Germanium 32 Ge 72.61 Nickel 28 Ni 8.693 Uranium 92 U 238.029 Sulfur 16 S 32.066 THE MOLE Worksheets
Measuring Matter Counting particles We always use the appropriate units for the number of objects. For example, we use the pair (2) to count the pairs, we use the dozen (12) to count pens or the packet (500) to count papers. Scientists also use specific units to count the atoms, particles or molecules. A mole (mol) is the amount of a substance that contains 6.02 10 23 representative particles of that substance. The mole is the SI unit for amount of a substance. The number 6.02 10 23 is called Avogadro s number, the number of representative particles in a mole. Seven elements exist in nature as diatomic molecules and they are H2, N2, O2, F2, Cl2, Br2, and I2. The representative particle for these elements is the molecule. Likewise, all molecular compounds such as H2O and CO2 exist as molecules and so the molecule is their representative particle. For ionic compounds such as NaCl and Ca(NO3)2, the representative particle is the formula unit. A mole of any substance contains Avogadro s number (6.02 10 23 ) of representative particles. 1) What is the SI unit for amount of a substance? Converting Between Moles and Particles We use the conversion factor to convert between different units 6.02 10 23 parcles 1mol, 1mol 6.02 10 23 parcles For the right results, there are two conditions to use the appropriate conversion factor I. The unit of result we want to get should be similar to the unit of the numerator in the conversion coefficient. II. The unit given in the question must resemble the unit of the denominator, which is what we multiple with the conversion coefficient. pg. 1
Converting Number of Particles to Moles The element carbon exists in two primary forms: graphite and diamond. How many moles of carbon atoms is 4.214 10 24 atoms of carbon? List the known quantities and plan the problem One suitable conversion factor will allow us to convert from the number of C atoms to moles of C atoms. number of C atoms = 4.214 10 24 atom 1 mole = 6.02 10 23 atoms 4.214 10 24 =? mol C 4.214 10 24 atoms C 1mol 6.02 10 23 atom = 7.84 mol C 2) How many moles of magnesium is 3.01 x 10 22 atoms of magnesium Mg? 3) How many moles are 1.20 x 10 25 atoms of phosphorous P? 4) How many moles contain 5.75 x 10 24 atoms Aluminum Al? 5) How many moles contain 2.50 x 10 20 atoms Iron Fe? 6) How many moles contain 3.75 x 10 24 molecule carbon dioxide CO2? pg. 2
7) How many moles contain 3.58 x 10 23 zinc chloride ZnCl2? Converting Moles to Number of Particles How many sucrose molecules in 3.5 mol? suitable conversion factor Number of sucrose moles = 3.5 mol 1 mole = 6.02 10 23 atoms 3.5 mol =? Molecule sucrose 3.5 mol 6.02 1023 molecule 1mol = 2.11 10 24 molecule sucrose 8) How many atoms are in 2.5 mol of zinc Zn? 9) How many Oxygen atoms in 5.0mol of O2 molecules? 10) How many molecules are in 0.400 moles of N2O5? 11) How many molecules are there in 4.00 moles of glucose, C6H12O6? pg. 3
Mass and mole 12) Do you expect that the mass of a dozen of watermelons and a dozen of olives will be the same? What's the reason? 13) Do you expect that the mass of a mol of sodium (Na) to be equal to a mole of iron (Fe)? What's the reason? One mole (abbreviated mol) is equal to the number of atoms in 12 grams of carbon-12; this number is referred to as Avogadro s number and has been measured as approximately 6.022x10 23. In other words, a mole is the amount of substance that contains as many entities (atoms, or other particles) as there are atoms in 12 grams of pure carbon-12. Molar Mass The molar mass of a compound tells you the mass of 1 mole of that substance. In other words, it tells you the number of grams per mole of a compound. The units for molar mass are, therefore, grams/mole. In 47.867 grams of Titanium one mole Atomic mass of Titanium is 47.867 amu 6.022 x 10 23 Titanium atoms However, molar mass can also be calculated by multiplying the atomic mass in amu by the molar mass constant (1 g/mol). To calculate the molar mass of a compound with multiple atoms, sum all the atomic mass of the constituent atoms. Calculating the molar mass of NaCl Atomic mass of sodium (22.99 g/mol Atomic mass of chlorine (35.45 g/mol) Combining them, the molar mass of NaCl is 58.44 g/mol. 11 Na 22.99 17 Cl 35.45 pg. 4
