DETERMINATION OF AN EMPIRICAL FORMULA 1 Empirical Formulas • Empirical formula (“formula unit”) -the lowest whole number ratio of atoms in an ionic compound. • There are two ways to determine the empirical formula for an ionic compound. 1. Using charges (use your ions and this is easy). C CRISS O S S 2. Mathematically (yippee!!!) 2 Method #1 – Charges EX: Write the empirical formula for the compound formed by Na & P c. K & Ne Na3P Sr & Cl SrCl2 No compound d. Cu & Cl CuCl or CuCl2 3 Method #2 – Mathematically • Step 1:Use the information given in the problem and dimensional analysis with the atomic mass of the element (from periodic table- round to 3 SDs) to find the number of moles you have • Step 2:Take all the mole values and divide them by the SMALLEST one to figure out a ratio • Step 3: Use the answers as subscripts 4 in the empirical formula Reference-Empirical Formulas 7.06 g of silver combine with an excess of fluorine to produce 8.30 g of a compound Silver 7.06g + Fluorine 1.24g ο Ag?F? 8.30g Found by subtracting! 7.06 g Ag X π ππππ π¨π πππ π π¨π .ππππ = .0654 moles Ag .ππππ = 1.00 or 1 Ag1F1 1.24 g F X π ππππ π ππ.π π π = .0653 moles F .ππππ .ππππ = 1.00 or 1 ANSWER = AgF 5 Reference-Empirical Formulas A compound contains 24.58% K, 35.81% Mn, and 40.50% O. Find the empirical formula (assume working with 100 grams of the compound and change percentages to grams) 24.58 g K X 35.81 g Mn X 40.50 g O X 1 ππππ πΎ 39.1 π πΎ = .629 mole K .πππ .πππ = 1.00 or 1 1 ππππ ππ = .652 moles Mn 54.9 π ππ .πππ .πππ = 1.04 or 1 1 ππππ π 16.0 π π π.ππ .πππ = 4.02 or 4 = 2.53 moles O 6 ANSWER = KMnO4 Uneven Empirical Formulas • When figuring empirical formulas mathematically, sometimes the resulting numbers don’t come out so clean • You can’t just assume and round how you choose 7 Reference- .05 Rule • Values used in these problems are obtained by experimentation. The 0.05 rule allows for experimental error: – If the value is within .05 of a whole number (+0.05 or - 0.05), then the value may be rounded to that whole number – Examples: 1.96 can be rounded to 2 • 1.07 cannot be rounded to 1 • 3.02 could be rounded to 3 • 1.93 cannot be rounded to 2 • IF one of the values is not within .05 of a whole number, all the values must be multiplied by an integer so that all values fall within .05 of whole 8 numbers Reference-Uneven Empirical Formulas 4.35 g sample of zinc is combined with an excess of the element phosphorus. 5.72 g of compound are formed. Calculate the empirical formula. Zinc + Phosphorous ο Zn?P? 4.35g 1.37g Found by 5.72g 4.35 g Zn X π ππππ ππ ππ.π π ππ = .0665 moles Zn subtracting! .ππππ .ππππ = 1.50 X 2 = 3.00 or 3 Not within .05 of a whole number π ππππ π· ππ· 1.37 g P X ππ.π = .0442 moles P .ππππ = 1.00 X 2 = 2.00 or 2 .