Chemistry: Atoms First PDF

® Because learning changes everything. Chemistry: Atoms First...

® Because learning changes everything. Chemistry: Atoms First Fifth Edition Julia Burdge and Jason Overby Chapter 6 Representing Molecules © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.  Chapter 6 Chemical Bonding I: Basic Concepts 6.1 The Octet Rule Lewis Structures Multiple Bonds 6.2 Electronegativity and Polarity Electronegativity Dipole Moment, Partial Charges, and Percent Ionic Character 6.3 Drawing Lewis Structures 6.4 Lewis Structures and Formal Charge 6.5 Resonance 6.6 Exceptions to the Octet Rule Incomplete Octets Odd Numbers of Electrons Expanded Octets © McGraw Hill LLC 2  6.1 The Octet Rule 1 According to the octet rule, atoms will lose, gain, or share electrons in order to achieve a noble gas electron configuration. Only valence electrons contribute to bonding. F 1s 22 s 2 2 p 5 valence electrons © McGraw Hill LLC 3  The Octet Rule 2 Only two valence electrons participate in the formation of the F2 bond. Pairs of valence electrons not involved in bonding are called lone pairs. Access the text alternative for slide images. © McGraw Hill LLC 4  Lewis Structures A Lewis structure is a representation of covalent bonding. Shared electron pairs are shown either as dashes or as pairs of dots. Lone pairs are shown as pairs of dots on individual atoms. © McGraw Hill LLC 5  Multiple Bonds 1 In a single bond, atoms are held together by one electron pair. In a double bond, atoms share two pairs of electrons. © McGraw Hill LLC 6  Multiple Bonds 2 A triple bond occurs when atoms are held together by three electron pairs. Access the text alternative for slide images. © McGraw Hill LLC 7  Multiple Bonds 3 Bond length is defined as the distance between the nuclei of two covalently bonded atoms. TABLE 6.1 Average Bond Lengths of Common Single, Double, and Triple Bonds Bond Type Bond Length ( pm ) Bond Type Bond Length ( pm ) C–H 107 C=N 138 O–H 96 C N 116 C–O 143 N– N 147 C =O 121 N =N 124 C O 113 N N 110 C–C 154 N–O 136 C =C 133 N =O 122 CC 120 O–O 148 C–N 143 O =O 121 © McGraw Hill LLC 8  Multiple Bonds 4 Multiple bonds are shorter than single bonds. For a given pair of atoms: triple bonds are shorter than double bonds. double bonds are shorter than single bonds. N N < N=N < N–N 110 pm 124 pm 147 pm © McGraw Hill LLC 9  Multiple Bonds 5 The shorter multiple bonds are also stronger than single bonds. We quantify bond strength by measuring the quantity of energy required to break it. H2 ( g ) → H ( g ) + H ( g ) Bond energy = 436.4 kJ/mol We will examine this in more detail in Chapter 10. © McGraw Hill LLC 10  6.2 Electronegativity and Polarity 1 There are two extremes in the spectrum of bonding: covalent bonds occur between atoms that share electrons. ionic bonds occur between a metal and a nonmetal and involve ions. Bonds that fall between these extremes are polar. In polar covalent bonds, electrons are shared but not shared equally. The delta, δ, is used to denote partial charges on the atoms. M:X M + X  − M+ X − Pure covalent bond Polar covalent bond Ionic bond Neutral atoms held Partially charged atoms Oppositely charged ions together by equally held together by held together by shared electrons unequally shared electrostatic attraction electrons © McGraw Hill LLC 11  Electronegativity and Polarity 2 Electron density maps show the distributions of charge. Electrons spend a lot of time in red and very little time in blue. nonpolar covalent polar covalent ionic Electrons are shared Electrons are not shared Electrons are not shared equally equally and are more but rather transferred likely to be associated from Na to F with F © McGraw Hill LLC 12  Electronegativity and Polarity 3 Electronegativity is the ability of an atom in a compound to draw electrons to itself. © McGraw Hill LLC 13  Electronegativity and Polarity 4 Electronegativity varies with atomic number. © McGraw Hill LLC 14  Electronegativity and Polarity 5 There is no sharp distinction between nonpolar covalent and polar covalent or between polar covalent and ionic. The following rules help distinguish among them: A bond between atoms whose electronegativities differ by less than 0.5 is general considered purely covalent or nonpolar. A bond between atoms whose electronegativities differ by the range of 0.5 to 2.0 is generally considered polar covalent. A bond between atoms whose electronegativities