tronic structure is not represented by any one of the Lewis structures but by the average of all of them. Review Answers 1. The pi bond (one of the bonds in the double bond) is distributed evenly over all three bonds. The Lewis structure pictured is only one of three resonance structures for this ion. Each of the bonds is approximately one and one-third bonds and the three bonds are identical. Electronic and Molecular Geometry Lesson Objectives • The student will state the main postulate in VSEPR theory. • The student will identify both the electronic and the molecular geometry for simple binary compounds. Introduction Many accurate methods now exist for determining molecular structure, the three-dimensional arrangement of the atoms in a molecule. These methods must be used if precise information about structure is needed. However, it is often useful to be able to predict the approximate molecular structure of a molecule. A simple model that allows us to do this is called the valence shell electron pair repulsion (VSEPR) theory. This model is useful in predicting the geometries of molecules formed in the covalent bonding of non-metals. The main postulate of this theory is that in order to minimize electron-pair repulsion, the electron pairs around the central atom in a molecule will get as far away from each other as possible. Electronic Geometry for a Central Atom with Two Pairs of Electrons Consider first the covalent compounds formed by family 2A. An example of these compounds is BeCl2. The central beryllium atom has two pairs of electrons in its valence shell. VSEPR theory tells us that these two pairs of electrons will move in the valence shell to get as far away from each other as possible. The greatest o distance these two pairs of electrons can get from each other is 180 across from each on opposite sides of the nucleus. If both of these pairs of electrons were overlapped by a chlorine atom, the two chlorine atoms would also be on opposite sides of the nucleus. The electronic geometry in this case is linear and if the electron pairs are shared, the molecule will also be linear. A “linear molecule” means that a straight line would pass through all the nuclei in the molecule. Figure 16: The electronic geometry of BeCl2 is linear and if both pairs of electrons are shared, the molecule is also linear. 387 (Created by: Richard Parsons, License : CC-BY-SA) Electronic Geometry for a Central Atom with Three Pairs of Electrons We will look at boron trichloride, BCl3, as an example molecule for the covalent molecules in family 3A. Boron has three valence electrons and each chlorine that overlaps a boron orbital contributes one more electron to boron’s valence shell. Therefore, boron will have six electrons or three pairs of electrons in its valence shell. The farthest away from each other that three pairs of electrons can get is at the points of a o planar triangle in the valence shell. Each bond angle will be 120 . This shape is known as trigonal planar. Figure 17: The trigonal planar electronic geometry of BH3. If all electron pairs are shared, the molecule will also be trigonal planar. (Created by: Richard Parsons, License : CC-BY-SA) In the trigonal planar shape, all four atoms are in a single plane. None of the atoms project above or below the plane of the paper. You should note that if one of the pairs of electrons is not shared, so there is only two attached chlorine atoms, the shape of the molecule will angular or bent. Electronic Geometry for a Central Atom with Four Pairs of Electrons We will use methane, CH4, as an example of the covalent bonding in family 4A. Carbon has four valence electrons and each hydrogen adds one more so the central atom in methane has four pairs of electrons in its valence shell. Those four pairs of electrons get as far away from each other as possible which forms a shape called tetrahedral. In the tetrahedral shape, the bond angle between any two hydrogen atoms is o 109.5 . Figure 18: The electronic geometry of carbon’s four pairs of electrons is tetrahedral and if all four pairs of electrons are shared, the molecule shape is also tetrahedral. (Source: CK-12 Foundation, Altered by: Richard Parsons, License: CC-BY-SA) Electronic Geometry for a Central Atom with Five Pairs of Electrons We will consider the molecules PCl3 and PCl5 as reference molecules for family 5A. In the PCl3 molecule, the central phosphorus atom has five valence electrons and each chlorine atom contributes one more electron so that the central atom has four pairs of electrons in its valence shell. These four pairs of electrons 388 will form the tetrahedral shape in the effort to maximize the distance between them. Therefore, the electronic geometry for this molecule is tetrahedral. When the molecule is formed, however, one