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Writing to Learn Identifying Graphs of Linear Functions

Precalculus: Graphical, Numerical, Algebraic | 8th Edition | ISBN: 9780321656933 | Authors: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock ISBN: 9780321656933 190

Solution for problem 2.1.1.87 Chapter 2.1

Precalculus: Graphical, Numerical, Algebraic | 8th Edition

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Precalculus: Graphical, Numerical, Algebraic | 8th Edition | ISBN: 9780321656933 | Authors: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock

Precalculus: Graphical, Numerical, Algebraic | 8th Edition

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Problem 2.1.1.87

Writing to Learn Identifying Graphs of Linear Functions (a) Which of the lines graphed on the next page are graphs of linear functions? Explain. (b) Which of the lines graphed on the next page are graphs of functions? Explain. (c) Which of the lines graphed on the next page are not graphs of functions? Explain.

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Chapter 15- Solubility ● K = [A] a [B]b sp eq eq ● Q < K sp ○ Reaction goes to the right ○ Can dissolve more solid and add more ins ○ Unsaturated ● Q = K sp ○ Reaction is at equilibrium ○ Cannot dissolve more solid and add more ions ○ Saturated ● Q > K sp ○ Reaction goes to left ○ Precipitate in contact with saturated solution Chapter 16- Thermodynamics ● First Law of Thermodynamics: ΔH ○ Heat of Reaction ■ Exothermic reactions: ● Give off heat and warm up the surroundings ● Ex) Combustion reactions ● -ΔH ● Heat of vaporization ■ Endothermic reactions: ● Give off “cold” and cool down the surroundings, absorbs heat. ● Ex) cold packs ● +ΔH ● Heat of fusion ○ Heat of formation ■ Standard State ● Pure solid or liquid ● 1M solutions ● Gases at 1 atm ● Usually 25°C ■ ΔH° (f) kj/mol ■ H ,2N ,2O 2 F 2 Cl2→ gas ■ Br →2liquid ■ I 2 P4, As4, S8, C (graphite) → solid ■ Metals are solid except Hg , [(l)and Ga], noble gases ○ Hess’s Law ■ State function ● Change independent of path ● Reversible change ● A + B → C ΔH 1 ● C → D ΔH 2 ● A + B → D ΔH + ΔH 1 2 ● A + B → C + D ΔH1 ● C + D → A + B -ΔH1 ● Flip equation → change sign ● Multiply equation, multiply ΔH ● Add equations, add ΔH ■ ΔH reaction: ● ∑{ΔH° (products)} - ∑{ΔH° (reactants)} f f ● ΔH° (flement) = 0 ● Second Law of Thermodynamics: ΔS to ΔG ○ Spontaneous reactions take place without continual input of energy ○ Entropy of Universe, S univ ■ ΔS univ 0 → spontaneous ■ ΔS univ 0 → nonspontaneous ■ ΔS = ΔS + ΔS universe system surroundings ■ ΔS surrΔH rxn ΔG = ΔH + TΔS rxn rxn rxn ■ ΔG rxn 0 → spontaneous ■ ΔG rxn 0 → nonspontaneous ○ ΔG (kj) ■ Free energy of reaction ● + endergonic → nonspontaneous ● - exergonic → spontaneous ■ State equation ■ ∑{ΔG° (pfoducts)} - ∑{ΔG° (refctants)} ■ ΔG° (flement) = 0 ○ Temperature of Spontaneity change ■ Set ΔG = 0 ■ T = ΔH°/ΔS° ■ At equilibrium, ΔG = 0 ○ Phase change entropy ■ Boiling point ● Before → nonspontaneous ● After → Spontaneous ● At BP → ΔG = 0 ● BP = ΔH° vapΔS°vap ● Third Law of Thermodynamics: Entropy ΔS ○ S of a substance cannot be zero, except on a perfect crystal at 0 K. ○ Dispersal of energy over the system; randomness or disorder ○ Units: ■ J/mol k ○ Phase ■ S < L < G ○ Pure vs. Mixture ■ Pure < Mixture ○ Temperature ■ Increase T, increase S ○ Pressure ■ Increase P, decrease S ○ Molecule Size ■ Increase size, increase S ○ Positive if S increases ○ Negative if S decreases ○ ΔS = ∑{ΔS°(products)} - ∑{ΔS°(reactants)} ○ ΔS (element) ≠ 0 ● Equilibrium and ΔG ○ Reaction line ■ A + B C + D ■ ΔG ● Magnitude: energy change to get to equilibrium ● Sign: direction to get to equilibrium ○ ΔG ∝ ln(Q/K) ○ ΔG = RTln(Q/K) ○ ΔG = RTln(Q) - RTln(K) ○ At Standard state: ■ Q = 1 ■ ΔG° = -RTln(K) Chapter 17- Redox ● Oxidation and Reduction ○ Oxidation ■ Gain oxygen ■ Lose hydrogen ■ Lose electrons ○ Reduction ■ Lose oxygen ■ Gain hydrogen ■ Gain electrons ● Ionic redox reactions ○ Identify what is being oxidized and reduced ○ Balance equation → must have equal numbers of electrons lost and gained ● Non-ionic redox reactions 1. Assign oxidation numbers (fake charges) ■ Metal cations → charge on cations ● Alkali = +1 ● Alkaline earth = +2 ● Al, Ga = +3 ■ Non-metals ● F = -1 ● O = -2 ● H = +1 ■ If you still cannot assign oxidation numbers, assign appropriate negative charge to unassigned atom closest to F. 2. Identify what is being oxidized and reduced 3. Balance electron transfer ■ Balance redox atoms using appropriate coefficients on whole species ● Reducing agent ○ Loses electrons and is oxidized in the reaction. ● Oxidizing agent ○ Gains electrons and is reduced in the reaction. ● Half-equations 1. Eliminate spectator ions 2. Identify what is being oxidized and reduced 3. Balance electrons ○ In acidic/basic solution 1. Assign oxidation numbers 2. Identify if being oxidized or reduced 3. Add electrons on appropriate side 4. Balance charges with H (if in acidic solution) or OH (if in basic solution) 5. Balance number of oxygen atoms 6. Check number of hydrogen atoms ● Potential ○ Positive potential is good ○ +E° red better oxidizing agent ○ +E° →oxetter reducing agent ● Cell potential (V) ○ E° cell E° red E° ox ● Galvanic Cells ○ Ex) Zn +(s) 2+(aq)n 2+(aq)Cu (s) ○ Zn |Zn 2+ ||Cu2+ |Cu (s) (aq) (aq) (s) ● E and ΔG ○ Potential ■ ΔG° = -nFE° ● F (Faraday) = 96500 J/mol e V - ■ E° = (RT/nF)lnk ΔG° K E° Spontaneous < 0 > 1 > 0 Nonspontaneo > 0 < 1 < 1 us ● Electrolytes ○ Metal → cation + electron(s) ■ Oxidation ○ Nonmetal + electron(s) → anion ■ Reduction ○ Metal + nonmetal → ionic compound ■ Spontaneous redox equation ○ Cation + electron(s) → metal ■ Reduction ○ Anion → nonmetal + electron(s) ■ Oxidation ○ Ionic compound → metal + nonmetal ■ Nonspontaneous redox equation ■ Need continual input of energy ● Electrolytic cell ● Molten ionic compounds ○ Cathode: cation → element ○ Anode: anion → Cathode Anode element ○ Ex) NaCl (l) NaBr (l) Na Br2 ● Aqueous ionic - compounds ○ Cathode: NaBr (aq) H2(g) 2OH Br2 ■ Cation → element AlF3(l) Al F2 ■ 2H O2+ 2e → H + 2 2OH (aq) - + AlF3(aq) H2(g) 2OH O2(g) 4H ○ Anode: ■ Anion → element CuNo 3(aq) Cu O2(g) 4H + ■ 2H O → O + 4e + - 4H + 2 2 CuBr Cu Br (aq) 2(l) 2 ○ Ex) NaCl (aq) CuBr 2(aq) Cu Br2 ● Equations: ○ Charge (C) = current (amps) x time (sec) - ○ 1 mol e = 96500 C = 1 Faraday Chapter 18 – Nuclear Chemistry  Nucleus = protons + neutrons  Protons o Mass: 1 o Charge: +1  Neutrons o Mass: 1 o Charge: 0  In a given atom, number of protons = atomic number (Z) = number of electrons  Mass of atom = mass number (A) = protons + neutrons 14  Ex) 6C  6 protons; 8 neutrons; A = 14  Nuclear Decay o Alpha Decay  Nucleus 1  Nucleus 2 + α particle  Mass: 4  Charge: +2  42He  Ex) 238 U  4 He + 234 U 92 2 90 o Beta Decay  Nucleus 1  Nucleus 2 + β n p+ e - particle   + Mass: 0  Mass 1 1 0 Charge: -1  0 β -1 Char 0 1 -1 14 0 14  Ex) ge 6C  -1 + 7C o Positron Decay  Nucleus 1  Nucleus 2 + positron  p + n β+ Mass: 0  Charge: +1 0 +  +  1 Mass 1 1 0  Ex) 5B  01 + 4Be Char 1 0 1 ge + - o Electron p e n Capture  +  Nucleus 1 + electron  Mass 1 1 0 Nucleus 2  Char 1 0 1 Mass: 0  ge Charge: -1  0-1- 8 0 - 8  Ex) 5B + -1  4Be  Nuclear Decay Factors o Too big – too many protons  Alpha decay o Neutron:Proton ratio  Too many neutrons o Beta decay  Too many protons o Positron decay o Electron capture  Ideal ratio o 1:1 o Even vs. Odd  Mass number o Even  153 stable nuclei o Odd  101 stable nuclei  Even number of protons o Even number of neutrons  148 stable nuclei o Odd number of neutrons  53 stable nuclei  Odd number of protons o Even number of neutrons  48 stable nuclei o Odd number of neutrons  4 stable nuclei 2 6 10 14  1H, 3Li, 5B, 7N o Magic numbers (stability)  2, 8, 20, 28, 50, 82  Decay Chain Reactions o Bismuth – 83 is the largest stable nucleus o Every nucleus after is radioactive and unstable o Ex) 23290h becomes 2082Pb after 6 alpha decays and 4 beta decays  Nuclear reactions o Neutron capture  Can change one isotope of an atom into another 1  0  Either increases number of neutrons (N) or decreases the number of protons (Z)  Increases N:Z ratio o Nuclear Fission  Big nucleus splits into smaller ones + neutrons  Lots of different products produced o Average 2.5 neutrons produced (some escape) o Chain reaction o Critical mass  Amount of material needed so that average 1 neutron per event reacts o Nuclear Fusion  Small nuclei combine into one big nucleus  Energetics o Law of Conservation of Mass and Energy  E = mc 2 2  Joules (J) = kg•m/s  WATCH UNITS o J  kJ o g kg  Binding Energy o Proton  1 amu  1.007276 amu o Neutron  1 amu  1.008665 amu 1 o H atom  1 amu  1.007825 amu o How to find binding energy: 1. Identify how many protons, electrons, and neutrons are in atom  Electrons + protons = H atom  Ex) Carbon-12 has 6 H atoms and 6 neutrons 2. Multiply the precise mass of each with the number of each atom  (6 x 1.007825) = 6.04695 amu  (6 x 1.008665) = 6.05199 amu 3. Add number of H atoms and neutrons  6.04695 + 6.05199 = 12.09894 amu 4. Find change in mass (∆m)  Carbon-12  12 amu  12.09894 – 12 = 0.09894 amu 5. Convert to kg/mol  0.09894 amu = 0.00009894 kg/mol 2 6. Plug in numbers into E = mc 8  E (J) = (0.00009894)(3.0 x 10 )  E = 8.90 x 10 kJ o How to find MeV/nucleon 1. Find change in mass (∆m)  Carbon-12  0.09894 amu 2. Convert to MeV  1 amu = 931.5 MeV  0.09894 amu = 92.16 MeV/atom 3. To find MeV/nucleon, divide by mass of atom  92.16 ÷ 12 = 7.69 MeV/nucleon

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Chapter 2.1, Problem 2.1.1.87 is Solved
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Textbook: Precalculus: Graphical, Numerical, Algebraic
Edition: 8th Edition
Author: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
ISBN: 9780321656933

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Writing to Learn Identifying Graphs of Linear Functions