atomic size (did already) Ionic size o Size of cation always smaller then size of atom o Size of anion always greater then size of atom Ex. Na will be larger then Na+ o Find chart to see trend (cant find picuture) Ionization energy o Energy required to remove an electron from an atom o As you go down a group ionization energy decreases o When you go across a period (left to right) ionization energy increases (opposite trend as atomic size) [3/5/09] Notes on homework: When transitions become ions and lsoe electrons they lose from the outermost energy levels Exceptions under Cr and Cu o ex. Mo3+ …4p64d3 (not – 5s24d1) or [Kr] 5s04d3 if two ions have the same number of electrons (isoelectronic), the one with less protons has a larger radius Ex. Se2+ Kr Sr2+ Rb+ Br Increasing atomic radius: Sr2+ Rb+ Kr Br- Se2+ Trends continued Electro negativity o Ability of an atom attract electrons when the atom is in a compound o As you go down a period electro negativity decreases (decreases when size rises) o When going across a group (left to right) it increases Metallic character o When going down a period it increases o When going across a group (left to right) it decreases Group 8a nobles cases energy levels fixed Group 1a – 7a representative elements group 7a called halogens Transition elements Fill up d sub levels Chapter 9 6/13/2009 10:13:00 PM [3/6/09] Types of chemical bonds Type of atom Type of bond Characteristic of bond Metal + non metal Ionic Transfer of electron from metal to non metal Non metal + non metal Covalent Metal + metal Share electrons Metallic Ionic compounds and Ionic bonds Valance electrons – electrons in the highest occupied energy level o Octet rule o Every atom wants to have 8 valence electrons (this results in them either gaining or giving up electrons) Na Na+ + electron 1s22s22p63s1 1s22s22p6 Lewis structure = electron dot structure o A diagram that shows the valance electrons as dots and bonds as dashes Go above, below, left and to the right (two on each side) The first two electrons go together on top The next three go on different sides Pauli exclusion rule After that you add a second to each side (that has one) o When an atom loses an electron, dots are not show (but + and –‘s are) o When it gains electrons the dots are shown (as well as + or – ‘s) Properties of compounds o Crystalline solids at room temperature o Ions arranged in repeating 3D pattern o Large attractive force (very strong bonds) High melting point and boiling point o Conduct electric current when melted or dissolved in water [3/11/09] Metallic bonding Metals: made of closely packed cations. Valance electrons of metal atoms can be modeled as sea of electrons. Electrons are mobile. o Since they are mobile they are: Good conductors Ductile Malleable Alloys: mixture of two or more elements. o Properties are similar to those of the elements they are made up of Ex. brass = alloy of copper + zinc Ex. Sterling silver = silver (92.5%) + copper (7.5%) [3/12/09] Covalent bonding (form molecular bonds) Lower boiling and melting points Weaker than ionic Molecular vs. ionic o Molecular Collection of molecules o Ionic Array of cations + anions Want to share electrons to fill outermost levels o H2 the two H’s share the two electrons Lewis structure H = H The dash (-) is the shared, bonded pair The dots are unshared lone pairs o F2 Share two electrons (can be seen by using dot structures) Lewis structure F – F (each F has six dots around it) o H2O H-O-H (O has a lone pair above and below) Rules for drawing Lewis structure 1. Count number of valance electrons in the entire compound 2. Use dashes between central atom and surrounding atoms (dashes represent a pair) o Central atom – atom that there is only one of 3. Draw lone pairs on surrounding atoms, then on central o keep in mind, H only needs 2, rest needs 8 4. Check that every atom has 8 (except H) and that we used the correct number of valance electrons [3/13/09] *put brackets around ions and write the charge outside on the upper right hand corner *when a structures could have more then one structure, all structures must be drawn (put all possibilities in brackets and “” between the brackets) o Resonance – actual bonding is a hybrid, or mixture, of the