differ by 2.0 or more is generally considered ionic. © McGraw Hill LLC 15  Worked Example 6.1 Classify the following bonds as nonpolar, polar, or ionic: (a) the bond in ClF, (b) the bond in CsBr, and (c) the carbon–carbon double bond in C2H4. Strategy Electronegativity values are: Cl (3.0), F (4.0), Cs (0.7), Br (2.8), C (2.5). Use this information to determine which bonds have identical, similar, and widely different electronegativities. Solution (a) The difference between the electronegativities of F and Cl is 4.0 − 3.0 = 1.0, making the bond in ClF polar. (b) In CsBr, the difference is 2.8 − 0.7 = 2.1, making the bond ionic. (c) In C2H4, the two atoms are identical. (Not only are they the same element, but each C atom is bonded to two H atoms.) The carbon–carbon double bond is C2H4 is nonpolar. Think About It By convention, the difference in electronegativity is always calculated by subtracting the smaller number from the larger one, so the result is always positive. © McGraw Hill LLC 16  Dipole Moment, Partial Charges, and Percent Ionic Character 1 Regions where electrons Regions where electrons Spend little time Spend a lot of time An arrow is used to indicate the direction of electron shift in polar covalent molecules. The consequent charge separation can be represented as: Deltas (δ) denote a partial positive or negative charge. Access the text alternative for slide images. © McGraw Hill LLC 17  Dipole Moment, Partial Charges, and Percent Ionic Character 2 A quantitative measure of the polarity of a bond is its dipole moment (μ).  = Qr Q is the charge. r is the distance between the charges. μ is always positive and expressed in debye units (D). 1 D = 3.336  10 −30 C  m C is Coulomb and m is meter. © McGraw Hill LLC 18  Dipole Moment, Partial Charges, and Percent Ionic Character 3 A quantitative measure of the polarity of a bond is its dipole moment (μ).  =Qr TABLE 6.2 Bond Lengths and Dipole Moments of the Hydrogen Halides Molecule Dipole Moment (D) HF 0.92 1.82 HCl 1.27 1.08 HBr 1.41 0.82 HI 1.61 0.44 © McGraw Hill LLC 19  Worked Example 6.2 1 Burns caused by hydrofluoric acid [HF(aq)] are unlike any other acid burns and present unique medical complications. HF solutions typically penetrate the skin and damage internal tissues, including bone, often with minimal surface damage. Less concentrated solutions actually can cause greater injury than more concentrated ones by penetrating more deeply before causing injury, thus delaying the onset of symptoms and preventing timely treatment. Determine the magnitude of the partial positive and partial negative charges in the HF molecule. Strategy Solve for Q. Convert the resulting charge in coulombs to units of electronic charge. According to Table 6.2,  = 1.82 D and r = 0.92 Å for HF. The dipole moment must be converted from debye to C  m and the distance between ions must be converted to meters. 3.336 10−30 C  m  = 1.82 D  = 6.07 10−30 C  m 1D 110−10 m r = 0.92 Å  = 9.2 10−11 m 1Å © McGraw Hill LLC 20  Worked Example 6.2 2 Solution In coulombs: ( Q =  r = 6.07  10−30 C  m ) ( 9.2 10 −11 ) m = 6.598  10−20 C In units of electronic charge: ( 6.598 10 −20 ) ( C (1e − ) 1.6022 10−19 C = 0.41e − ) Therefore, the partial charges in HF are +0.41 and −0.41 on H and F, respectively. Think About It Calculated partial charges should always be less than 1. If a “partial” charge were 1 or greater, it would indicate that at least one electron had been transferred from one atom to the other. Remember that polar bonds involve unequal sharing of electrons, not a complete transfer of electrons. Access the text alternative for slide images. © McGraw Hill LLC 21  Dipole Moment, Partial Charges, and Percent Ionic Character 4 Although the designations “covalent,” “polar covalent,” and “ionic” can be useful, sometimes chemists wish to describe and compare chemical bonds with more precision. Comparing the calculated dipole moment with the measured values gives us a quantitative way to describe the nature of a bond using the term percent ionic character.  (observed) percent ionic character =  100%  (calculated assuming discrete charges) © McGraw Hill LLC 22  Dipole Moment, Partial Charges, and Percent Ionic Character 5 The figure below demonstrates the relationship between percent ionic character and the electronegativity difference in a heteronuclear diatomic molecule. © McGraw Hill LLC 23  Worked Example 6.3 1 Using data from Table 6.2, calculate the percent ionic character of the bond in HI. Strategy Calculate the dipole moment in HI assuming that the charges on H and I are +1 and −1, respectively; then calculate the percent ionic character. The magnitude of the charges must be expressed in coulombs (1e− = 1.6022 10−19 C); the bond length (r) must be expressed as meters (1 Å = 1 10 −10 m ); and the calculated dipole moment should be expressed as debyes (1 D = 3.336  10 −30 C  m ). Setup From Table 6.2, the bond length in HI is 1.61 Å (1.61 10−10 m) and the measured dipole moment of HI is 0.44 D. © McGraw Hill LLC 24  Worked Example 6.3 2 Solution The dipole we would expect if the magnitude of the charges were 1.6022  10−19 C is  = Q  r = (1.6022  10−19 C )  (1.61 10−10 m ) = 2.58  10−29 C  m Converting to debyes gives ( ) 2.58  10−29 C  m  (1 D ) 3.336  10−30 C  m = 7.73 D The percent ionic character of the H–I bond is ( 0.44 D) ( 7.73 D)  100% = 5.7%. Think About It A purely covalent bond (in a homonuclear diatomic molecule such as H2) would have 0 percent ionic character. In theory, a purely ionic bond would be expected to have 100 percent ionic character, although no such bond is known. © McGraw Hill LLC 25  6.3 Drawing Lewis Structures 1 Follow these steps when drawing Lewis structure for molecules and polyatomic ions. 1) Draw the skeletal structure of the compound. The least electronegative atom is usually the central atom. Draw a single covalent bond between the central atom and each of the surrounding atoms. 2) Count the total number of valence electrons present; add electrons for negative charges and subtract electrons for positive charges. 3) For each bond in the skeletal structure, subtract two electrons from the total valence electrons. 4) Use the remaining electrons to complete octets of the terminal atoms by placing pairs of electrons on each atom. Complete the octets of the most electronegative atom first. 5) Place any remaining electrons in pairs on the central atom. 6) If the central atom has fewer than eight electrons, move one or more pairs from the terminal atoms to form multiple bonds between the central atom and terminal atoms. © McGraw Hill LLC 26  Drawing Lewis Structures 2 Draw the Lewis Structure for ClO3−. Solution: Step 1 Draw the skeletal structure of the compound. The least electronegative atom is usually the central atom. Draw a single covalent bond between the central atom and each of the surrounding atoms. Access the text alternative for slide images. © McGraw Hill LLC 27  Drawing Lewis Structures 3 Draw the Lewis Structure for ClO3−. Solution: Step 2 Count the total number of valence electrons present; add electrons for negative charges and subtract electrons for positive charges. Cl :1  7 = 7e − O : 3  6 = 18e − Charge : 1e − Total: 26 valence e − © McGraw Hill LLC 28  Drawing Lewis Structures 4 Draw the Lewis Structure for ClO3−. Solution: Step 3 For each bond in the skeletal structure, subtract two electrons from the total valence electrons. 3 bonds  2e − = 6e − 26 − 6 = 20e − left over Access the text alternative for slide images. © McGraw Hill LLC 29  Drawing Lewis Structures 5 Draw the Lewis Structure for ClO3−. Solution: Step 4 Use the remaining electrons to complete octets of the terminal atoms by placing pairs of electrons on each atom. Complete the octets of the most electronegative atom first. 6 electrons used in single bonds 20 electrons must be placed in the structure starting with terminal atoms The structure now has a total of 24 valence electrons of the available 26. Access the text alternative for slide images. © McGraw Hill LLC 30  Drawing Lewis Structures 6 Draw the Lewis Structure for ClO3−. Solution: Step 5 Place any remaining electrons on the central atom. The structure now has a total of 24 Lewis structures for polyatomic ions valence electrons of the available 26. are enclosed by square brackets. 