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In Exercises 67 to 72, use the Binomial Theorem | Ch 8 - 71

College Algebra | 7th Edition | ISBN: 9781439048610 | Authors: Richard N. Aufmann, Vernon C. Barker, Richard D. Nation ISBN: 9781439048610 198

Solution for problem 71 Chapter 8

College Algebra | 7th Edition

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College Algebra | 7th Edition | ISBN: 9781439048610 | Authors: Richard N. Aufmann, Vernon C. Barker, Richard D. Nation

College Algebra | 7th Edition

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Problem 71

In Exercises 67 to 72, use the Binomial Theorem to expand each binomial or find the requested term. Find the fifth term in the binomial expansion of (3x - 4y)7.

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General Chemistry I Study Guide Exam 3 Chapter 7  Valence Shell Electron Pair Repulsion (VSEPR) – predicting molecular shape; basic idea is that electrons repel each other; electrons are found in different domains (lone pairs/single bonds/double bonds/triple bonds) o electrons will arrange themselves as far as possible o arrangements minimize repulsive interactions o make sure to know the different types and bond angles of molecular geometry  Electron domain geometry- arrangement of electron domains around central atom  Bond angle- angle between two adjacent A-B bonds  4 Steps To determine geometry- o Draw lewis structure o Count the number of electron domains around the central atom o Determine electron-domain geometry by applying VSEPR model o Determine molecular geometry by considering the positions of the atoms only  Lone pairs take up more space than bonded pairs of electrons  Van der Waal’s Forces o London forces – natural attraction between all molecules  Increases with molar mass  Size of electron cloud determines strength  Similar molecular weight = same London force strength  Weakest of all forces  Only type between nonpolar molecules o Dipole-dipole forces- attraction between oppositely charged portions of 2 or more polar molecules  The more polar, the stronger the attraction forces (higher melting and boiling point)  Stronger the London forces  Bigger the dipole moment, the more polar the molecule  Hydrogen bonds – special type of dipole attraction where a hydrogen gets trapped between two highly electronegative elements (F, O, N) o Both molecules MUST have a hydrogen directly attached to a F, O, or N. o Strongest attraction of the 3 intermolecular forces  Dispersion forces – result from Coulombic attractions between instantaneous dipoles of non-polar molecules  Valence Bond Theory – atoms share electrons when atomic orbitals overlap o the H-H bond in H2 forms when the singly occupied 1s orbitals of the 2 H atoms overlap o A bond forms when single occupied atomic orbitals on 2 atoms overlap o The 2 electrons shared in the region of orbital overlap must be opposite spin o Formation of a bond results in a lower potential energy for the system  Hybridization- accounts for observed bond angles in molecules that could not be described by the direct overlap of atomic orbitals o If the s orbital and 3 p orbitals hybridize, then it is sp3 hybridization  Example – methane CH4  Steps to determine hybridization- o Draw lewis structure o Count electron domains on the central atom. This will be equal to the number of hybrid orbitals o Draw the ground state orbital diagram for the central atom o Maximize number of unpaired valence electrons by promotion o Combine the necessary number of atomic orbitals to generate required number of hybrid orbitals o Place electrons in hybrid orbitals, putting one electron in each orbital before pairing any electrons  Sigma bond – forms when sp2 hybrid orbitals overlap st o 1 bond between ANY 2 atoms is ALWAYS a sigma bond  Pi bond – when the overlap of the orbitals does NOT lie on a line drawn between the 2 nuclei o Only p orbitals can form pi bonds nd rd o The 2 or 3 bonds of a double or triple bond are always pi bonds o Pi bonds are not as strong as sigma bonds because the orbitals do not overlap as much in a pi bond Chapter 8  For chemical reactions, each species on the left is a reactant  Each species on the right is a product  (g) – gas; (l) – liquid; (aq) – aqueous; (s) – solid  Equations must be balanced so the law of conservation of mass is obeyed o Achieved by writing stoichiometric coefficients to the left of the chemical formulas o Steps for balancing  Change coefficients of compounds before changing the coefficients of elements  Treat polyatomic ions that appear on both sides of the equation as units  Count atoms or polyatomic ions carefully  Combination reaction – 2 or more reactants combine to form a single product  Decomposition – 2 or more products form from a single reactant  Combustion – substance burns in presence of oxygen o ALWAYS produces CO2 and H2O o Incomplete if CO or C is produced  A 1.50 g sample of hydrocarbon undergoes complete combustion to produce 4.40 g of CO 2nd 2.70 g of H O2 What is the empirical formula of this compound  A 0.250 g sample of hydrocarbon undergoes complete combustion to produce 0.845 g of CO a2d 0.173 g of H O.2What is the empirical formula of this compound  Know how to use the mole ratios the determine how much product will form from a balanced equation  Limiting reactant – the reactant that is used up first o Excess reactants are present in quantities greater than necessary to react with the quantity of the limiting reactant o A 2.00 g sample of ammonia is mixed