extremes represented by the resonance structure Exceptions to octet rule o 1. Odd number of valance electrons cant have an odd number greater then 8 [3/16/09] Exceptions to octet rule (continued…) o 2. Expanded octet When more then 4 atoms are with the central atom Ex. PCl5 The central atom may have more then 8 electrons through bonds, or bonds and lone pairs Chapter 10 6/13/2009 10:13:00 PM [3/16/09] VSEPR theory Valence shell electron pair repulsion Explains 3D shape of molecules Repulsion between electron pairs causes molecular shapes to adjust so that valance electrons pairs stay as far apart as possible o When electrons have lone pairs the angle is smaller (w/o – 109.5 w/ - 107) Pictures 414-415 [3/17/09] Number of Number of Electron pair Example Molecular Bond angle electrons pairs (contains lone pairs) lone pairs (on central atom) geometry 2 0 Linear BeCl2 Cl – Be - Cl 180° 3 0 Trigonal planer BF3 Trigonal planar 120° 3 1 Trigonal planer SO2 Bent <180° 4 0 Tetrahedral CCl4 Tetra 109.5° 4 1 Tetrahedral NH3 Trigonal < 109.5° geometry (actual shape) pyramidal 4 2 Tetrahedral H2O Bent < 109.5° 4 3 Tetrahedral HF Linear 180° 5 0 Trigonal bipyromidal PCl5 Trigonal bipyromidal 90° and 120° 5 1 Trigonal bipyromidal SF4 Distorted tetrahydron <90°, <120° 5 2 Trigonal bypyromidal ICl3 T-shaped <90°, <120° 5 3 Trigonal bypyromidal I3- Linear 180° 6 0 Octahedral SF6 Octahedral 90° 6 1 Octahedral BrF5 Square pyramidal <90° 6 2 Octahedral XeF4 Square planar <90° [3/23/09] Polar bonds + molecules non polar covalent bond o when atoms in a bond pull equally, the bonding electrons are shared equally ex. all diatomic molecules are non polar polar covalent bonds o between atoms where electrons are shared unequally o *the more EN (electric negative) atom attracts electrons more strongly and gains a slightly negative charge, the less EN atom gains a slightly positive charge ex. Hδ+-Clδ one way is to put a lower case delta - δ on top of each atom, the one on top of the H will receive a δ+ and the Cl a δ– or you can make a positive sign on the H and an arrow continue to the Cl Difference in EN Type of bond (all covalent) Example 0-0.4 Non polar covalent H2 (0) 0.4-1.0 Moderately polar H-Cl (0.9) 1.0-2.0 Very polar H-F (1.9) ≥ 2.00 Ionic Na-Cl (2.1) Polar molecule – one end of the molecule is slightly negative and the other is slightly positive o sometimes called a dipole Symmetry o polar bonds and not symmetric shapes produce a polar molecule ex. H2O is polar even though its symmetric because it is bent needs to be polar along x and y axis o polar bonds that are symmetric produce non polar molecules ex. O=C=O (with a plus on top of the C with arrows going both ways) since its symmetric and linear the bond polarity cancels each other out Chapter 11 6/13/2009 10:13:00 PM [3/25/09] Classifying reactions (not part of chap 11) Combination/synthesis o 2MG(s) + O2(g) 2MGO o when two or more substances react to produce one new substance Decomposition o 2MGO(s) 2MG(s) + O2 Single replacement/double replacement o One element replaces another in a compound o Zn(s) + Cu(NO3) Cu (s) + Zn(NO3) Double replacement o Exchange of cat ions between 2 compounds o Na2S + Cd(NO3)2 CdS + N NaNO3 Combustion o Burning o An element or a compoundreacts with O2 Usually products are CO2 H2O o 2C8H18 + 25 O2 19 CO2 + 18 H2O Chapter 11 Solid, liquid, gas Solid o Most dense, except for ice o Definite shape, definite volume. Liquid o Medium density o Indefinite shape, definite volume Gas o Low density. o Indefinite volume and shape Attraction and forces Attractions between molecules. o Intermolecular forces o Weaker then intra molecular forces o Defines the state of the matter Van der Waals (London dispersion forces) o Weakest form o Caused by the motion of the electrons. Occurs between non-polar ad polar molecules Dipole-Dipole forces o Between 2 Polar molecules o Slightly negative region of one molecule is attracted to the positive region of another. o Higher molar mass has higher boiling point, if they have the same type of molecular bond Hydrogen bond o Attractive forces in which a hydrogen covalently bonded to a highly electro-negative atom (N, O, F) o Strongest form – highest boiling point Surface tension o Resistance of