of the pairs of electrons is not shared. The resulting molecular geometry is called pyramidal. Figure 19: The tetrahedral electronic geometry forms a pyramidal molecule when one pair of electrons is unshared. (Source: CK-12 Foundation, Modified by: Richard Parsons, License: CC-BY-SA) It is important to note the difference between the pyramidal molecule in Figure 19 and the trigonal planar molecule discussed earlier. In the trigonal planar molecule, none of the attached atoms is below or above the plane of the central atom. In this pyramidal molecule, however, all three of the attached atoms are below the plane of the central atom. In the PCl5 molecule, the phosphorus has five valence electrons and each chlorine adds one more so the central atom will be surrounded by five pairs of electrons in its valence shell. When these five pairs of electrons maximize the distance between them, the shape is called trigonal bipyramidal. This shape has three attached atoms in a plane with the central atom and then has atoms attached to the two ends of the molecule. Figure 20: The trigonal bipyramidal electronic geometry of PCl5. (Source: CK-12 Foundation, License: CC-BY-SA) o The bond angles between the three atoms in the plane with the central atom are all 120 and the bond angles o between the two end atoms and the other three are all 90 . Electronic Geometry for a Central Atom with Six Pairs of Electrons The two types of electronic geometry in family 6A can be seen in the molecules SF2 and SF6. In SF2, the central sulfur atom has six valence electrons and each fluorine adds one more so that the central atom is surrounded by four pairs of electrons. The resultant electronic geometry is the tetrahedral shape we have seen twice before. However, when the compound SF2 is formed, two of the pairs of electrons are unshared. The resultant molecular shape is called angular or bent. 389 Figure 21: SF2 has tetrahedral electronic geometry but two of the pairs of electrons are not shared so the resultant molecular geometry is angular. (Created by: Richard Parsons, License : CC-BY-SA) In the molecule SF6, sulfur has six valence electrons and each fluorine contributes another electron so the central atom is surrounded by six pairs of electrons. The maximum distance six pairs of electrons can separate produces a geometry called octahedral. Figure 22: The octahedral electronic shape of six electron pairs. (Created by: Richard Parsons, License : CC-BY-SA) o The bond angle between any two adjacent attached atoms is 90 . The shape name is based on the number of triangular plates that can be placed on the surface of the molecule and if you count carefully, you will see that it is eight, hence octahedral. Summary of Electronic Geometry Electron Pairs 1 2 3 Hybridization None sp 2 Electronic Geometry Linear Linear Trigonal Planar 4 sp 3 Tetrahedral 5 sp d 3 Trigonal Bipyramidal 6 sp d 3 2 Octahedral sp Examples of Molecular Shapes The electronic geometry for a given number of electron pairs surrounding a central atom is always the same. That number of electron pairs will distribute themselves in the same way to maximize their separation. The same thing cannot be said for molecular geometry. The molecular shape depends not only on the electronic geometry but also on the number of the electron pairs that are shared. In this section, we will go through a 390 number of examples of molecules where some number of the pairs of electrons are not shared. Beginning with members of family 3A, there are very few options. We will consider the shapes of the BH3 - molecule and the BH2 ion. In BH3 molecules, the central atom is surrounded by three pairs of electrons, so the electronic geometry is trigonal planar, and when all three electron pairs are shared, the molecular geom- etry is also trigonal planar. In the case of the BH2 ion, there are still three pairs of electrons around the central atom (3 from boron, 1 each from the two hydrogens, and 1 electron that came from outside the ion), so the electronic geometry remains trigonal planar. The shape of the ion, however, will be a shape known as bent or angular. Figure 23: Trigonal planar molecular shape and angular shape when one pair of electrons is unshared. (Created by: Richard Parsons, License : CC-BY-SA) When the central atom is surrounded by four pairs of electrons, the electronic geometry will always be tetrahedral. When all four electron pairs are shared, such as with CH4, the molecular shape will also be tetrahedral. In the case of ammonia, NH3, however, three of the four pairs of electrons are shared but the fourth pair is unshared. This results in a molecular shape called pyramidal. If a second pair of electrons is - unshared, such as with the NH2 ion, the shape is angular again. Figure 24: Four