ππππ 9 ANSWER = Zn3P2 Let’s Do It!!! A compound is found to contain 72.3% Fe and 27.7% O by weight. Calculate the empirical formula. Assume in 100 g of compound there would be 72.3 g Fe and 27.7 g O 10 72.3g Fe 1 mole Fe X —————— 55.8 g Fe 1.30 mole = 1.00 1.30 mole = 1.30 mole Fe X 3 = 3.00 = 3 1 mole O 27.7g O X —————— = 1.73 mole O 16.0 g O 1.73 mole =1.33 X 3 = 3.99 = 4 1.30 mole Fe3O4 11 Review • Number your paper from 1-5 and answer the following questions. Two will be cumulative review! • 1. Which of these is the correct symbol for Chlorine-35? • a. 35 Cl 17 • b. 17 Cl 37 • c. 17 35 Cl 12 Review • A • 2. Which is the correct answer with the right number of SD’s if we add 75g and 25.0g? – a. 105 g – b. 10Ε g – c. 100.0 g – d. 105.0 g 13 Review • B • 3. Which is correct if we consider our rounding rule? – a. 4.02 couldn’t be rounded to 4 but 1.93 can be rounded to 2 – b. 4.02 couldn’t be rounded to 4 and 1.93 can’t be rounded to 2 – c. 4.02 can be rounded to 4 and 1.93 can be rounded to 2 – d. 4.02 can be rounded to 4 and 1.93 14 can’t be rounded to 2 Review • D • 4. Zinc + Phosphorous ο Zn?P? 4.35g ?g 5.72g – a. 4.35 g – b. 2.37 g – c. 1.37 g – d. 1.47 g 15 Review • C • 5. If I have 32.0g of O, then how many moles is this? – a. 2.0 moles – b. 2.5 moles – c. 2 moles – d. 20 moles 16 Review • A 17 Molar Mass • KC4H5O6 is the empirical formula for cream of tartar • How many atoms of oxygen are in 1 formula unit of cream of tartar? 6 atoms O 18 Molar Mass • KC4H5O6 • How many atoms are in 1 formula unit of cream of tartar? 16 atoms 1 potassium 4 carbon 5 hydrogen 6 oxygen 19 Molar Mass • KC4H5O6 • How many formula units are in 1 mole of cream of tartar? 6.02 x 1023 formula units 20 Molar Mass • KC4H5O6 • How many atoms of oxygen are in (PER) 1 mole of cream of tartar? • ? atoms O/mole KC4H5O6 = 6 atoms O 1 formula unit KC4H5O6 x 6.02 x1023 formula unit KC4H5O6 1 mole KC4H5O6 3.61 x 1024 atoms O/mole KC4H5O6 21 Molar Mass • KC4H5O6 • How many moles of oxygen atoms are in 1 mole of cream of tartar? • Let’s put this in perspective………. 22 How many wheels are in a dozen bicycles? 1 bicycle = 2 wheels 1 dozen bicycles = 2 dozen wheels 23 1 mole bicycles = 2 mole wheels How many dozen hydrogen atoms are in 1 dozen water molecules? H2O 1 water = 2 hydrogen 1 dozen water = 2 dozen hydrogen 1 mole water = 2 mole hydrogen 24 Molar Mass • So……… • KC4H5O6 • How many moles of oxygen atoms are in 1 mole of cream of tartar? 6 moles O 25 Molar Mass • KC4H5O6 • What is the mass of the oxygen atoms in (PER) 1 mole of cream of tartar? ? g O/ mole KC4H5O6 6 moles O x 1 mole KC4H5O6 16.0 g O = 96.0 g O 1 mole O mole KC4H5O6 26 Let’s Do It!!! • How many atoms in one formula unit? Magnesium Acetate: Mg(C2H3O2)2 1-Mg 4-C 6-H 4-O 15 total atoms 27 Let’s Do It!!! • How many formula units in one mole of Magnesium Acetate: Mg(C2H3O2)2 6.02 x 1023 28 Let’s Do It!!!! • How many oxygen atoms are in one formula unit? Magnesium Acetate: Mg(C2H3O2)2 4 oxygen atoms 29 Let’s Do It!!! • How many oxygen