2e − remain to be added to the structure. Access the text alternative for slide images. © McGraw Hill LLC 31  Drawing Lewis Structures 7 Draw the Lewis Structure for ClO3−. Solution: Step 6 If the central atom has fewer than eight electrons, move one or more pairs from the terminal atoms to form multiple bonds between the central atom and terminal atoms. All atoms already have an octet in this structure. © McGraw Hill LLC 32  Drawing Lewis Structures 8 © McGraw Hill LLC 33  Worked Example 6.4 1 Draw the Lewis structure for carbon disulfide (CS2). Setup Step 1: C and S have identical electronegativities. We will draw the skeletal structure with the unique atom, C, at the center. S—C—S Step 2: The total number of valence electrons is 16: 6 from each S atom and 4 from the C atom  2 ( 6 ) + 4 = 16 . Step 3: Subtract 4 electrons to account for the bonds in the skeletal structure, leaving us 12 electrons to distribute. Step 4: Distribute the 12 remaining electrons as 3 lone pairs on each S atom. Access the text alternative for slide images. © McGraw Hill LLC 34  Worked Example 6.4 2 Draw the Lewis structure for carbon disulfide (CS2). Setup Step 5: There are no electrons remaining after step 4, so step 5 does not apply. Step 6: To complete carbon’s octet, use one lone pair from each S atom to make a double bond to the C atom. Solution Think About It Counting the total number of valence electrons should be relatively simple to do, but it is often done hastily and is therefore a potential source of error in this type of problem. Remember that the number of valence electrons for each element is equal to the group number of that element. © McGraw Hill LLC 35  6.4 Lewis Structures and Formal Charge 1 Formal charge can be used to determine the most plausible Lewis Structure when more than one possibility exists for a compound. Formal charge = valence electrons − associated electrons To determine associated electrons: 1) All the atom’s nonbonding electrons are associated with the atom. 2) Half the atom’s bonding electrons are associated with the atom. © McGraw Hill LLC 36  Lewis Structures and Formal Charge 2 Determine the formal charges on each oxygen atom in the ozone molecule (O3). © McGraw Hill LLC 37  Worked Example 6.5 1 The widespread use of fertilizers has resulted in the contamination of some groundwater with nitrates, which are potentially harmful. Nitrate toxicity is due primarily to its conversion in the body to nitrite (NO −2 ), which interferes with the ability of hemoglobin to transport oxygen. Determine the formal charges on each atom in the nitrate ion (NO3− ). Strategy Follow the six steps to draw the Lewis structure of (NO3− ). For each atom, subtract the associated electrons from the valence electrons. Setup The N atom has five valence electrons and four associated electrons (one from each single bond and two from the double bond). Each singly bonded O atom has six valence electrons and seven associated electrons (six in three lone pairs and one from the single bond). The doubly bonded O atom has six valence electrons and six associated electrons (four in two lone pairs and two from the double bond.) © McGraw Hill LLC 38  Worked Example 6.5 2 Solution The formal charges are as follows: +1 (N atom), −1 (singly bonded O atoms), and 0 (doubly bonded O atom). Think About It The sum of formal charges ( +1) + ( −1) + ( −1) + ( 0 ) = −1 is equal to the overall charge on the nitrate ion. © McGraw Hill LLC 39  Lewis Structures and Formal Charge 3 When there is more than one possible structure, the best arrangement is determined by the following guidelines: 1) A Lewis structure in which all formal charges are zero is preferred. 2) Small formal charges are preferred to large formal charges. 3) Formal charges should be consistent with electronegativities. © McGraw Hill LLC 40  Worked Example 6.6 1 Formaldehyde (CH2O), which can be used to preserve biological specimens, is commonly sold as a 37 percent aqueous solution. Use formal charges to determine which skeletal arrangements of atoms shown here is the best choice for the Lewis structure of CH2O. H—C—O—H Strategy The complete Lewis structures for the skeletons shown are: © McGraw Hill LLC 41  Worked Example 6.6 2 Strategy The complete Lewis structures for the skeletons shown are: In the structure on the left, the formal charges are as follows: Both H atoms: 1 valence e − − 1 associated e − (from single bond) = 0 C atom: 4 valence e − − 5 associated e − (two in the lone pair, one from the single bond, and two from the double bond) = −1 O atom: 6 valence e − − 5 associated e − (two from the lone pair, one from the single bond, and two from the double bond) = +1 Access the text alternative for slide images. © McGraw Hill LLC 42  Worked Example 6.6 3 Strategy The complete Lewis structures for the skeletons shown are: In the structure on the right, the formal charges are as follows: Both H atoms: 1 valence e − − 1 associated e − (from single