liquid to an increase in surface area. o Energy required to overcome intermolecular forces in liquid The stronger the intermolecular force the higher the surface tension. Viscosity o High viscosity= high resistance to flowing. Capillary Action o Spontaneous rising of a liquid in narrow tube. Cohesive Intermolecular forces among molecules of liquid Adhesive Intermolecular forces between liquid molecules and its container. [3/26/09] Capillary action cohesive – intermolecular forces among molecules of liquid adhesive – forces between liquid molecular and container Heating curve for water B – 0° C D – 100° C E – gas is really vapor [3/27/09] ΔHfus – molar heat of fusion Heat absorbed by one mole of a solid as it melts to a liquid at its melting point Water: 6.01 KJ / mol (to melt one mole to water- B) o How many grams of ice at 0 C will melt if 2.25 KJ of heat is added? 2.25 KJ / 6.01 (KJ/mol) = .374 mol H2O x 18 g / mol = 6.74 g ice ΔHsolid = - ΔHfus Go from liquid to solid ΔHvap = molar heat of vaporization Amount of heat to vaporize 1 mol of liquid to vapor at boiling point Water: 40.7 KJ / mol (to vaporize one mol of water – D) o This plateau is much greater, since more energy is required Since its easier to break bonds of a solid then of a liquid ΔHvap = - ΔHcond Go from vapor to liquid Heat: q Measured in joules or calories o 4.184 J = 1 cal Heat capacity Amount of heat required to increase the temperature of an object by 1 degree Celsius Specific heat (c) Amount of heat required to increase temperature by 1 g of substance by 1 degree Celsius J/g° C Cal /g° C Water 4.184 1 Ice 2.1 .5 Iron 0.46 .11 q = mcΔT q – heat absorbed/ released o if positive absorbed o if negative released m – mass (g) c – specific heat ΔT – change in temperature (always final – initial ) o Tf - Ti Ex. 27 g H2O from 10 C to 90 C (answer in J) o (27 g)*(4.184 j/g°C)*(80°C) = 9037.44 J changing temperature not phase [3/31/09] Sublimation = solid gas Heat = molΔH o Change phase not temperature 49.5 g liquid water boiled at 100°C. then heat vapor to 120° C. how much heat is required? Heat of vaporization for water is 2.1 j/g° C 49.5 g /18 g/mol = 2.75 mol 2.75 mol x 40.7 kj/mol = 11.93 KJ q = 49.5 (2.1 j/g C)(20 C) = 2079 J = 2.079 KJ answer: 14.009 KJ 33.3 g ice at 0 C heated until steam at 150 C. Calculate heat required. Info o Specifc heat for liquid = 4.184 j / g C o Heat of fusion for water = 6.01 KJ/mol o Specific heat of water vapor = 2.1 j /g C o Heat of vaporization for water = 40.7 kj/mol Steps o S L - 0° C 1.85 * 6.01 kj/mo = 11.1185 KJ o L - 0° 100° C 33.g (4.184 j/gC)(100°C) = 13932 j 13.9 KJ o L V - 100° C 1.85 mol * 40.7 kj/mol = 75.3 KJ o V – 100° 150° C 33.3 g (2.1 J/gC)(50°) = 3496.5 J 3.5 KJ o answer: 103.8 Vaporization liquid vapor Evaporation When vaporization occurs at the surface of a liquid that’s not boiling [4/6/09] X axis – temperature (Celsius) Y axis – pressure Phases on the right is vapor In the middle its water on the left is ice Triple point Where all three lines meet, pressure and temperature where all three phases exist in equilibrium with each other Along the lines there is equilibrium between the phases they separate Critical point Liquid and gas become super critical fluid Questions – 514 Q 84: o A. Normal bp: 184.4 C o B. Normal mp: 113.6 C C. Solid Chapter 12 6/13/2009 10:13:00 PM Chapter 12 (solutions) sections 4,5, and 7 [4/2009] Solubility Maximum quantity of a substance that will dissolve in a certain amount of water at a specified temperature Graphs X = temperature Y = grams dissolved in 100g H2O The curve will show a saturated solution o Unsaturated solution Contains less dissolved solute then the amount of a that solvent can normally hold at that temperature o Supersaturated solution Solution that contains more solute than could be dissolved Concentration can be expressed in different ways Molarity = mol solute / L solution o Symbol (M) Molality = mol solute / Kg solvent o Symbol (m) 500 grams H2O produce .06 molal KI solution. How many grams KI dissolve x / .5 = .06 .03 mol *166 g / mol = 4.98 g KI o since solvent find g solution and subtract g solute to get g solvent (and change into kg) Mole fraction (X) = mol solute / totally mol solution o C2H6O2 – 1.25 