atoms are in one mole of this substance? Magnesium Acetate: Mg(C2H3O2)2 (4) (6.02 x 1023) = 2.41 x 1024 atoms O 30 Let’s Do It!!! • How many moles of oxygen atoms are in one mole of this substance? Magnesium Acetate: Mg(C2H3O2)2 4 moles of Oxygen 31 Let’s Do It!!! • What is the mass of oxygen atoms in one mole of this substance? Magnesium Acetate: Mg(C2H3O2)2 • ? g O= 1 mole Mg(C2H3O2)2 x 4 moles O x 16.0 g O 1 mole Mg(C2H3O2)2 1 mole O = 64.0 g O = 64.0g/ 1 mole 32 Molar Mass • We can use this information about what makes up a compound to figure out a compound’s total molar mass • Molar mass- the mass in grams of 1 mole of a compound • It’s the mass of one mole: grams KC4H5O6/mole KC4H5O6 • Also called formula weight, gram formula weight, molecular weight 33 Reference- Molar Mass • Calculate the molar mass of magnesium iodide, MgI2 from its parts. How many grams are in 1 mole? Mg 1 mole (24.3g Mg/mole )= 24.3 g Mg I 2 mole (127 g I/mole) = 254 g I 278 g/mole MgI2 34 (for SD use place value!) Reference- Molar Mass Calculate the molar mass (grams in one mole) of ammonium sulfite, (NH4)2SO3 In 1 mole of the compound there are: 2 moles of N 8 moles of H 1 mole of S 3 moles of O SD by place units always X 14.0 g N/mole= 28.0g N X 1.01 g H/mole = 8.08gH X 32.1 g S/mole =32.1 g S X 16.0 g O/mole=48.0g O value 116.2g g/mole 1mole (NH4)2SO353 Molar Mass • Molar mass can be used to convert between moles and grams • For an element: 1 mole = 6.02x1023 atoms = atomic mass • For a compound: • 1 mole = 6.02x1023 formula units = molar mass 36 Reference- Molar Mass as a Conversion Factor • What is the mass of 1.35 moles of (NH4)2SO3? • Earlier we found the molar mass: 116.2g (NH4)2SO3 = 1mole (NH4)2SO3 ? g (NH4)2SO3 = 1.35 moles (NH4)2SO3 x 116.2 g (NH4)2SO3 1 mole (NH4)2SO3 = 157 g (NH4)2SO3 37 Reference- Molar Mass as a Conversion Factor • 75.2 g (NH4)2SO3 is how many moles of (NH4)2SO3? ? moles (NH4)2SO3 = 75.2 g (NH4)2SO3 1 mole (NH4)2SO3 X ---------------------116.2 g (NH4)2SO3 = .647 moles (NH4)2SO3 38 Let’s Do It!!!! • How many moles are in 87.4 g of aluminum monohydrogen phosphate Al2(HPO4)3 ? • This is a two part problem: remember you first have to find the molar mass! 39 Let’s Do It!!! • Find the molar mass of aluminum monohydrogen phosphate, Al2(HPO4)3 2 moles Al (27.0g Al/mole) = 3 moles H (1.01g H/mole) = 3 moles P (31.0 g P/mole) = 12 moles O (16.0 g O/mole)= 54.0 g Al 3.03 g H 93.0 g P 192 g O_ 342 g mole Al2(HPO4)3 MASS OF ONE MOLE!!! 40 So 342 g Al2(HPO4)3 = 1 mole Al2(HPO4)3 Let’s Do It!!!! • Then find the number of moles in 87.4 g of aluminum monohydrogen Obviously, this is phosphate less than one mole! • Molar mass = 342 g/mole • ? moles Al2(HPO4)3 = 87.4 g Al2(HPO4)3 x 1 mole Al2(HPO4)3 342 g Al2(HPO4)3 = .256 moles Al2(HPO4)3 41 Review • Number your paper from 1-5 and answer the following questions. Two will be cumulative review! • 1. What