Moles to Grams In order to convert the moles of a substance to grams, you will need to multiply the mole value of the substance by its molar mass. What we have Moles # grams 1mole What we want where, # grams 1mole is the molar mass of the substance. Calculate the mass of 3 mol of copper Cu Number of Copper moles = 3.0 mol 1 mole Cu = 63.546 g Cu 3.0 mol =? g Cu 3.00 mol Cu 63.546 g Cu 1 mol Cu = 191 g Cu 14) Calculate the mass of 0.0450 mol of chromium Cr 15) Calculate the mass of 3.57 mol of aluminum Al 16) Calculate the mass of 3.54 x 102 mol of Cobalt Co pg. 5
Grams to Moles What we have grams 1 mol # grams What we want 17) How many calcium moles in 525 g? 18) How many moles in 25.5 g of silver Ag 19) How many moles in 1.25 103 g of zinc Zn 20) How many moles in 1.00 Kg of iron Fe pg. 6
Mass to Atoms It is not possible to convert from mass to the number of atoms directly. It must be converted from mass to number of moles, then converted from number of moles to number of atoms How many gold atoms are in a 31.1 g coin? 1 st step, calculating number of moles Mass of gold = 31.1 g Au 1 mole Au = 196.97 g Au 1 mole Au = 6.02 10 23 atom Au 31.1g Au =? atom 31.1 g Au 0.158 mol Au 6.02 1023 atom 1 mol Au 1 mol Au = 0.158 mol Au 196.97 g Au = 9.51 10 22 atom Au 2 nd step, calculating number of atoms 21) How many atoms in 11.5 g of mercury Hg 22) How many atoms in 55.2 g of Lithium Li 23) How many atoms in 0.230 g of Lead Pb 24) Calculate the number of oxygen molecules in 1.00 g of it pg. 7
Atoms to Mass We follow the previous steps where we convert the number of atoms to the number of moles and then turn the number of moles into a mass but, in reverse direction A balloon contains 5.50 x 10 22 atoms of helium, calculate the helium mass in the balloon 25) What mass of 1.50 10 15 atom of Uranium U 26) A balloon contains 5.50 x 1022 atoms of helium, calculate the helium mass in the balloon. 27) What mass of 1.50 10 15 atom of Nitrogen N pg. 8
Just one step We can make the calculations in just one step instead of two by multiplying the two conversation factors. How many gold atoms are in a 31.1 g coin? Mass of gold = 31.1 g Au 1 mole Au = 196.97 g Au 1 mole Au = 6.02 10 23 atom Au 31.1g Au =? atom Mass of gold = 31.1 g Au 1 mole Au = 196.97 g Au 1 mole Au = 6.02 10 23 atom Au 31.1g Au =? atom 31.1 g Au 1 mol Au = 0.158 mol Au 196.97 g Au 0.158 mol Au 6.02 1023 atom = 9.51 10 22 atom Au 1 mol Au One step 31.1 g Au 1 mol Au 196. 97 g Au 6. 02 1023 atom 1 mol Au = 9.51 10 22 atom Au 28) How many atoms in 55.2 g of Lithium Li 29) What mass of 1.50 10 15 atom of Uranium U pg. 9
Chemical formulas and moles Moles of compounds We previously calculated the number of moles, mass and the number of atoms for some elements as well as for some diatomic molecules, but what about compounds Compounds consist of groups of chemically bonded elements, each with a specific percentage of participation. For example, the Freon (Dichlorodifluoromethane) CCl2F2. CCl2F2 Elements ratio C Cl F 1 2 2 Conversation agents 1 mol C 1mol CCl 2 F 2 2 mol Cl 1mol CCl 2 F 2 2 mol F 1mol CCl 2 F 2 In this case we can calculate the number of moles in specific mass of Freon as well as the number of moles of each component a mol of Freon contains Avogadro s number of molecules so it contains the same ratio of each elements multiplied to Avogadro s number. Calculate the number of fluorine moles in 5.50 mol of Freon # moles of Freon = 5.50 mol #moles of Fluorine =? 