mol XC2H6O2 = 1.25/5.25 = .238 o H2O – 4 mol 4/5.25 = .762 Mass percent = (mass of solute / mass of solution) * 100 Colligative properties Properties that depend only on the amount of solute and not on their identity 1. Vapor pressure lowering o a solution has lower vapor pressure then its pure solvent 2. Boiling point elevation o difference in temperature between boiling point of solution and boiling point of pure solvent o ΔTb = Kb * M Kb – molal boiling point elevation constant Water: Kb = .512 °C/M o Q: 1.5 m NaCl solution in H2O. what is boiling point? ΔTb = (.512 °c/m)(1.5 m) = .77 °C 100.77 °C (pure water boiling point is 100 so you add .77 [4/21/09] 3. Freezing point depression o ΔTf – Kf * m Kf: molal freezing point depression constant H2O – Kf = 1.86 °C/m o Q. 100 g C2H6O2 in .5 kg H2O. calculate freezing point 100g / 62 g/ mol = 1.612 mol 1.612 mol/ .5 g = 3.224 m 3.224 * 1.86 °C / m = 6°C 0C – 6°C = 6 °C [4/22/09] Q: suppose that there are two water solutions, one of glucose (180 g/mol), the other of sucrose (342 g/mol) each contains 50 grams of solute in 1,000 grams of water. Which has the higher boiling point? The lower freezing point? Glucose: o 50 g/180 g/mol = .27 mol o ΔTb = .512 (.27/1) = .14 + 100 = 100.14 o ΔTf =1.86(.27) = .52 -.52 C Sucrose: o 50 g / 342 g/mol = .146 mol o ΔTb = .512(.146/1) = .07 + 100 = 100.07 o ΔTf = 186(.146) = .27 -.27 C Q: Calculate the freezing point depression of a benzene solution containing 400 grams of solvent and 200 grams of solute (C3H6O). Kf for benzene is 5.12 C/m 200g /58 g/mol =3.44 mol (3.44 mol /.4 kg)5.12 C/m = 44.14 C o if given freezing point, subtract this number from that Heterogeneous mixtures: Suspension o Mixture that particles begin to settle out of solution upon standing o greater then 1000 nm diameter In a solution they are about 1 nm Colloid o Particles range in size from 1 nm to 1000 nm chapter 15 6/13/2009 10:13:00 PM [4/24/09] Acids and Bases Acids o Sour o Dissolve many metals o Litmus paper turns red o HCl, H2SO4, HNO3 Base o Bitter o Slippery feel o o o o o Litmus paper turns blue NaOH KOH NH3 NaHCO3 Definitions Acid Base Arrhenius Produces H+ in solutions Produces OH- in solution Bronsted Lowry H+ donor H+ acceptor Lewis Accept electrons pair Donate electron pair formula o NH4+ + OH- NH3 + H2O NH4+ - acid (H+ donor) OH- - base (H+ acceptor) NH3 - conjugate base (loses an H+) H2O - conjugate acid (gains an H+) o Some substances can be both acids and base, these are called amphoteric concentration o [H+] = 1 x 10-7 M o [OH-] = 1 x 10-7 M They are neutral o Kw = [H+] x [OH-] = 1 x 10-14 M2 Ion product constant for H2O o [H+] > [OH-] acidic o [H+] < [OH-] base ex. [H+] = 1 x 10-5 M then the [OH-] = 1 x 10-9 M divide - 10-15 / 10-5 its acidic pH scale o pH = -log[H+] (H+ = H3O+) o range from 1 to 14 1 to 7 – acid 7 – neutral 7 to 14 – basic o ex. OH- = 4 x 10-11 M 14-10.4 = 3.6 pOH o pOH = -log[OH-] o 1 to 7 – basic o 7 – neutral o 7 to 14 –acidic pH + pOH = 14 the hardest [4/27/09] be Questions: 1. Calculate pH if [OH-] = 4.3 x 10-11 M o pOH = -log (4.3 x 10-11) 14-ans = 3.65 ph 2. [OH-] = 1 x 10-3 M, what Is [H+]? Basic, acidic, natural? o 1 x 10-11 M Log scale Every pH change of 1 is a concentration change of 10x Given pH, find [H+] o Method 1 pH = -log x -ph = log x x = log-1 (-pH) o Method 2 pH = -log x -ph = log x 10^(-pH) = x ex. pH = 4.8 o –10^-4.8 = 1.6 x 10-5 M [5/4/09] Acid base indicator Its acid form and base form have different color in solution Strength of acid + bases Strong acids – completely ionize in solution o Ex. HCl, H2SO4, HNO3 HCl + H2O H3O+ + Cl- - 100 % ionized Weak acid – partially ionized in solution o Ex. Acetic acid CH3COOH + H2O H3O+ + CH3COO- (partial ionization – can tell by double arrow) Strong Base o Ex. Mg(OH)2 , Ca(OH)2 Weak base o Ex. NH3 Concentration / strength o Concentration How much acid is dissolved in solution Concentrated/ dilute o Strength Extend of ionization Strong weak Neutralization reaction Acid +Base Salt + Water o Mix solution of strong acid and strong base and we get a neutral solution results o Salt = compound consisting of anion from aid and cation from base Ex. HCl + NaOH H2O + NaCl Ex. H2SO4 + 2KOH 2H2O + K2SO4 Q: How many moles of potassium