does Avogadro’s number, 6.02 x 1023, mean? – a. There are that many grams in a mole – b. There are that many moles in a gram – c. There are that many moles in an atom – d. There are that many atoms in a mole 42 Review • D • 2. Which of these is false? • a. protons repel protons • b. protons attract neutrons • c. protons attract electrons • d. neutrons don’t repel anything because they have no charge 43 Review • B • 3. How many elements are in this compound? KC4H5O6 – a. 4 – b. 15 – c. 16 – d. 10 44 Review A • 4. How many moles of oxygen would be in 3 moles of KC4H5O6 ? – a. 3 – b. 6 – c. 18 – d. 48 45 Review • C • 5. If H2O has a molar mass of 18, what does this mean? – a. There are 18 moles of water in a gram – b. There are 18 moles of oxygen in a mole of water – c. There are 18 grams in a mole of water – d. There are 10 moles of oxygen and 8 moles of hydrogen in each water molecule 46 Review • C 47 % Composition • As we learned before, when we have multiple elements that make up a compound, each one has a certain ratio • We call this the compound’s empirical formula • From an empirical formula we can figure out each element’s percent composition 48 Reference-% Composition • Find percent composition of Al(C2H3O2)3 (1 moles Al)(27.0 g/mole) = 27.0 (6 moles C) (12.0 g/mole) = 72.0 (9 moles H) (1.01 g/mole) = 9.09 (6 moles O)(16.0 g/mole) = 96.0 27.0 72.0 9.09 96.0 g Al /204.1 g C /204.1 g H /204.1 g O /204.1 g Al gC gH gO 204.1 g Al(C2H3O2)3 g Al(C2H3O2)3 x 100 = g Al(C2H3O2)3 x 100 = g Al(C2H3O2)3 x 100 = g Al(C2H3O2)3 x 100 = 13.2 % 35.3 % 4.45 % 47.0 %49 ~100% % Composition • We can use this information further • How many grams of aluminum can be obtained from 1.50 moles of aluminum acetate? • ? grams Al = 1.50 moles Al(C2H3O2)3 x πππ.π π ππ₯ ππππππ π π¦π¨π₯π ππ₯ ππππππ ππ. π π π¨π X πππ. π π π¨π πͺππ―ππΆπ π π = 40.5 g Al OR 1.50 moles Al(C2H3O2)3 x π π¦π¨π₯π ππ₯ π π¦π¨π₯π ππ₯ ππππππ X π 27.0 g Al 1 mole Al = 40.4 g Al 50 π Let’s Do It!!! • Find the percent composition of iron (III) dichromate, Fe2(Cr2O7)3 (2 moles Fe)(55.8 g/mole) = 112 g Fe (6 moles Cr)(52.0 g/mole) = 312 g Cr (21 moles O)(16.0 g/mole) = 336 g O 76Ε g Fe2(Cr2O7)3 112 g Fe/76Εg Fe2(Cr2O7)3 x 100 = 14.7 % 312 g Cr/76Εg Fe2(Cr2O7)3 x 100 = 41.1 % 336 g O/76Εg Fe2(Cr2O7)3 x 100 = 44.2 % ~100% 51 Let’s Do It!!! • How many moles of iron can be obtained from 525 g of iron (III) dichromate, Fe2(Cr2O7)3? • ? moles of Fe = 525 g Fe2(Cr2O7)3 = 1.38 π π¦π¨π₯ππ¬ π π π π¦π¨π₯π Fe (Cr O ) 2 2 7 3 X X π π¦π¨π₯π Fe2(Cr2O7)3 moles Fe πππ π Fe2(Cr2O7)3 OR 525 g Fe2(Cr2O7)3 X π π¦π¨π₯π Fe 112 g Fe X 76Εg Fe2(Cr2O7)3 ππ.