5.50 mol Fereon What we have What we want 2 mol F = 11 mol F 1 mol Freon 30) Calculate the number of aluminum ions in 1.25 mol of aluminum oxide Al2O3 31) Calculate the number of chloride ions in 2.50 mol of zinc chloride ZnCl2 32) Calculate the number of moles of Hydrogen in 1.25 mol Glucose C6H12O6 33) Determine the number of moles of sulfate ions in 3.00 mol of Fe2(SO4)3 pg. 10
Molar mass of compounds The molar mass means the mass of one mole of matter The molar mass of an element means the mass of one mole of the element. The molar mass of the sodium element is 23 g/mol. The molar mass of the chlorine element is 71 g/mol, although the atomic mass of the chlorine element is 35.5 g /mol, that is because Chlorine exists as diatomic molecule Cl2. The molar mass of a compound can be calculated by combining the mass of components of one mole according to the number of elements Calculating the molar mass of Potassium Chromate compound K2CrO4 Elements mol ratio Molar mass 39.10 g K K 2 2mol K K2CrO4 molar mass Cr 1 1mol Cr O 4 4mol O 1mol K = 78.20 g 52.00 g Cr 1mol Cr = 78.20 g 16.00 g O 1mol O = 64.00g 194.20 g/mol Calculate the molar mass of NaOH Na mol ratio = 1 Na molar mass 23 g/mol O mol ratio = 1 O molar mass 16 g/mol H mol ratio = 1 H molar mass 1 g/mol Molar mass of NaOH =? g/mol Na mol ratio = 1 Na molar mass 23 g/mol O mol ratio = 1 O molar mass 16 g/mol H mol ratio = 1 H molar mass 1 g/mol Molar mass of NaOH =? g/mol One step 23 g Na 1mol Na 1mol Na 16 g O 1mol O 1mol O 23 g H 1mol H 1mol H = 23.00 g = 16.00 g = 1.00 g Molar mass = 23.00 + 16.00 + 1.00 = 40 g/mol (1mol Na 23 g Na 16 g O ) + ( 1mol O 1mol Na 1mol O ) 23 g H + ( 1mol H 1mol H ) = 40 g/mol 34) Calculate the molar mass of KC2H3O2 pg. 11
35) Calculate the molar mass of Sr(NO3)2 Convert Compounds Moles to Mass What is the mass of 2.50 mol of compound (C3H5)2S in grams 1 st step, calculating total molar mass C mol ratio = 6 C molar mass 12.01 g/mol H mol ratio = 10 H molar mass 1 g/mol S mol ratio = 1 S molar mass 32.07 g/mol Number of moles of (C3H5)2S = 2.50 mol 12.01 g C 1 g H 32.07 g S (6mol C ) + (10 mol H ) + (1mol S 1mol C 1mol H 1mol S ) 2.50 mol (C 3 H 5 ) 2 S = 114.21 g/mol 114.21 g mol 1mol (C 3 H 5 ) 2 S = 286 g (C 3H 5 ) 2 S 2 nd step, convert molar mass to mass 36) What is the mass of 3.25 mol of sulfuric acid H2SO4 in grams 37) What is the mass of 4.35 10-2 mol of Zinc chloride ZnCl2 in grams pg. 12
Convert compound mass to moles 38) Calculate the number of moles in 325 g calcium hydroxide Ca(OH)2 39) Calculate the number of moles in 22.6 g silver nitrate AgNO3 40) Calculate the number of moles in 2.50 kg Iron Oxide III Fe2O3 41) Calculate the number of moles in 25.4 mg Lead chloride PbCl4 pg. 13
Converting the mass of a compound number of particles To calculate the number of particles of a substance using its mass, we must follow specific steps. 1. Calculate the molar mass of the compound. 2. Convert the mass of the compound to number of moles. 3. Converting moles of compound to moles of particle. 4. Convert the number of moles to number of particles sample of 35.6 g aluminum chloride, calculate 1) Number of aluminum ions 2) Number of chloride ions 3) The mass in grams for the formula unit 26.98 g Al 35.45 g Cl (1 mol Al ) + (3 mol Cl ) = 133.33 g/mol 1mol Al 1mol Cl Mass of AlCl 3 = 35.6 g Number of Al 3+ ions =? Number of Cl - ions =? The mass in grams for the formula unit =? Mass for the formula unit means, the mass for just one particle of the compound. 35.6 g AlCl 3 1 mol AlCl 3 133.33 g AlCl 3 = 0.267 mol AlCl 3 1 mol Al3+ 0.267 mol AlCl 3 = 0.267 mol Al 3+ 1 mol AlCl 3 0.267 mol Al 3+ 6.02 1023 Al 3+ 1 mol Al 3+ = 1.61 10 23 ion Al 3+ 3 mol Cl 0.267 mol AlCl 3 = 0.801 mol Cl 1 mol AlCl 3 0.801 mol Cl 6.02 1023 Cl 1 mol Cl = 1.61 10 23 ion Cl 133.33 g AlCl 3 1 mol AlCl 3 1 mol AlCl 3 6.02 10 23 AlCl 3 = 0.267 mol AlCl 3 1 2 3 pg. 14