hydroxide are needed to completely neutralize 1.56 mol of phosphoric acid? o H3PO4 + 3KOH 3H2O + K3PO4 1.56 mol x (3 KOH / 1 H3PO4) Titration The process of adding a known amount of solution of known concentration to determine the concentration of another solution Standard solution (know concentration of) we kept titrating until neutralization occurred, which is called the end point Ex. a 25 ml solution of H2SO4 is neutralized by adding 18 ml of 1 M NaOH what is concentration H2SO4? o H2SO4 + 2NaOH 2H2O + Na2SO4 1M = x mol / .018 L .018 mol NaOH .009 mol H2SO4 .009 mol / .025 L = .36 M [5/5/09] Buffer A solution where the pH remains relatively the same Made of weak acids and its salt or a weak base and its salt Ex. CH3COOH + NaCH3COO = acid buffer o Acetic acid + salt o Ex. add acid: if H+ were added to this then the salt would split up into its ions and it would combine with CH3COOo Ex. Add Base: OH- + CH3COOH H2O + CH3COO- 6/13/2009 10:13:00 PM [5/5/09] Thermo chemistry Potential energy o Energy stored in chemical bonds Kinetic energy o Energy of motion Heat transfer or work o 1. Heat – symbol “q” amount of energy transferred from one object to another, higher temp. to lower temp. o W= o ΔE = endothermic – reaction that absorbs heat q>0 exothermic - reaction that releases heat q<0 can be found by MCΔT -PΔV ΔV > 0 W < 0 Work being done by system ΔV < 0 W > 0 Work done on system Unit is jules V – final – initial q+w Internal energy in system Unit is jules + - Q Endothermic Exothermic W Work done on Work done by system system Energy in Energy out ΔE o 101.3 J = 1 L*atm [5/6/09] Q: System compresses 5L to 3.5 L pressure 740 mmHg realeses 20.6 KJ heat find ΔE -(740/760)*-1.5L = 1.46 Heat of 1.56 * 101.3 J = 148 J 148 j - 20.6 kj = -20.47 KJ reaction Exothermic o CaO (s) + H2O Ca(OH)2 (s) ΔH = -65.2 KJ (of heat must be released) o Ca(OH)2 (s) + 65.2 KJ Endothermic o Ca(OH)2 (s) CaO (s) + H2O ΔH = 65.2 KJ CaO (s) + H2O – 65.2 Kj NaHCO3 (s) Na2CO3 (s) + H2O (g) + CO2 (g) ΔH = 129 KJ Calculate heat required to decompose 2.24 mol NAHCO3? 2.24 mol * (129 KJ / 2 mol) = 144.5 KJ Q: 3H2 +N2 2NH3, ΔH = -4.5 KJ o If 16 g NH3, find heat released? o (16/17) = .941 Mol .941 mol (-4.5 KJ/ 2) = -2.118 KJ Heat of combustion o Q: 2 o o Heat of reaction for complete burning of one mole of substance o Ex. Methan CH4 CH4 + 2O2 CO2 + 2H2O , ΔH = -802.3 KJ 267 KJ heat o mass CH4? = 276 KJ (1 mol / 802.3 Kj) = .333 mol .33 mol X 16 g / mol 5.32 g Enthalpy = ΔH [5/11/09] Hess’ law C(s, diamond) C(s, graphite) o A. C (s, graphite) + O 2 CO 2 ΔH = -393.5 o Want o o B. C (s, diamond) + O2 CO 2 ΔH = -395.4 to use reactions a and b to get first reaction Reaction B stays the same Reaction A is flipped The sign is flipped so its now 393.5 KJ o The two reactions can now be added (393.5) + (-395.4) = ΔH= -1.9 KJ When adding two or more reactions, you can also add heats of reactions o Flip a reactions ΔH: change sign o Multiply a reaction multiply everything by same coefficient o Sometimes reactions will have to be multiplied and fliped Q: C + ½O2 CO, find ΔH o C + O2 CO2, ΔH = -393.5 KJ o CO + ½O2 CO2, ΔH = -283 KJ Flip second reaction: CO2 CO + ½O2 , ΔH = 283 KJ Add both reactions together: C + O2 + CO2 CO + ½O2 + CO2 Cross out: C + ½O2 CO ΔH = -110.5 KJ Standard heats of formation Symbol- ΔH°f Change in enthalpy that accompanies the formation of one mole of a compound from its elements ΔH°f = 0 for free elements and diatomic [5/13/09] ΔH° = Σ(np ΔH°f,product) – Σ (nr ΔH°f,reaction) standard heat of reaction = Σ( # mol product x standard heat of formation) – Σ(# mol reaction x standard heat of formation) Ex. 2 CO + O2 2CO2, ΔH = o ΔH = 2(ΔH°f CO2) – (2ΔH°f CO + 1ΔH°f O2) o = 2(-393.51) – (2 (-110.53) + 0) o = -566 KJ Ex. 2NO + O2 2NO2 o 2(22.18) – (2(90.25) - 0) = -113 KJ Gibbs free energy energy available to do work symbol ΔG Spontaneous reaction Occurs naturally Releases free energy ΔG < 0 Non spontaneous reaction Doesn’t occur naturally Requires energy input ΔG > 0 Entropy Measure of a disorder of a system Law of disorder o Natural tendency for system is to move in the system of more disorder (randomness) Symbol ΔS o Increases in S favors spontaneous reaction For a given substance the entropy for the Ssolid < Sliquid < Sgas S increases when divide substances In reaction when # mol product > # mol reactant S increases When t increases , s increases [5/14/09] Gibbs Helmholtz Equation ΔSrxn ΔG = ΔH – TΔS o Temperature is in Kelvin ΔG < 0 o Spontaneous ΔG > 0 o Non spontaneous = Σ(npS°products) – Σ(nrS°reactnats) 6/13/2009 10:13:00 PM Rates and Equilibrium Rate = measure of speed of any change in some time interval o Usually- Δ[ ] / time Activation o Minimum energy that colliding particles must obtain in order to react o Ea is activation energy This is exergonic o Large activation energy slower process o endergonic o the top of activation energy is the activated complex which is a transition state What factors affect the rate of a reaction o Temperature increases Rate increases o Particle size is smaller (surface area) rate increases o Increases in concentration increase in[ ] and increase in rate o Catalyst Speeds up reaction, without being used Lower activation energy (catalyst supposed written on time of arrows) Rate law o Expression for rate of reaction in terms of [ ] of reactions o Rate constant (K) [5/15/09] equilibrium conversion of reactants to products and conversion of products to reactants occur simultaneously double arrow symbolizes a reversible reaction o one reaction is the forward reaction, the other is the reverse reaction rate of forward reaction is same as rate of reverse reaction o called dynamic equilibrium Le Châtelier’s principle A system at equilibrium responds to a stress by moving in the direction that relieves the stress o Had graph Stresses: temperature, pressure, concentration, volume o If any of these are changed, the reaction will shift in another direction to balance the stress [5/18/09] cont. Concentration o Ex. H2CO3 CO2 + H2O At equilibrium. If you add H2CO3 forward reaction is favored, shifts to right At equilibrium, add CO2. Shifts to left At equilibrium remove H2O, shift to right o Changing the concentration any reactant or product disturbs the equilibrium and the system adjusts to minimize the effect Temperature o Increases the temperature causes equilibrium position to shift in direction that absorbs heat If decreases, then shifts to direction that releases heat o Ex. 2SO2 + O2 2SO3 (ΔH= -x exothermic) If exothermic then heat is product, if endothermic then heat is a reactant So reaction shifts left Pressure o If increases in pressure, system wants to decrease it, so it shifts in direction of fewer moles of gas o Ex. N2(g) + 3H2(g) 2NH3(g) Only look at moles of gas If pressure increases, shifts right If pressure decreases, shift left Volume o If volume rises, pressure decreases o If volume decreases, pressure increases o Ex. 2KClO3(s) 2KCl(s)+3O2(g) if volume decreases, shifts left Q. PCl5(g) PCl3(g) + Cl2(g) ΔH= 92.5 KJ o Add Cl2 left o Increases pressure left o Decrease temperature left o Increases volume right Q. CaCO3(s) CaO(s) + CO2(g) o Add CaCO3 no effect Equilibrium Constant (Keq) Ratio of product concentrations, to reactant concentrations, with each concentration raised to a power equal to the number of moles of the substance in balanced equation Ex. aA +bB cC + dD o Keq = [C]c[D]d / [A]a[B]b Keq > 1 products favored over reactants Keq < 1 reactants N2O4(g) 2NO2(g) A liter at equilibrium at 10 C, .0045 mol N2O4, .03 mol NO2 Calculate Keq o .032 M2 / .0045 M = .02 M unit will be different every time at equilbirum: 2 L flask o .2 mol PCl5 o .3 mol H2O o .6 mol HCl o .3 mol POCl3 PCl5(g)+H2O(g) 2HCl(g)+POCl3(g) o Find Keq Keq = (.3 M)2(.15 M) / (.1 M)(.15 M) = .9 M [5/19/09] Q. 1 mol H2 and 1 mol I2. In a 1 L flask. At eqm, 1.56 mol HI H2+I2 2HI To solve this we need to make an ice chart (make one when given initial concentrations) H2 2HI Initial 1 I2 1 Change -1.56/2 -1.56/2 + 1.56 Equilibrium .22 .22 1.56 0 Keq = 1.56 m2 / (.22m)(.22m) = 50.3 Q. at eqm [SO3] = .25 M, calculate K Given: .6 mol SO2, .06 mol O2, in 2 L container 2SO2(g) + O2(g) 2SO3(g) Keq = [SO3]2 / [SO2]2[O2] 2SO2 O2 2SO3 Initial .3 Change .3-.25 = .05 (.3-.25)/2 = + .25 .125 Equilibrium m]2 .05 m]2 .3 0 .175 .25 m-1 Keq = [.25 / [.05 [.175 m] = 143 Q. Initial - 3 mol H2, 3 mol I2, 1 L container. Keq = 45.9 Find all at eqm H2 2SHI Initial 3 I2 3 Change -x /2 -x /2 +x Equilibrium 