π π ππ = 1.39 moles Fe 52 Reference- Advanced Molar Mass • How many grams of Mg are needed to combine with 2.00 g of N to make magnesium nitride? Magnesium + Nitrogen ο Magnesium nitride (Mg3N2) ?g 2.00 g (3 moles Mg) (24.3 g Mg/mole) = 72.9 g Mg (2 mole N) (14.0 g N/mole) = 28.0 g N 100.9 g Mg3N2 72.9 g Mg + 28.0 g N = 100.9 Mg3N2 2.00 g N x 72.9 g Mg = 5.21g Mg 28.0 g N 53 Reference- Advanced Molar Mass • OR THE EASY WAY!!! Magnesium + Nitrogen ο Magnesium nitride (Mg3N2) ?g 2.00 g 72.9 g Mg + 28.0 g N = 100.9 Mg3N2 ? g Mg = 2.00 g N x 1 mole N x 3 mole Mg x 24.3 g = 14.0 g N 2 mole N 1 mole Mg = 5.21g Mg 54 Reference- Advanced Molar Mass • How many grams of nitrogen are needed to combine with 5.00 g Mg to make magnesium nitride? Magnesium + Nitrogen ο Magnesium nitride Mg3N2 5.00 g ?g 72.9 g Mg + 28.0 g N = 100.9 Mg3N2 ?gN= 5.00 g Mg x 28.0 g N = 1.92 g N 72.9 g Mg 55 Reference- Advanced Molar Mass • OR THE EASY WAY!!! Magnesium + Nitrogen ο Magnesium nitride Mg3N2 5.00 g ?g ?gN= 5.00 g Mg x 1 mole Mg x 2 mole N x 24.3 g = 24.3 g Mg 3 mole Mg 1 mole Mg = 1.92 g N 56 Reference- Advanced Molar Mass • How many grams of Mg are needed to make 25 g of magnesium nitride? Magnesium + Nitrogen ο Magnesium nitride – Mg3N2 ?g 25g 72.9 g Mg = 28.0 g N = 100.9 Mg3N2 ? g Mg= 25 g Mg3N2 x 72.9 Mg 100.9 g Mg3N = 18 g Mg 2 57 Reference- Advanced Molar Mass OR THE EASY WAY!!! • How many grams of Mg are needed to make 25 g of magnesium nitride? Magnesium + Nitrogen ο Magnesium nitride Mg3N2 ?g 25g ? g Mg = 25 g Mg3N2x 1 mole Mg3N2 x 3 mole Mg x 24.3 g = 100.9 g Mg3N2 1 mole Mg3N2 1 mole Mg molar mass = 18 g Mg 58 Let’s Do It!!! • How many grams of magnesium nitride can be made from 12.5 g of magnesium? 72.9 g Mg = 28.0 g N = 100.9 Mg3N2 Magnesium + Nitrogen ο Magnesium nitride – Mg3N2 12.5 g ?g 59 Let’s Do It!!! • How many grams of magnesium nitride can be made from 12.5 g of magnesium? 72.9 g Mg = 28.0 g N = 100.9 Mg3N2 Magnesium + Nitrogen ο Magnesium nitride – Mg3N2 12.5 g 12.5 g Mg x 100.9 g Mg3N 72.9 g Mg ?g 2 = 17.3 g Mg3N2 60 Let’s Do It!!! OR THE EASY WAY!!! • How many grams of magnesium nitride can be made from 12.5 g of magnesium? Magnesium + Nitrogen ο Magnesium nitride Mg3N2 12.5g ? g Mg3N2 = = ?g molar mass 12.5 g Mg x 1 mole Mg x 1 mole Mg3N2 x 100.9g Mg3N2 24.0 g Mg 3 mole Mg 1 mole Mg3N2 = 17.5 g Mg3N2 61 Review • Number your paper from 1-5 and answer the following questions. Two will be cumulative review! • 1. Atoms with the same atomic number but different mass numbers are • a. different elements • b. ions • c. isotopes of the same element • d. isotopes of different elements 62 Review • D • 2.An alpha particle • a. has a negative charge • b. can penetrate a sheet of aluminum • c. is identical to a helium nucleus • d. all of the above 63 Review • C • 3. How many moles of Cr are in a mole of Fe2(Cr2O7)3 – a. 6 – b. 3 – c. 2 – d. 1 64 Review • A • 4. What is the percent composition of hydrogen and oxygen in water? – a. 80% O and 20% H – b. 88.9% O and 11.2% H – c. 75% O and 35% H – d. 66.6% H and 33.3% O 65 Review • B • 1 mole O x 16.0 g O = 16.0 g 16.0/18.0 x 100 1 mole O • 2 moles H x 1.01 g H = 2.02 2.02/18.0 x 100 1 mole