pairs of electrons shared and none unshared produces tetrahedral molecular shape, three pairs shared and one pair unshared produces pyramidal, and two pairs shared with two pairs unshared produces angular. (Source: CK-12 Foundation, Modified by: Richard Parsons, License: CC-BY-SA) When the central atom is surrounded with five pairs of electrons, the electronic geometry is trigonal bipyramidal. If all the electron pairs are shared, the molecular geometry will also be trigonal bipyramidal. An example of such a molecule is PF5. If one of the pairs of electrons is not shared, the molecular shape is called a distorted tetrahedron which is sometimes called seesaw. An example of a molecule with trigonal bipyramidal electronic geometry and a molecular shape of a distorted tetrahedron is SF4 (see Figure 25B). This molecule has five electron pairs around the central atom but only four of them are shared. When the electronic geometry is trigonal bipyramidal and two of the pairs of electrons are unshared, the shape is called T-shaped. An example of a T-shaped molecule is ClF3 (Figure 25C). ClF3 has five pairs of electrons around the central atom and only three of them are shared. When the trigonal bipyramidal electronic geometry has only two of 391 - the pairs of electrons shared, the molecular geometry produced is linear as in I3 (Figure 25D). Figure 25: Trigonal bipyramidal electronic geometry produces all these molecular shapes depending on how many electron pairs are shared and unshared. (Source: CK-12 Foundation, Modified by: Richard Parsons, License: CC-BY-SA) Figure 25A shows a molecule whose central atom is surrounded by five pairs of electrons and all five pairs are shared. The result is trigonal bipyramidal electronic geometry and trigonal bipyramidal molecular geometry. Figure 25B shows a molecule whose central atom is surrounded by five pairs of electrons, one of which is unshared. The resultant molecular shape is a distorted tetrahedron. Figure 25C represents a molecule like ClF3. The chlorine central atom has seven valence electrons and each fluorine atom contributes one more. The total number of electrons is ten or five pairs. With only three attached atoms, two of the electron pairs are left unshared. The first pairs of electrons that are left unshared in trigonal bipyramidal electronic geometry are the pairs around the middle of the molecule. The resultant molecular shape is called T-shape. - In the ion, I3 , the central iodine atom has seven valence electrons, two more are contributed by the attached iodine atoms, and one more electron comes from outside the ion. The total electron pairs around the central atom is five pairs and three of the pairs are unshared. The resultant shape of the ion is linear. Beginning with octahedral electronic geometry (six pairs of electrons), a number of molecular shapes can be produced depending on the number of electron pairs that are shared and unshared (see Figure 26). 392 Figure 26: Octahedral electronic geometry produces all these molecular shapes depending on how many electron pairs are shared and unshared. (Source: CK-12 Foundation, Modified by: Richard Parsons, License: CC-BY-SA) When electron pairs are unshared in trigonal bipyramidal electronic geometry, the first pairs that are unshared are the pairs around the center. When electron pairs are unshared in octahedral electronic geometry, the first pairs that are unshared are the ones on the ends of the molecule. Summary of Molecular Geometry Valence Shell Electron Valence Shell Electron Valence Shell Electron Molecular Geometry Pairs Total Pairs Shared Pairs Unshared 1 1 0 Linear 2 2 0 Linear 2 1 1 Linear 3 3 0 Trigonal Planar 3 2 1 Angular 3 1 2 Linear 4 4 0 Tetrahedral 4 3 1 Pyramidal 4 2 2 Angular 4 1 3 Linear 5 5 0 Trigonal Bipyramidal 5 4 1 Distorted Tetrahedron 5 3 2 T-shaped 5 2 3 Linear 5 1 4 Linear 6 6 0 Octahedral 6 5 1 Square Pyramidal 6 4 2 Square Planar 6 3 3 T-shaped 6 2 4 Linear 6 1 5 Linear Only Sigma Bonds Affect Electronic and Molecular Geometry In the process of determining the number of electron pairs around the central atom for the purpose of predicting electronic or molecular geometry, double bonds and triple bonds should be counted as one effective pair. The electron pairs, in order to repel other electron pairs, must be placed between the nuclei of the two atoms. In pi bonds, the electron density is above and below the plane of the bond and therefore, do not contribute to electron pair Figure 27: One of the resonance Lewis strucrepulsion. For the VSEPR model, multiple bonds count as ture for the nitrate ion. (Created by: Richard only one effective pair of electrons. We can use the nitrate ion, 393 NO3 , as an example. In order to determine the shape of the nitrate Parsons, License: CC-BY-SA) ion, we