42) 45.6 g Sample of ethanol, Calculate a) Number of carbon atoms b) Number of hydrogen atoms c) Number of oxygen atoms 43) 2.25g sample of sodium sulfate, calculates a) Number of sodium ions b) Number of sulfate ions c) The mass of the grams of the formula unit pg. 15
Percent Composition Empirical formula and molecular formulas Chemists often need to know what elements are present in a compound and in what percentage. The percent composition: is the percent by mass of each element in a compound. mass of element % by mass = mass of compound 100 A certain newly synthesized compound is known to contain the elements zinc and oxygen. When a 20.00 g sample of the sample is decomposed, 16.07 g of zinc remains. Determine the percent composition of the compound. 1 st step, List the known quantities and plan the problem 2 nd step, subtract to find the mass of oxygen in the compound Oxygen mass = Sample mass Zink mass Sample mass = 20.00 g Zn mass = 16.07 g percent composition (Zn) =? percent composition (O) =? Oxygen mass = 20.00 g 16.07 g = 3.93 g % by mass = % by mass (Zn) = % by mass (O) = mass of element mass of compound 100 16.07 g 20.00 g 3.93 g 20.00 g 100 = 80.35% Zn 100 = 19.65% O 3 rd step, calculate 44) A chemist determines that 1.26 g of iron reacts with 0.54 g of oxygen to form rust. What is the percent composition of each element in the new compound? 45) In the lab, a chemist analyzed a sample of methanol and found that it was made of 6.2 g of carbon, 4.1 g of hydrogen, and 15.9 g of oxygen. What is the percent composition of each element? pg. 16
46) In an experiment, a student took a 12.2 g sample of table sale and chemically separated the chlorine from the sodium. He determined that there were 5.2 g of chlorine in the sample. What is the percent composition of each element in the table salt? 47) A compound contains 1.2 moles of carbon and 3.2 moles of hydrogen. What is the percent composition by mass of each element in the compound? 48) In an experiment, 0.05 moles of iron and 0.05 moles of sulfur are heated in a test tube to create a new substance. What is the percent composition by mass of each element in the new compound? 49) A chemist breaks down a compound into 3.4 moles of carbon and 6.8 moles of oxygen. What is the percent composition by mass of each element in the compound? pg. 17
50) In an experiment, 2.0 moles of oxygen atoms react with 80.1 g of calcium to form a new compound. What is the percent composition by mass of each element in the new compound? Percent Composition from a Chemical Formula The percent composition of a compound can also be determined from the formula of the compound % by mass = mass of element in one mol of compound molar mass of compound 100 What is the percent composition of CO2? One mole of Carbon Dioxide. one mole of carbon atoms. 2 moles of Oxygen atoms. Mass 1mol C = 12 g /mol Mass 1mol O = 16 g/ mol Mass of One mol CO2 = mass of 1mol C + mass of 2mol O % by mass = Mass of One mol CO2 = 12 g/mol + 2 (16) Mass of One mol CO2 = 44 g/mol mass of element in one mol of compound molar mass of compound % by mass (C) = 12g 44 g % by mass (O) = 32 g 44 g 100 = 27.30 % C 100 = 72.70 % O 100 51) What is the relative percentage composition of phosphoric acid H2SO4? pg. 18
52) Calculate the mass percentage of calcium chloride compound CaCl2 53) What is the percent composition by mass for each element in hydrogen peroxide, H2O2? 54) What is the percent composition by mass for each element in carbon dioxide, CO2? 55) What is the percent composition by mass for each element in carbon monoxide, CO? pg. 19