3 – (x/2) 3 – (x/2) X 0 45.9 = x2 / (3-(x/2))2 radicalize entire thing √45.9 (3-(x/2)) = x (6.77*3) – 6.77x/2 = x 20 - 3.85x = x 20 = 4.86x x = 4.11 4.11 is concentration of HI o So 3-(4.11/2)/ = .95 M Which is concentration of H2 and I2 [5/22/09] N2O4(g) 2NO2(g) Kc = 0.513 Initially: o [N2O4] = .05 M Find: eqm concentrations o Keq = N2O4 2NO2 Initial .05 0 Change -X 2X Equilibrium .05-X 2X (2x)2 / (.05–x) = .513 4x2+.513x-.026 = 0 x = .0395 or a negative number (but cant be negative) Plug in x in equilibrium .01 M, and .08 M At a certain temperature Keq = .05 for the reaction: N2(g) + O2(g) 2NO(g) What is the concetration of NO at equilibrium when placed in a flask with .8 M N2 and .2 M O2 initially? N2 O2 2NO Initial .8 .2 0 Change -x -x 2x Equilibrium .8-x .2-x 2x 6/13/2009 10:13:00 PM [5/26/09] Redox Oxidation o Loss of electrons Reduction o Gain of elections (OIL RIG - Oxidation involved Loss, Reduction involves gain) Mg + S Mg2+ + S2o Sulfur is reduced oxidizing agent o Magnesium gains reducing agent Ex. Silver nitrate reacts with copper to form copper (II) nitrate and silver. What is oxidized? What is reduced? o Copper – reduced o AgNO3 – oxidized Oxidation number o A positive or negative number assigned to an element to indicate its degree of oxidation or reduction Chang of S S2 Oxidation number -2 Rules for assigning oxidation number o 1) Oxidation number of monatomic ion is equal to its charge Ex. Br- -1 o 2) Oxidation number of hydrogen in a compounds is +1, except when in metal hydrides, such as NaH, where it is -1 o 3) Oxidation number of oxygen in a compound is -2, except in peroxides, H2O2, where it is -1 o 4) Oxidation number of uncombined element is zero (ex. diatomic molecules…) o 5) For neutral compound, sum of oxidation numbers = 0 o 6) For polyatomic ions, sum of oxidation numbers = charge of polyatomic ions ex. o SO2 S: +4 O: -2 o CO32+ C: +4 O: -2 o Na2SO4 (do one on outside first, then figure out one in middle) Na: +1 S: +6 O -2 o (NH4)2S N: -3 H: +1 S: -2 o KMnO4 K: +1 Mn: +7 O: -2 [5/27/09] Use oxidation numbers to identify oxidizing agent + reducing agent 2AgNO3 + Cu Cu(NO3)2 + 2Ag o AgNO3 – oxidizing agnet o Cu – reducing agent Cl2 + 2HBr 2HCl + Br2 o Cl2 – Oxidizing agent o HBr – reducing agent Balancing redox reactions in acidic solution 1) Use oxidation numbers to write out half reactions o Ex. MnO4- + Fe2+ Fe3+Mn2+ MnO4- Mn2+ Fe2+ Fe3+ 2) Balance each half reaction separately o a) Balance all elements except H and O o b) Balance O by adding H2O MnO4- Mn2+ + 4H2O o c) Balance H by adding H+ 8H+ + MnO4- Mn2+ + 4H2O o d) Balance charge by adding e 5e- + 8H+ + MnO4- Mn2+ + 4H2O Fe2+ Fe3+ + 1e- 3) Multiply half reactions so that they have equal number of electrons o 5e- + 8H+ + MnO4- + 5Fe2+ Mn2+ + 4H2O + 5Fe3+ + 5e4) Add, simply and check o The 5e- cancel each other 8H+ + MnO4- + 5Fe2+ Mn2+ + 4H2O + 5Fe3+ Check that charges balance Ex. HNO3 + H2S S + NO o HNO3 NO HNO3 NO + 2H2O 3H+ + HNO3 NO + 2H2O + 3e must multiply this by 2 o H2S S H2S S + 2H+ + 2e must multiply this by 3 + 6H + 2HNO3 + 3H2S +6H+ + 6e- +2NO + 4H2O + 6e [6/1/09] Electrochemistry Electrochemical conversion between electric and chemical energy o Voltaic cells (galvanic cells) is where this process takes place Convert chemical energy into electric energy o Anode is where oxidation takes places Ex. Zn o Cathode were reduction takes place Ex. Cu Way to remember o An Ox Red Cat o Each are called half cells o Together they produce energy Connected by a salt bridge, which is the redox reaction Electrolytic cells Supply energy to bring about a chemical change electrons are pushed from anode to cathode o redox reanction is non spontaneous [6/2/09] Organic chemistry Compounds containing carbon hydrocarbons o Contain hydrogen and carbon o 3 classes saturated Alkanes All carbon – carbon bonds are single bonds o Simplest form is one c with four H called Methane all alkanes end with –ane formula for all is CnH2n+2 methane, ethane, propane, butane, pentane, hexane, heptane, octane, nonane, decane unsaturated aromatic o structural isomers have same molecular formula but different structures [6/3/09] continued hydrocarbons saturated o Branched chain alkanes Substituent group – atom or group