count the number of electron pairs that are surrounding the central nitrogen atom. Since double bonds count as a single electron pair for the VSEPR model, we would count three pairs of electrons in the central atom valence shell and therefore, the shape would be determined as trigonal planar. Examples of Determining Molecular Geometry Example 1 + Determine the shape of the ammonium ion, NH4 . Solution Step one is to determine the number of electron pairs around the central nitrogen atom. Electrons = 5 (from nitrogen) + 4 (one from each hydrogen) – 1 (the positive charge on the ion indicates this ion has lost one electron to the outside) = 8 electrons = 4 electron pairs Step two is to choose the electronic geometry based on the number of electron pairs. The electronic geometry of a central atom with four pairs of electrons = tetrahedral. Step three is to determine the number of valence shell electron pairs that are shared and unshared and choose the molecular geometry. Since all four pairs of electrons are shared in this ion, the ionic shape will be tetrahedral. Example 2 Determine the molecular shape of the PF5 molecule. Electrons in the valence shell of phosphorus = 5 (phosphorus) + 5 (one from each fluorine) = 10 electrons = 5 pairs of electrons. The electronic geometry is trigonal bipyramidal and because all five pairs of electrons are shared, the molecular geometry will also be trigonal bipyramidal. Example 3 Determine the shape of the ICl3 molecule. Solution The number of electrons surrounding the central iodine atom is 7 electrons from the iodine atom plus 1 from each chlorine atom yielding a total of 10 electrons which is 5 pairs. Therefore, the electronic geometry is trigonal bipyramidal. Since only three of the electron pairs are shared, the molecular geometry is T-shaped. Example 4 Determine the shape of the CO2 molecule. Solution 394 Since there are multiple bonds involved in this molecule, we need to write the Lewis structure for the molecule to make sure we do not count any double or triple bonds for VSEPR model determinations. Figure 28: The Lewis structure for carbon dioxide. (Created by: Richard Parsons, License: CC-BY-SA) Only the sigma bonds count in determining the electron pairs surrounding the central carbon atom. This molecule, therefore, has two electron pairs in the valence shell of the central atom and that produces linear electronic geometry and since both pairs are shared, the molecular geometry will also be linear. Example 5 Determine the shape of the SO2 molecule. Solution We will write the Lewis structure to check for multiple bonds. Figure 29: The Lewis structure for sulfur dioxide. (Created by: Richard Parsons, License: CC-BY-SA) In writing the Lewis structure for SO2, we determine a double bond is necessary to provide an octet of electrons for the central sulfur atom. Therefore, this molecule has three pairs of electrons around the central atom and its electronic geometry will be trigonal planar. Since only two of the electron pairs are shared, the molecular geometry is angular. Example 6 Determine the molecular shape of the XeF4 molecule. Solution The number of electrons surrounding the central atom in XeF4 is eight from the Xe and one each from the four fluorine atoms for a total of 12 electrons or 6 pairs of electrons. Six pairs of electrons around the central atom produces octahedral electronic geometry and since two pairs are unshared, the molecular geometry will be square planar. Lesson Summary • VSEPR theory suggests that the valence shell electron pairs due to electrostatic repulsion will spread themselves around the central atom in an attempt to maximize the distance between them. • The electronic geometry of a molecule is dependent only on the number of electron pairs in the valence shell of the central atom. • Molecular geometry is dependent on the electronic geometry and on the number of electron pairs that are unshared. 395 • Only sigma bonds contribute to electronic and molecular geometry. Review Questions 1. Write a Lewis structure for OF2 that obeys the octet rule. (Beginning) 2. Write a Lewis structure for H2CO that obeys the octet rule. (C is the central atom.) (Intermediate) 3. What is the geometrical shape of the H2CO molecule? (Challenging) 4. What is the bond angle in SCl2? (Challenging) 5. What is the molecular shape of ICl3? (Challenging) 6. What is the molecular shape of XeCl4? (Challenging) - - 7. The ion I3 molecule has been produced in the lab but the molecule F3 has not. Offer an explanation as - to why F3 cannot be produced in the lab. (Challenging) 8. The molecule shown here is methanal. What is the hybridization of the carbon atom in this molecule? (Intermediate) 9. The molecule shown here is acetylsalicylic acid, better known as aspirin. A. What is the