with 4.00 g of oxygen. Which is the limiting reactant and how much excess reactant remains after the reaction has stopped o try example 8.7 in chemistry book  Theoretical yield – amount of product that forms when all of the limiting reactant reacts to form the desired product  Actual yield – amount of product actually determined from the reaction  Percent yield – tells what percentage the actual yield is of the theoretical yield Chapter 9  Solution – homogenous mixture of 2 or more substances  Solvent – substance present in largest amount  Solute – other substances present  Electrolyte – a substance that dissolves in water to yield a solution that conducts electricity  Dissociation – electrolyte breaks apart into its constituent ions  Ionization – a molecular compound forms ions when it dissolves  Nonelectrolyte – a substance that dissolves in water to yield a solution that does not conduct electricity  Strong electrolyte – dissociates completely o Example- strong acids (HCl), strong bases (NaOH)  Weak electrolyte – a compound that produces ions upon dissolving but exists in solution predominantly as molecules that are not ionized  Precipitate – insoluble product that separates from a solution  Hydration – occurs when water molecules remove the individual ions from an ionic solid surrounding them so the substances dissolves  Solubility – maximum amount of solute that will dissolve in a given quantity of solvent at a specific temperature  Double replacement/metathesis – reactions in which cations in 2 ionic compounds exchange anions  Ionic equation – compounds that exist completely as ions in solution are represented as those ions  Net ionic equation – an equation that includes only the species that are involved in the reaction o Ions that appear on both sides are called spectator ions and are not included in the overall reaction  Oxidation/reduction – chemical reaction in which electrons are transferred from one reactant to another (also called redox) o Oxidation = LOSS o Reduction = GAIN o OIL RIG or LEO goes GER o (oxidation Is loss, reduction is gain); (loss equals oxidation, gain equals reduction)  redox – sum of an oxidation half-reaction and a reduction half reaction  oxidation number – charge an atom would have if electrons were transferred completely o elements have an oxidation number of zero o steps to determine oxidation number  start with the ones you know  the total contribution to charge must sum to zero if it is a neutral compound; if not, it must sum to the charge of the compound.  Displacement reaction – an atom or an ion in a compound is replaced by an atom of another element  Molarity (M) – molar concentration; defined as the number of moles of solute per liter of solution o M = mol/L  Dilution – process of preparing a less concentrated solution from a more concentrated one  Moles of solute before dilution = moles of solute after dilution  McVc = MdVd Chapter 10  System – a part of the universe that is of specific interest  Surroundings – rest of the universe outside of the system  Thermochemistry – study of heat in chemical reactions  Heat – transfer of thermal energy o Either absorbed or released o Si unit is a Joule, J  Exothermic process – occurs when heat is transferred from the system to the surroundings  Endothermic process – occurs when heat is transferred from the surroundings to the system  Thermodynamics – study of the interconversion of heat and other kinds of energy  3 types of systems o open system – can exchange mass and energy with the surroundings o closed system – allows the transfer of energy but not mass o isolated system – does not exchange either mass or energy with its surroundings  state functions – properties that are determined by the state of the system, regardless of how that condition was achieved o pressure o volume o energy o temperature  First law of thermodynamics – energy can be converted from one form to another, but not created nor destroyed  Pressure increases when volume is constant  Volume increases when pressure is constant  Enthalpy of reaction – the difference between the enthalpies of the products and the enthalpies of reactants I have notes that may help with thermodynamics, however, they go further than where we are in class, so just ignore that part. I think we may be learning it on Tuesday, but if not, ignore it. Thanks! Also, I recommend looking in the book for practice problems. She usually picks problems straight from the book or the internet! Good Luck!

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Chapter 8, Problem 71 is Solved
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Textbook: College Algebra
Edition: 7
Author: Richard N. Aufmann, Vernon C. Barker, Richard D. Nation
ISBN: 9781439048610

College Algebra was written by and is associated to the ISBN: 9781439048610. The answer to “In Exercises 67 to 72, use the Binomial Theorem to expand each binomial or find the requested term. Find the fifth term in the binomial expansion of (3x - 4y)7.” is broken down into a number of easy to follow steps, and 30 words. Since the solution to 71 from 8 chapter was answered, more than 253 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 71 from chapter: 8 was answered by , our top Math solution expert on 01/02/18, 08:47PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 9 chapters, and 4425 solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 7.

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In Exercises 67 to 72, use the Binomial Theorem | Ch 8 - 71