of atoms that take place of hydrogen atom in hydrocarbon molecules Called alkyl group = hydrocarbon substituent To name group Get rid of -ane and add –yl o Ex. ethyl Naming branched chain alkanes 1) find the longest chain of carbons not linearly 2) number the carbons, starting at end closest to substituent groups 3) name substituent groups and add numbers form: number - group o ex. 2 – methyl 4) use prefixes to indicate appearance of more then one of the same group ex. if you have two methyls it becomes dimethyl o sprefixes: di, tri, tetra, penta 5) list substituent groups in alphabetical order (not including prefixes) ex. 4 – ethyl 2,3 – dimethyl 6) put this together with rest of group (no spaces, hyphens between number and letters, commas between numbers) ex. 4-ethyl-2,3-dimethylheptane [6/4/09] unsaturated hydrocarbon o 1) Alkanes have a C = C (double bond) end in –ene, formula is CnH2n form: Number double bond same way we number substituent groups If double or triple bond, number so that the double bond or triple bond would have the lowest number Put the number where double bond is where you would place the substituent group before the name of hydrocarbon o 2) Alkynes have a carbon carbon triple bond formula is CnH2n-2 end in –yne Put the number where triple bond is where you would place the substituent group before the name of hydrocarbon [6/5/09] Hydrocarbon classes o Aromatic hydrocarbons Derived from benzene (C6H6) Ring shape Drawn as a hexagon with a circle in the middle Each corner has a carob with a hydrogen coming off of it Naming Start with substituent group closest to lowest numbers If benzene in the substitution group then it has the name Phenyl Replacing Hydrogens o Functional group - Can be a nonmetal atom or a small group of atoms 1) Halogen anything in group 7 R- X (rest of chain + this) naming with chloro, fluoro, bromo, ioh o ex. 1,3-dichlorobutane 2) alcohol replacing H with –OH : a hydroxyl group R- OH ( rest of chain + OH) 3) Carboxylic acid C = O, C – OH, C - R (same C) Carboxyl group -COOH 4) Ester R – (C double bonded with O and single bodn with another O which is bonder with) – R 5) Amine R – NH2 Amino group [6/8/08] continued o functional group 6) Amide R – (C double bonded with O and bonded with) – N - (bonded a H and a R) 7) Keytone O = C (which is bonded to two diffrent R) 8) Aldehyde O = C (bonded with one H and one R) 9) Ether R-O–R 6/13/2009 10:13:00 PM Final Significant figures Changing units Accuracy vs precision models Atomic mass moles Avogados number Covalent and ionic bonds Molecular and empirical formula Percent composition Naming acids Stoichiometry, limiting reactant o Theoretical o Excess reactant Molarity Concentration Solubility rules o Precipitations reactions Complete molecular, complete ionic, net ionic Gas laws o Know direct or indirect Kinetic molecular theory What is an ideal gas o Real gases act like them under high temperatures and low pressure o 1 mol = 22.4 L at STP (273, 22.4, 1 ) law of effusion partial pressure waves o frequencies, ray length, type of rays – don’t need to know order as go further from nucleus o ladder – spaces, higher energies o electron must jump – quantum of energy o absorb and release orbitals o electron configurations o orbital energy diagrams o afbau principal o exclusion o hunds rule o exceptions trends groups o elements bonds lewis structures o resonance structures VSEPR theory Polar vs non polar o Drawing polar bonds If they are on same axis they cancel out and are not polar Forces o Van der wells, dipole, hydrogen Single and Double replacement Heating Curve Phase diagram Solubility curve Molarity and Molality Boiling point elevation Colligative properties Conjugate acids and bases Strength of acids and bases Concentration of Acids and Bases Titration ThermoChemistry o Probably can lay off buffers (that’s what she said(not direct quote)) o Still haveto know how to do standard heat of formatio questions (she will give it) o Entropy o Gibbs German guy equation o Raes if reation o Equilibrium o Pics of such o Chattlears principle o equation for euilibrium and ice charts(only for gasses) Redox Electrochemistry Organic Chemistry last semester o midterm – 30 o o o o test -20 quiz – 20 lab – 15 hw -15