hybridization of carbon 1? (Intermediate) B. What is the hybridization of carbon 2? (Intermediate) C. What is the hybridization of carbon 3? (Intermediate) D. What is the total number of pi bonds in the molecule? (Intermediate) Further Reading / Supplemental Links Website with lessons, worksheets, and quizzes on various high school chemistry topics. • 396 Lesson 4-4 is on Geometry of Molecules. • Lesson 4-5 is on Polarity. http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson31.htm Vocabulary unshared electron An unshared electron pair, also known as a non-bonding pair of electrons or as a lone pair pair of electrons, is two electrons in the same orbital in the outer shell of an atom that are not used in the formation of a covalent bond. electronic geome- The geometric arrangement of orbitals containing the shared and unshared electron pairs try surrounding the central atom of a molecule or polyatomic ion. molecular geome- The specific three-dimensional arrangement of atoms in molecules. try Review Answers 1. 2. 3. From the Lewis structure for this molecule drawn in problem 2, the number of shape contributing electron pairs around the central atom is three. Therefore, the electronic geometry would be trigonal planar and since all three electron pairs are shared, the molecular geometry would also be trigonal planar. 4. The electronic geometry for SCl2 is tetrahedral and because only two of the electron pairs are shared, the molecular shape is angular or bent. 5. The electronic geometry for ICl3 is trigonal bipyramidal and with only three of the electron pairs shared, the molecular geometry is T-shaped. 6. The electron geometry for XeCl4 is octahedral and with only four of the electron pairs shared, the molecular geometry is square planar. - 7. The I3 molecule is produced by having an electron in the central atom promoted into a d orbital. Fluorine cannot do this because it doesn’t have any d orbitals. 2 8. Since only sigma bonds are involved in hybridization, this carbon atom has sp hybridization. 9. 2 A. sp 397 2 B. sp 3 C. sp D. 5 pi bonds Molecular Polarity Lesson Objectives • The student will determine whether bonds are polar or non-polar. • The student will determine whether simple molecules are polar or non-polar. Introduction Two atoms of the same electronegativity will share electrons equally in a pure covalent bond. Any molecule that contains atoms of only one element, like H2 or F2, has pure covalent bonding. Two atoms with different electronegativities will have either the distorted electron distribution of a polar bond or the complete electron transfer of an ionic bond. Table 1 interprets the bonding between two elements in terms of the difference in their electronegativities. Table 1: Electronegativity Difference and Type of Bond Electronegativity Difference Ionic Character (%) Covalent Character (%) Bond Type 0.0 0 100 Covalent 0.5 5 95 Covalent 1.0 20 80 Covalent 1.5 40 60 Polar 2.0 60 40 Polar 2.5 75 25 Ionic 3.0 90 10 Ionic The Cause of Polar Bonds When covalent bonds form between identical atoms such as in H2, N2, O2, and so on, the electrons shared in the bonds are shared exactly equally. The two atoms have the same electronegativity and therefore, the same pull on the shared electrons. The center of negative charge for the entire molecule will be in the exact center of the molecule. This will coincide with the center of positive charge for the molecule. When the center of negative charge and the center of positive charge coincide, there is no charge separation and no dipole. Figure 30: The center of positive and negative charge in a molecule. 398 (Created by: Richard Parsons, License: CC-BY-SA) If the two atoms sharing the bonding pair of electrons are not of the same element, the atom with the greater electronegativity will pull the shared electrons closer to it. Because of the resulting uneven distribution of electrons, the center of negative charge will not coincide with the center of positive charge and a dipole is created on the molecule. When the centers of positive and negative charge do not coincide, a charge separation exists and a dipole is present. Figure 31: Sketch of a polar molecule showing the separation of the centers of positive and negative charge. (Created by: Richard Parsons, License: CC-BY-SA) The end of the molecule with the more electronegative atom will have a partial negative charge and the end of the molecule with the more electropositive atom will have a slight positive charge. The symbols δ+ and δ- are used because these are not full 1+ and 1- charges. This polarity is much less of a charge separation than in an ionic bond. These charges are only fractions of full 1+ and 1- charges. How much polarity a bond will experience depends on the difference in the