Empirical formula Determining Empirical Formulas An empirical formula is one that shows the lowest whole-number ratio of the elements in a compound. Because the structure of ionic compounds is an extended three-dimensional network of positive and negative ions, all formulas of ionic compounds are empirical. For example: The molecular formula for hydrogen peroxide is H2O2. This means there are two hydrogen atoms and two oxygen atoms in one molecule of hydrogen peroxide. The ratio between these elements is 1:1, For every hydrogen atom present in the molecule, there is one oxygen atom. The empirical formula is HO. A compound consisting of 40.05% S and 59.95% O write the empirical formula. In 100g of the compound 40.05 g S 59.95 g O 40.05 g (S) 59.95 g (O) 1 mol S = 1.249 mol S 32.07 g S 1 mol O = 3.7474mol O 16.00 g O 1.249 mol S 1.249 3.7474mol O 1.249 = 1 mol S = 3 mol O Empirical formula SO 3 Calculate number of moles of the components. Divide numbers of moles by the smallest to get the moles ratio. Write the empirical formula using the mole ratio 56) A chemical analysis of a sample of methyl acetate provides the following elemental data: 48.64% carbon (C), 8.16% hydrogen (H), and 43.20% oxygen (O). the empirical formula of the compound. pg. 20
57) compound consists of 36.84% N and 63.16% O Write the empirical formula of the compound. 58) Aspirin consists of 60% C, 35.56% O and 4.44% H Write the empirical formula of the compound pg. 21
Molecular formula Molecular formulas give the kind and number of atoms of each element present in a molecular compound. In many cases, the molecular formula is the same as the empirical formula. The molecular formula of methane is CH4 and because it contains only one carbon atom, that is also its empirical formula. benzene Acetylene Properties Mole ratio Molecular Weight 78.11 Molecular Weight 26.04 Boiling Point 80.1 o C Boiling Point -84.222222 C Melting Point 5.5 o C Melting Point 80.8 C C : H 6 : 6 1 : 1 C : H 1 : 1 Empirical formula CH CH Molecular Weight 78.11 26.04 Empirical formula weight 13.02 g/mol 13.02 g/mol Molecular Weight 78.11 n = Empirical formula weight 13.02 g/mol = 6 26.04 13.02 g/mol = 2 Molecular formula = (Empirical formula) n C6H6 C2H2 pg. 22
Succinic acid is a substance produced by lichens. Chemical analysis indicates it is composed of 40.68% C, 5.08% H, and 54.24% oxygen and has a molar mass of 118.1g/mol. Determine the empirical formula for succinic acid. 40.68 g C 45.24 g O 5.08 g H 1 mol C = 3.387 mol C 12.01 g C 1 mol O = 3.390 mol O 16.00 g O 1 mol H = 5.04 mol H 1.008 g H 3.387 mol C 1 mol C 3.387 3.390 mol O 1 mol O 3.387 5.04 mol H 1.5 mol H 3.387 Percent by mass C = 40.68% Percent by mass H = 5.08% Percent by mass O = 45.24% molar mass = 118.1g / mol Empirical formula? 2 1 mol C = 2 mol C 2 1 mol O = 2 mol O 2 1.5 mol H = 3 mol H Empirical formula C 2 H 3 O 2 Multiple by 2 to obtain whole number. Molecular formula? 2mol C 2mol O 3mol H 12.01 g C 1mol C 16.00 g O 1mol O = 24.02 g C = 32.00 g O 1.008 g H 1mol H = 3.024 Empirical formula weight = 24.02 + 32.00 + 3.024 = 59.04 g/mol n = Molecular Weight Empirical formula weight = 118.1 g/mol 59.04 g/mol = 2 Molecular formula = (Empirical formula) n (C 2 H 3 O 2 ) 2 Molecular formula C 4 H 6 O 4 pg. 23
59) Ilmenite contains 5.41g of iron, 4.64g of titanium and 4.65g of oxygen determine the molecular formula of this compound pg. 24
60) A compound containing 49.98g carbon and 10.47g hydrogen, determine the molecular formula of this compound if its mass is 58.12g / mol pg. 25
61) Using the corresponding diagram, the molecular formula of the compound was derived if its mass was 110.0g / mol pg. 26
