If your sample is made of one element, like copper, locate the atomic mass on the periodic table. Platinum (atomic radius = 1.38 ) crystallizes in a cubic closely packed structure. The rotated view emphasizes the fcc nature of the unit cell (outlined). Arrange the three types of cubic unit cells in order of increasing packing efficiency. The density of a metal and length of the unit cell can be used to determine the type for packing. Is the structure of this metal simple cubic, bcc, fcc, or hcp? We get an answer in #"moles"#, because dimensionally #1/(mol^-1)=1/(1/(mol))=mol# as required. Because the atoms are on identical lattice points, they have identical environments. Valence Bond Theory and Hybridization (M9Q3), 51. B. B. Because density is the mass of substance per unit volume, we can calculate the density of the bulk material from the density of a single unit cell. If given the mass of a substance and asked to find the number of atoms in the substance, one must first convert the mass of the substance, in grams, to moles, as in Example \(\PageIndex{1}\). From there, I will use the fact that there are 4 atoms of gold in the unit cell to determine the density. Explanation: To calculate the n of moles of Ca that they are in 137 g, we can use the next relation: n = mass/atomic mass = (137 g)/ (40.078 g/mol) = 3.4 mol. Propose two explanations for this observation. For each mole of a molecule contains Avogadro's number of molecules (NA = 6.022 x 10). Gypsum is a mineral, or natural substance, that is a hydrate of calcium sulfate. Report. Only one element (polonium) crystallizes with a simple cubic unit cell. 0.316 mols (6.022x1023 atoms/ 1mol) = 1.904x1023 atoms of O, 0.055 mols (6.022x1023 atoms/ 1mol) = 3.312x1022 atoms of K, 4. What conclusion(s) can you draw about the material? How many Fe atoms are in each unit cell? If we choose the first arrangement and repeat the pattern in succeeding layers, the positions of the atoms alternate from layer to layer in the pattern ABABAB, resulting in a hexagonal close-packed (hcp) structure (part (a) in Figure 12.7). How many atoms are in 195 grams of calcium? Core and Valence Electrons, Shielding, Zeff (M7Q8), 43. In a cubic unit cell, corners are 1/8 of an atom, edges are 1/4 of an atom, and faces are 1/2 of an atom. Most questions answered within 4 hours. D) CO, The analysis of a compound shows it contains 5.4 mol C, 7.2 mol H, and 1.8 mol N. What is the empirical formula of the compound? D. 2.0x10^23 (The mass of one mole of calcium is 40.08 g.).00498 mol. (CC BY-NC-SA; anonymous by request). The hcp and ccp structures differ only in the way their layers are stacked. around the world. 2 chlorine atoms are needed. I'll call it the reference cube. (b) Placing an atom at a B position prohibits placing an atom at any of the adjacent C positions and results in all the atoms in the second layer occupying the B positions. The atomic mass of Copper is 63.55 atomic mass units. The number of atoms can also be calculated using Avogadro's Constant (6.022141791023) / one mole of substance. B) CHN The mole concept is also applicable to the composition of chemical compounds. So #"Moles of calcium"# #=# #(197*cancelg)/(40.1*cancelg*mol^-1)#. The density of a metal and length of the unit cell can be used to determine the type for packing. + 126 (17) + 128 (3) = 12686/100 = 126.86 amu 2. Which of the following is this compound? Because the atoms are on identical lattice points, they have identical environments. To do this, we need to know the size of the unit cell (to obtain its volume), the molar mass of its components, and the number of components per unit cell. The arrangement of atoms in a simple cubic unit cell. The line that connects the atoms in the first and fourth layers of the ccp structure is the body diagonal of the cube. C. .045 g \[3.00 \; \cancel{g\; K} \left(\dfrac{1\; mol\; K}{39.10\; \cancel{g\; K}}\right) = 0.0767\; mol\; K \nonumber \]. B. 4) Determine mass of one formula unit of CaF2: 78.074 g/mol divided by 6.022 x 1023 formula units / mole = 1.2965 x 10-22 g. 5) Determine number of formula units in one unit cell: There are 4 formula units of CaF2 per unit cell. What is the total number of atoms contained in 2.00 moles of iron? B. In principle, all six sites are the same, and any one of them could be occupied by an atom in the next layer. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question You should check your copy of the Periodic Table to see if I have got it right. The number of moles in a system can be determined using the atomic mass of an element, which can be found on the periodic table. A. SO2 .5 Legal. D. 4 E. 89%, Mass percent of titanium in TiCl2? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. A. C. N2O The total number of atoms in a substance can also be determined by using the relationship between grams, moles, and atoms. Electron Configurations, Orbital Box Notation (M7Q7), 41. How many moles of calcium atoms do you have if you have 3.00 10 atoms of calcium. (1 = 1 x 10-8 cm. Some metals crystallize in an arrangement that has a cubic unit cell with atoms at all of the corners and an atom in the center, as shown in Figure 2. Calorimetry continued: Types of Calorimeters and Analyzing Heat Flow (M6Q5), 31. Does gold crystallize in a face-centered cubic structure or a body-centered cubic structure? Explain how the intensive properties of a material are reflected in the unit cell. E. 1.4 x 10^24, What is the amss of 1.5 x 10^21 water molecules? 9. Verifying that the units cancel properly is a good way to make sure the correct method is used. .75 A. The most efficient way to pack spheres is the close-packed arrangement, which has two variants. 39.10 grams is the molar mass of one mole of K. Grams can be canceled, leaving the moles of K. How many grams is in 10.00 moles of calcium (Ca)? If the metallic radius of tungsten is 139 pm, what is the structure of metallic tungsten? Using Avogadro's number, #6.022 xx 10^23"particles"/"mol"#, we can calculate the number of atoms present: #color(blue)(3.82# #cancel(color(blue)("mol Ca"))((6.022xx10^23"atoms Ca")/(1cancel("mol Ca")))#, #= color(red)(2.30 xx 10^24# #color(red)("atoms Ca"#, 84931 views (ac) Three two-dimensional lattices illustrate the possible choices of the unit cell. The following table provides a reference for the ways in which these various quantities can be manipulated: status page at https://status.libretexts.org, 1/Molar mass (mol/g) Avogadro's constant (atoms/mol)). ), Then, the density of Ca = [latex]\frac{2.662\;\times\;10^{-22}\;\text{g}}{1.745\;\times\;10^{-22}\;\text{cm}^{3}}[/latex] = 1.53 g/cm3. Calculation of Atomic Radius and Density for Metals, Part 2 Electron Configurations for Ions (M7Q10), 46. Note, however, that we are assuming a solid consists of a perfect regular array of unit cells, whereas real substances contain impurities and defects that affect many of their bulk properties, including density. 2) Calculate the volume of the unit cell: 3) Calculate the mass of TlCl in one unit cell: 4) Determine how many moles of TlCl are in the unit cell: 5) Formula units of TlCl in the unit cell: Face-centered cubic has 4 atoms per unit cell. Note that an answer that uses #N_A# to represent the given number would be quite acceptable; of course you could multiply it out. In this question, the substance is Calcium. 4.0 x10^23 in #23*g# of sodium metal? What is the approximate metallic radius of lithium in picometers? 5. E. FeBr, A compound is 30.4% N and 69.6% O. Multiply moles of Ca by the conversion factor 40.08 g Ca/ 1 mol Ca, with 40.08 g being the molar mass of one mole of Ca. 1 Ca unit cell [latex]\frac{4\;\text{Ca atoms}}{1\;\text{Ca unit cell}}[/latex] [latex]\frac{1\;\text{mol Ca}}{6.022\;\times\;10^{23}\;\text{Ca atoms}}[/latex] [latex]\frac{40.078\;\text{g}}{1\;\text{mol Ca}}[/latex] = 2.662 10. . How many grams are 10.78 moles of Calcium (\(\ce{Ca}\))? For Free. A simple cubic cell contains one metal atom with a metallic radius of 100 pm. Simple cubic and bcc arrangements fill only 52% and 68% of the available space with atoms, respectively. No packages or subscriptions, pay only for the time you need. Multiply moles of Ca by the conversion factor (molar mass of calcium) 40.08 g Ca/ 1 mol Ca, which then allows the cancelation of moles, leaving grams of Ca. What is the approximate metallic radius of the vanadium in picometers? Aluminum (atomic radius = 1.43 ) crystallizes in a cubic closely packed structure. cubic close packed (identical to face-centered cubic). What is the coordination number of an aluminum atom in the face-centered cubic structure of aluminum? Which of the following is this compound? Then divide the mass by the volume of the cell. UW-Madison Chemistry 103/104 Resource Book by crlandis is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. Ca looses 2 electrons. (d) The triangle is not a valid unit cell because repeating it in space fills only half of the space in the pattern. I will use that assumption and the atomic radii to calculate the volume of the cell. 6. (b) Density is given by density = [latex]\frac{\text{mass}}{\text{volume}}[/latex]. 