electronegativities of the atoms. No Dipole is Present on Symmetrical Molecules In the case of a symmetrical molecule with polar bonds, the symmetry of the electron displacements of two or more electron pairs will keep the center of negative charge in the center of the molecule coincident with the center of positive charge. When the centers of positive and negative charge are coincident, no dipole will occur. Figure 32: The Lewis structure for carbon dioxide. (Created by: Richard Parsons, License: CC-BY-SA) For example, in the CO2 molecule, both carbon-oxygen bonds are polar but the shift of bonding electrons toward the oxygen is the same on both sides of the carbon atom and the center of negative charge remains in the center. All bonds between non-metallic atoms that are not the same atom will be polar bonds. However, having polar bonds is not enough to guarantee than the molecule will be polar. If the molecule has those polar bonds in a symmetrical shape, the center of negative charge does not move away from the center of positive charge, and the molecule will not be polar. For a particular molecule to be symmetrical, all the attached atoms must be the same atom. For example, CH4 is a symmetrical molecule but CH3Cl is not symmetrical. Symmetrical Molecular Shapes 399 Molecular Geometry Example Molecule Symmetry Linear F2 Symmetrical Linear BeH2 Symmetrical Trigonal Planar BH3 Symmetrical Angular H2O Not Symmetrical Pyramidal NH3 Not Symmetrical Tetrahedral CH4 Symmetrical Trigonal Bipyramidal PCl5 Symmetrical Distorted Tetrahedron SF4 Not Symmetrical T-shaped ClF3 Not Symmetrical Octahedral SF6 Symmetrical Square Pyramidal ClF5 Not Symmetrical Square Planar XeF4 Symmetrical All molecules that have polar bonds and are not symmetrical will have a dipole on the molecule. Lesson Summary • Covalent bonds between atoms that are not identical will produce polar bonds. • Molecules with polar bonds and non-symmetrical shapes will have a dipole. Review Questions 1. What two requirements should be satisfied for a molecule to be polar? (Beginning) 2. BF3 contains polar bonds but the molecule is not polar. Why not? (Intermediate) 3. Which of the following molecules will be polar: ICl5, XeCl4, SeCl6? (Challenging) 4. Which of the following molecules will be polar: PCl3, SCl2, SiF4? (Challenging) 5. Which of the following molecules will have the largest dipole moment? (Intermediate) A. C2H2 B. CH2Cl2 C. BF3 D. CH3CH2OH E. HF 6. Which of the following molecules will have a triple bond? (Intermediate) A. C2H2 400 B. CH2Cl2 C. BF3 D. CH3CH2OH E. HF 2 7. Which of the following molecules has a central atom with sp hydridized orbitals? (Intermediate) A. C2H2 B. CH2Cl2 C. BF3 D. CH3CH2OH E. HF Further Reading / Supplemental Links http://learner.org/resources/series61.html''' The learner.org website allows users to view streaming videos of the Annenberg series of chemistry videos. You are required to register before you can watch the videos but there is no charge. The website has one video that relates to this lesson called Molecular Architecture . http://www.sparknotes.com/testprep/books/sat2/chemistry/section4section8.rhtml http://www.up.ac.za/academic/chem/mol_geom/mol_geometry.htm http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch8/lewis.html#step http://en.wikipedia.org/wiki/Molecular_geometry Vocabulary polar bond A covalent bond in which the shared pair of electrons are not shared equally owing to a difference in the electronegativity of the two atoms. molecular symme- The property of a molecule that enables it to undergo inversion try through a line, a point, or a plane, and its new state is indistinguishable from its original state. dipole A pair of equal and opposite charges separated by a small distance; a molecular dipole is produced when the centers of positive and negative charge do not coincide. Review Answers 1. A molecule will be polar if 1) it contains at least one polar bond, and 2) if the molecule is not symmetrical. 2. The molecular shapes for these three molecules are, respectively, square pyramidal, square planar, and octahedral. Square planar and octahedral are symmetrical and therefore, neither of those molecules will be 401 polar. The square pyramidal molecule, ICl5, will be polar. 3. The molecular shapes for these three molecules are, respectively, T-shaped, angular, and tetrahedral. T-shaped and angular molecules are not symmetrical and therefore are always polar. 4. The molecular shapes for these three molecules are, respectively, pyramidal, angular, and tetrahedral. Pyramidal and angular molecules are not symmetrical and are always polar. SiF4 is symmetrical and will not be polar. 5. E 6. A 7. C 402 CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. 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