62) Write the empirical morphine formula by indicating the data in the table Element Mass (g) Carbon 17.900 Hydrogen 1.680 Oxygen 4.225 Nitrogen 1.228 pg. 27
Formula of Hydrates Many ionic compounds naturally contain water as part of the crystal lattice structure. A Hydrate is a compound that has one or more water molecules bound to each formula unit. Ionic compounds that contain a transition metal are often highly colored. Interestingly, it is common for the hydrated form of a compound to be of a different color than the anhydrous form, which has no water in its structure. A hydrate can usually be converted to the anhydrous compound by heating. Anhydrous cobalt(ii) chloride Cobalt(II) chloride hexahydrate color Blue Distinctive magenta formula CoCl2 CoCl2 6H2O It is useful to know the percent of water contained within a hydrate. We use Romanian numbers to describe how many water molecules are there in the hydrate. Name the following hydrates: 63) CaCl2. 8H 2 O 64) FeSO4. 6H 2 O 65) LiOH. H 2 O 66) PbCl2. 3H 2 O 67) Li2CrO4. 5H 2 O 68) Na2SO4. 10 H 2 O 69) Hg(NO 3 ) 2. H 2 O 70) SnCl4. 5H 2 O 71) LiNO3. 3H 2 O pg. 28
Write the formulas for the following hydrates: 72) Barium Phosphate dihydrate 73) Copper(II)sulfate pentahydrate 74) Cobalt chloride hexahydrate 75) Magnesium sulfate heptahydrate 76) Nickel (II) sulfate hexahydrate 77) Copper (I) Bromide tetrahydrate 78) calcium nitrate dihydrate 79) cobalt (II) fluoride tetrahydrate 80) odium phosphate tetrahydrate Hydrates are ionic compounds (salts) that have a definite amount of water as part of their chemical formula. The number of moles of water per mole of ionic substance is usually an integer. This water of hydration is released as vapor when the hydrate is heated. The water in a hydrate is bound loosely, and so is relatively easily removed by heating. Most hydrates lose their water of hydration at temperatures slightly above 100 o C. Sometimes the water is liberated in stages, with one or more lower hydrates being observed during the heating process. The remaining solid is known as the anhydrous salt. The general reaction for heating a hydrate is: Hydrate (s) Anhydrous salt (s) + water (g) The percent of water in a hydrate can be found experimentally by accurately determining the mass of the hydrate and the mass of the anhydrous salt. The difference in mass is due to the water lost by the hydrate. The percent of water in the original hydrate can be calculated easily: % H2O = ( Mass of water Mass of hydrate ) x 100 pg. 29
To determine a hydrate formula A sample of 5g of hydrate barium chloride after heating has become a mass of 4.26g Write the hydrate salt formula of barium chloride Sample mass = 5g mass without water = 4.26g Water mass = 5g 4.26g = 0.74g H2O 0.74g H 2 O 1 mol H 2O 18.02 g H 2 O = 0.041 mol H 2O 4.26g BaCl 2 1 mol BaCl 2 208.23 g BaCl 2 = 0.0205 mol BaCl 2 X = mol H 2O mol BaCl 2 = 0.041 mol H 2 O 0.0205 mol BaCl 2 = 2 1 formula BaCL2. 2H2O 1 st step, calculate water mass 2 nd step, calculate water and cpmpound moles 3 rd step, calculate water and cpmpound moles ratio 4 th step, write the formula 81) A sample of 2,5g blue hydroxyl sulfate remained after heating 1.59g of white anhydrous copper sulphate. What is the hydrate salt formula 82) Write the hydrate salt formula represented by the adjacent shape pg. 30
Uses of hydrate salts Calcium chloride is used as a laboratory d and is placed in closedloop containers called desiccators to keep chemicals dry. Calcium sulphate is added to organic solvents such as ethanol and ethyl ether to keep them dry Sodium hydroxide is used to store solar energy, which dissolves in the 10 water molecules when the temperature reaches 32 C The solution absorbs energy and lose water. When the atmosphere cools, the solution releases energy and crystallizes again pg. 31