11. edge length: 3.903 ; density: 21.79 g/cm, edge length: 4.045 ; density: 2.709 g/cm. To calculate the density we need to know the mass of 4 atoms and volume of 4 atoms in FCC unit cell. The density of tungsten is 19.3 g/cm3. The hexagonal close-packed (hcp) structure has an ABABAB repeating arrangement, and the cubic close-packed (ccp) structure has an ABCABC repeating pattern; the latter is identical to an fcc lattice. 10 Determine the number of atoms of O in 10.0 grams of CHO, What is the empirical formula of acetic acid, HCHO? And so we take the quotient, 169 g 40.1 g mol1, and multiply this by N A,Avogadro's number of molecules, where N A = 6.022 1023 mol1. If the cubic unit cell consists of eight component atoms, molecules, or ions located at the corners of the cube, then it is called simple cubic (part (a) in Figure 12.5). Join Yahoo Answers and get 100 points today. Calculate the density of metallic iron, which has a body-centered cubic unit cell (part (b) in Figure 12.5) with an edge length of 286.6 pm. Using cross multiplication: 1 mole of Ca contains 6.022 x 10 atoms. See the answer. Table 12.1 compares the packing efficiency and the number of nearest neighbors for the different cubic and close-packed structures; the number of nearest neighbors is called the coordination number. Assuming that the rest of the sample is water, how many moles of H2O are there in the sample? Determine the number of atoms of O in 92.3 moles of Cr(PO). Resonance Structures and Formal Charge (M8Q3), 48. Dec 8, 2015 0.650 g Au contain 1.99 1021atoms. In this example, multiply the mass of \(\ce{K}\) by the conversion factor (inverse molar mass of potassium): \[\dfrac{1\; mol\; K}{39.10\; grams \;K} \nonumber \]. 1. C. C4H14O (b) Because atoms are spherical, they cannot occupy all of the space of the cube. 2.9: Determining the Mass, Moles, and Number of Particles is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. Solutions and Solubility (part 2) (M3Q2), 12. As we shall see, such substances can be viewed as consisting of identical spheres packed together in space; the way the components are packed together produces the different unit cells. This is called a body-centered cubic (BCC) solid. Add the contributions of all the Au atoms to obtain the total number of Au atoms in a unit cell. The total number of atoms in a substance can also be determined by using the relationship between grams, moles, and atoms. 8. How does the coordination number depend on the structure of the metal? (The mass of one mole of calcium is 40.08 g.). Follow. Actually, however, these six sites can be divided into two sets, labeled B and C in part (a) in Figure 12.6. 32g Atomic mass of Chloride- 35.45 amu and valence of Chloride is 7. one calcium atom is needed. Heating Curves and Phase Diagrams (M11Q2), 60. Which of the following compounds contains the largest number of atoms? The atoms at the corners touch the atoms in the centers of the adjacent faces along the face diagonals of the cube. Converting the mass, in grams, of a substance to moles requires a conversion factor of (one mole of substance/molar mass of substance). C) CH Each atom contacts six atoms in its own layer, three in the layer above, and three in the layer below. The hcp and ccp arrangements fill 74% of the available space and have a coordination number of 12 for each atom in the lattice, the number of nearest neighbors. Scientists who study ancient marine life forms usually obtain fossils not from the sea floor, but from areas that were once undersea and have been uplifted onto the continents. Please see a small discussion of this in problem #1 here. E. 2.4 x 10^24, What is the mass of 20 moles of NH3? Cell 2: 8 F atoms at the 8 vertices. To do so, I will use the Pythagorean Theorem. B. S2O3 Problem #11: Many metals pack in cubic unit cells. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. A) C.HO This arrangement is called a face-centered cubic (FCC) solid. Solutions and Solubility (part 1) (M3Q1), 11. Can crystals of a solid have more than six sides? A) CH (Elements or compounds that crystallize with the same structure are said to be isomorphous.). Identify the metal, determine the unit cell dimensions, and give the approximate size of the atom in picometers. The molar mass is used to convert grams of a substance to moles and is used often in chemistry. What is the empirical formula of this substance? The experimentally measured density of a bulk material is slightly higher than expected based on the structure of the pure material. Figure 3. Explain your answer. A. 1.00 mole of H2SO4. ), 0.098071 mol times 6.022 x 1023 atoms/mol = 5.9058 x 1022 atoms, 1 cm divided by 4.08 x 10-8 cm = 24509804 (this is how many 4.08 segments in 1 cm), 24509804 cubed = 1.47238 x 1022 unit cells. So: The only choice to fit the above criteria is answer choice b, Na3N. (CC BY-NC-SA; anonymous by request). (CC BY-NC-SA; anonymous by request). For instance, consider methane, CH4. A 1.000-g sample of gypsum contains 0.791 g CaSO4. How many grams of carbs should a type 1 diabetic eat per day? B. Explanation: Calculate the moles of gold by dividing the given mass by its molar mass, 196.966569 g/mol (atomic weight on periodic table in g/mol). Get a free answer to a quick problem. a gas at -200. Unit cells are easiest to visualize in two dimensions. Because a crystalline solid consists of repeating patterns of its components in three dimensions (a crystal lattice), we can represent the entire crystal by drawing the structure of the smallest identical units that, when stacked together, form the crystal. 10. Number of atoms = Mass Molar mass Avogadro's number. So there are 2.46 moles of Ca (or Ca atoms). Using Figure 12.5, identify the positions of the Au atoms in a face-centered cubic unit cell and then determine how much each Au atom contributes to the unit cell. Explaining Solubility and Surface Tension through IMFs (M10Q4), 58. For all unit cells except hexagonal, atoms on the faces contribute \({1\over 2}\) atom to each unit cell, atoms on the edges contribute \({1 \over 4}\) atom to each unit cell, and atoms on the corners contribute \({1 \over 8}\) atom to each unit cell. The "molar mass" of (1/2)NaCl is half of 58.443. 1) I will assume the unit cell is face-centered cubic. In this this chemical reactions, the moles of H and O describe the number of atoms of each element that react to form 1 mol of \(\ce{H_2O}\). Cubic closest packed structure which means the unit cell is face - centered cubic. In the United States, 112 people were killed, and 23 are still missing0. Complete reaction with chlorine gas requires 848.3 mL of chlorine gas at 1.050 atm and 25C. D. FeBr3 D. 3.6 x 10 ^24 C) C.H.N. What volume in mL of 0.3000 M NaCl solution is required to produce 0.1500 moles of NaCl? A. C. 80 g B. C6H6 J.R. S. 1) Determine the volume of the unit cell: Note that I converted from to cm. answered 07/07/21, Experienced Tutor with BS Degree Specializing in ACT Preparation. Sites B and C differ because as soon as we place a sphere at a B position, we can no longer place a sphere in any of the three C positions adjacent to A and vice versa. How do you calculate the number of moles from volume? Also, one mole of nitrogen atoms contain, Example \(\PageIndex{1}\): Converting Mass to Moles, Example \(\PageIndex{2}\): Converting Moles to mass, constant, it is also easy to calculate the number of atoms or molecules present in a substance (Table. How do you calculate the moles of a substance? Most of the substances with structures of this type are metals. Calorimetry continued: Phase Changes and Heating Curves (M6Q6), 33. 4.366mol * 6.022*10^23atoms/mol = 2.629*10^24 atoms of Ca in 175g of Ca. C. 2 The lengths of the edges of the unit cells are indicated by a, b, and c, and the angles are defined as follows: , the angle between b and c; , the angle between a and c; and , the angle between a and b. A teacher walks into the Classroom and says If only Yesterday was Tomorrow Today would have been a Saturday Which Day did the Teacher make this Statement? Therefore, the answer is 3.69 X Explanation: We're asked to calculate the number of atoms of Ca in 153 g Ca. Figure 12.5 The Three Kinds of Cubic Unit Cell. 10.0gAu x 1 mol . In CCP, there are three repeating layers of hexagonally arranged atoms. Calculate its density. To recognize the unit cell of a crystalline solid. Explain your reasoning. Problem #3: (a) You are given a cube of silver metal that measures 1.015 cm on each edge. C. 2.25 Atoms on a corner are shared by eight unit cells and hence contribute only \({1 \over 8}\) atom per unit cell, giving 8\({1 \over 8}\) =1 Au atom per unit cell. Problem #1: Many metals pack in cubic unit cells. The cubic hole in the middle of the cell has a barium in it. Vanadium is used in the manufacture of rust-resistant vanadium steel. For instance, consider the size of one single grain of wheat. By multiplying the number of moles by Avogadro's constant, the mol units cancel out, leaving the number of atoms. 