bond) = 0 C atom: 4 valence e − − 4 associated e − (one from each single bond, and two from the double bond) = 0 O atom: 6 valence e − − 6 associated e − (four from the two lone pairs and two from the double bond) = 0 Formal charges all zero © McGraw Hill LLC 43  Worked Example 6.6 4 Solution Of the two possible arrangements, the structure on the left has an O atom with a positive formal charge, which is inconsistent with oxygen’s high electronegativity. Therefore, the structure on the right, in which both H atoms are attached directly to the C atoms and all atoms have a formal charge of zero, is the better choice for the Lewis structure of CH2O. Think About It For a molecule, formal charges of zero are preferred. When there are nonzero formal charges, they should be consistent with the electronegativities of the atoms in the molecules. A positive formal charge on oxygen, for example, is inconsistent with oxygen’s high electronegativity. © McGraw Hill LLC 44  6.5 Resonance 1 A resonance structure is one of two or more Lewis structures for a single molecule that cannot by represented accurately by only one Lewis structure. Resonance structures are a human invention. Resonance structures differ only in the positions of their electrons. © McGraw Hill LLC 45  Resonance 2 The carbonate ion, another example of resonance The skeletal structure of benzene showing resonance © McGraw Hill LLC 46  Worked Example 6.7 1 High oil and gasoline prices have renewed interest in alternative methods of producing energy, including the “clean” burning of coal. Part of what makes “dirty” coal dirty is its high sulfur content. Burning dirty coal produces sulfur dioxide (SO2), among other pollutants. Sulfur dioxide is oxidized in the atmosphere to form sulfur trioxide (SO3), which subsequently combines with water to produce sulfuric acid—a major component of acid rain. Draw all possible resonance structures of sulfur trioxide. Strategy Following the steps for drawing Lewis structures, we determine that a correct Lewis structure for SO3 contains two sulfur–oxygen single bonds and one sulfur–oxygen double bond. But the double bond can be put in any one of three positions in the molecule. © McGraw Hill LLC 47  Worked Example 6.7 2 Solution Think About It Always make sure that resonance structures differ only in the position of the electrons, not in the positions of the atoms. © McGraw Hill LLC 48  6.6 Exceptions to the Octet Rule: Incomplete Octets Exceptions to the octet rule fall into three categories: 1) The central atom has fewer than eight electrons due to a shortage of electrons. H — Be — H only 4 total valence electrons in the system Elements in group 3A also tend to form compounds surrounded by fewer than eight electrons. Boron, for example, reacts with halogens to form compounds of the general formula BX3 having six electrons around the boron atom. © McGraw Hill LLC 49  Exceptions to the Octet Rule: Odd Numbers of Electrons 2) The central atom has fewer than eight electrons due to an odd number of electrons. 17 valence electrons in the system Molecules with an odd number of electrons are sometimes referred to as free radicals. © McGraw Hill LLC 50  Exceptions to the Octet Rule: Expanded Octets 3) The central atom has more than eight electrons. Sulfur has 6 bonds corresponding to 12 electrons Atoms in and beyond the third period can have more than eight valence electrons. In addition to the 3s and 3p orbitals, elements in the third period also have 3d orbitals that can be used in bonding. © McGraw Hill LLC 51  Worked Example 6.8 1 Draw the Lewis structure of chlorine dioxide (ClO2). Strategy The skeletal structure is O — Cl — O This puts the unique atom, Cl, in the center and puts the more electronegative O atoms in terminal positions. There are a total of 19 valence electrons (7 from the Cl and 6 from each of the two O atoms). We subtract 4 electrons to account for the two bonds in the skeleton, leaving us with 15 electrons to distribute as follows: three lone pairs on each O atom, one lone pair on the Cl atom, and the last remaining electron also on the Cl atom. Solution Access the text alternative for slide images. © McGraw Hill LLC 52  Worked Example 6.8 2 Think About It ClO2 is used primarily to bleach wood pulp in the manufacture of paper, but it is also used to bleach flour, disinfect drinking water, and deodorize certain industrial facilities. Recently, it has been used