1 point How many chlorine atoms are there in 20.65 moles of aluminum chloride? The unit cell has an edge of 546.26 pm and has a density of 3.180 g/cm3. Ni Lithium Li Copper Cu Sodium Na Zinc Zn Potassium K Manganese Mn Cesium Cs Iron Fe Francium Fr Silver Ag Beryllium Be Tin Sn Magnesium Mg Lead Pb Calcium Ca Aluminum Al Strontium Sr Gold Au Barium . Because atoms on a face are shared by two unit cells, each counts as \({1 \over 2}\) atom per unit cell, giving 6\({1 \over 2}\)=3 Au atoms per unit cell. Lithium crystallizes in a bcc structure with an edge length of 3.509 . Many other metals, such as aluminum, copper, and lead, crystallize in an arrangement that has a cubic unit cell with atoms at all of the corners and at the centers of each face, as illustrated in Figure 3. A 10 -liter cylinder containing oxygen at 175 atm absolute is used to supply O2\mathrm{O}_2O2 to an oxygen tent. Here is one face of a face-centered cubic unit cell: 2) Across the face of the unit cell, there are 4 radii of gold, hence 576 pm. (c) Using the volume of a silver atom and the formula for the volume of a sphere, calculate the radius in angstroms of a silver atom. Upvote 0 Downvote Add comment Report Still looking for help? Calculate the edge length of the face-centered cubic unit cell and the density of aluminum. 44 g. How many grams are in 2.05 1023 molecules of dinitrogen pentoxide? (8 [latex]\frac{1}{8}[/latex] = 1 atom from the corners), (6 [latex]\frac{1}{2}[/latex] = 3 atoms from the corners), UW-Madison Chemistry 103/104 Resource Book, Next: Ionic Crystals and Unit Cell Stoichiometry (M11Q6), Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. The simple cubic and bcc lattices have coordination numbers of 6 and 8, respectively. What are the 4 major sources of law in Zimbabwe. Solution: Using the generic expression to convert g to atoms: Number of Atoms = (Given Mass/Molar Mass) * Avogadro's Number Number of Atoms = (78/40.078) * 6.02 * 10^ {23} Number of Atoms = 1.9462 * 6.02 * 10^ {23} Number of Atoms = 1.171 * 10^ {+24} Step-by-step solution. #calcium #earth #moon. The cubic hole in the middle of the cell is empty. What are the 4 major sources of law in Zimbabwe? What is are the functions of diverse organisms? The nuclear power plants produce energy by ____________. Browse more videos. Metal atoms can pack in primitive cubic, body-centered cubic, and face-centered cubic structures. All the alkali metals, barium, radium, and several of the transition metals have body-centered cubic structures. #5xxN_A#, where #N_A# is #"Avogadro's number"#. From there, we take the 77.4 grams in the original question, divide by 40.078 grams and we get moles of Calcium which is 1.93 moles. Calcium sulfate, CaSO4, is a white, crystalline powder. How many formula units must there be per unit cell? Molarity, Solutions, and Dilutions (M4Q6), 23. Cell 1: 8 F atoms at the 8 vertices. Identify what defines a unit cell; distinguish between the three common cubic unit cell types and their characteristics. Solution. In this case, the mole is used as a common unit that can be applied to a ratio as shown below: \[2 \text{ mol H } + 1 \text{ mol O }= 1 \text{ mol } \ce{H2O} \nonumber\]. A 21.64 g sample of a nonreactive metal is placed in a flask containing 12.00 mL of water; the final volume is 13.81 mL. 10 See the answer Show transcribed image text Expert Answer 100% (1 rating) B) CHO A face-centered Ca unit cell has one-eighth of an atom at each of the eight corners (8 [latex]\frac{1}{8}[/latex] = 1atom) and one-half of an atom on each of the six faces (6 [latex]\frac{1}{2}[/latex] = 3), for a total of four atoms in the unit cell. Our discussion of the three-dimensional structures of solids has considered only substances in which all the components are identical. 1 atom. What is the difference in packing efficiency between the hcp structure and the ccp structure? The density of iron is 7.87 g/cm3. (a) In this single layer of close-packed spheres, each sphere is surrounded by six others in a hexagonal arrangement. 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