to eradicate the toxic mold in homes in New Orleans that were damaged by the devastating floodwaters of Hurricane Katrina in 2005. © McGraw Hill LLC 53  Worked Example 6.9 1 Draw the Lewis structure of boron triiodide (BI3). Strategy The skeletal structure is There are a total of 24 valence electrons (3 from the B and 7 from each of the three I atoms). We subtract 6 electrons to account for the three bonds in the skeleton, leaving 18 electrons to distribute in lone pairs on each I atom. Solution © McGraw Hill LLC 54  Worked Example 6.9 2 Think About It Boron is one of the elements that does not always follow the octet rule. Like BF3, however, BI3 can be drawn with a double bond in order to satisfy the octet of boron. This gives rise to a total of four resonance structures. © McGraw Hill LLC 55  Worked Example 6.9 3 Draw the Lewis structure of arsenic pentafluoride (AsF5). Strategy The skeletal structure already has more than an octet around the As atom. There are 40 total valence electrons [5 from A s (Group 5A) and 7 from each of the five F atoms (Group 7A)]. We subtract 10 electrons to account for the five bonds in the skeleton, leaving 30 to be distributed. Next, we place three lone pairs on each F atom, thereby completing all their octets and using up all the electrons. Solution © McGraw Hill LLC 56  Worked Example 6.9 4 Draw the Lewis structure of xenon tetrafluoride (XeF4). Strategy Follow the steps for drawing Lewis structures. The skeletal structure is There are 36 total valence electrons (8 from Xe and 7 from each of the four F atoms). We subtract 8 electrons to account for the bonds in the skeleton, leaving 28 to distribute. We first complete the octets of all four F atoms. When this is done, 4 electrons remain, so we place two lone pairs on the Xe atom. Solution © McGraw Hill LLC 57  Worked Example 6.9 5 Think About It Atoms beyond the second period can accommodate more than an octet of electrons, whether those electrons are used in bonds or reside on the atoms as lone pairs. © McGraw Hill LLC 58  Worked Example 6.10 1 Draw two resonance structures for sulfurous acid (H2SO3): one that obeys the octet rule for the central atom, and one that minimizes the formal charges. Determine the formal charges on each atom in both structures. Strategy Begin by drawing the skeletal structure and counting the total number of valence electrons. Use the steps outlined in Section 6.4 to draw the first structure and reposition one or more lone pairs to adjust the formal charges for the second structure. Note that each hydrogen in an oxoacid is attached to an oxygen atom, and not directly to the central atom. The total number of valence electrons is 26 (6 from S, 6 from each O, and 1 from each H). © McGraw Hill LLC 59  Worked Example 6.10 2 Solution Following the steps we get the first structure: From the top O atom, which has three lone pairs, we reposition one lone pair to create a double bond between O and S to get the second structure. Incorporating the double bond results in every atom having a formal charge of zero. Access the text alternative for slide images. © McGraw Hill LLC 60  Worked Example 6.10 3 Think About It In some species, such as the sulfate ion, it is possible to incorporate too many double bonds. Structures with three and four double bonds to sulfur would give formal charges on S and O that are inconsistent with the electronegativities of these elements. In general, if you are trying to minimize formal charges by expanding the central atom’s octet, only add enough double bonds to make the formal charge on the central atom zero. © McGraw Hill LLC 61  Exceptions to the Octet Rule: The bond between B– N has both the electrons contributed by the N atom. This type of bond is a coordinate covalent or dative bond. This type of bond formation is an example of a Lewis acid– base process. BF3 is a Lewis acid: it can accept a pair of electrons. NH3 is a Lewis Base: it donates a pair of electrons. Access the text alternative for slide images. © McGraw Hill LLC 62  6 Chapter Summary: Key Points Octet Rule. Exceptions to the Octet Rule: Lewis Structures. Incomplete Octets. Bonds: Odd Numbers of Electrons. Single and Multiple. Expanded Octets. Electronegativity: Lewis Base and Lewis Acid. Polar and Nonpolar Bonds. Coordinate Covalent Bond. Percent Ionic Character. Dipole Moment. Drawing Lewis Structures. Formal Charge. Resonance Structures. © McGraw Hill LLC 63