H • 5. How many grams of water can be made from 10 grams of hydrogen and excess oxygen? – – – – a. 90 g b. 10 g c. 20 g d. 0 g 66 Review • A • 5. How many grams of water can be made from 10 grams of hydrogen? EASY WAY!! – – – – a. 90 g b. 10 g c. 20 g d. 0 g ? g H2O = 10 g H molar mass x 1 mole H x 1 mole H2O x 18.0 g H2O 1.01 g H 2 mole H 1 mole H2O 67 Hydrates • Hydrated compounds- compounds with molecules of water held in their crystal structure • These compounds contain an anhydrous (nonwater) part and a hydrous (water based) part 68 Hydrates Anhydrous compound Water Ex.) CaSO4 . 7H2O • Compounds with molecules of water held in their crystal structure • Very common in nature • Water can be removed by heating, leaving behind what is called the anhydrous compound. 69 Reference-Naming Hydrated Compounds • The following is tacked on the name obtained from the ions H2O monohydrate 2 H2O dihydrate 3 H2O trihydrate 4 H2O tetrahydrate 5 H2O pentahydrate 6 H2O hexahydrate 7 H2O heptahydrate 8 H2O octahydrate 9 H2O nonahydrate 10 H2O dekahydrate CaSO4 ο· 7 H2O -- named as calcium sulfate heptahydrate70 Reference-Empirical Formula of Hydrates • Find the empirical formula of a hydrate of CaSO4 hydrate that is 28.5% H2O • To solve this problem, find the simplest mole ratio between the anhydrous part of the compound (CaSO4) and the water (H2O) • H2O =28.5 % CaSO4 =71.5 % (100% - 28.5%) 71 Reference-Empirical Formula of Hydrates 71.5 g CaSO4 x 1 mole CaSO4 = .525 mole CaSO4 136.2 g CaSO4 molar mass of CaSO4 ..525 = 1.00 = 1 .525 28.5 g H2O x 1 mole H2O = 1.58 mole H2O 18.0 g H2O •When you are finding formulas of hydrates they ALWAYS come out even! 1.58 = 3.01 = 3 .525 CaSO4 ο· 3 H2O 72 Reference- Molar Mass of a Hydrate • Find the molar mass of CaSO4 ο· 7 H2O • First we find the molar mass for H2O and treat the water like it’s an element! 2 mole H X 1.01 g/mole = 2.02 g 1 mole O X 16.0 g/mole = 16.0 g 18.0 g/mole (MEMORIZE THIS)73 Reference- Molar Mass of a Hydrate CaSO4 ο· 7 H2O 1 mole Ca x 1 mole S x 4 mole O x 7 mole H2O x 40.1 g/mole 32.1 g/mole 16.0 g/mole 18.0 g/mole = 40.1 g = 32.1 g = 64.0 g = 126 g 262 g/mole (SD by place value) 74 Reference- % Composition of a Hydrate • Find the % composition of CaSO4 ο· 7 H2O • The water is treated like an element! % Ca = 40.1 g Ca X 100% = 15.3 % Ca 262 g compound %S= 32.1 g S X 100% 262 g compound %O= 64.0 g O 262 g compound % H2O = = 12.3 % S X 100% = 24.4 % O 126 g H2O X 100% = 262 g compound 48.1 % H2O 75 Using Molar Mass or % Composition of a Hydrate • How much water do we get when we heat 2.00 g of CaSO4 ο· 7 H2O? 2.00 g x .481 = .962 g H2O OR 2.00 g CaSO4ο·7 H2O x 126 g H2O = 0.962 g H2O 262 g CaSO4ο·7 H2O 76 Review • Number your paper from 1-5 and answer the following questions. Two will be cumulative review! – 1. What is the actual mass of a hydrogen-3 atom? • a. 6.02 x 1023 g • b. 1.67 x 1024 g • c. 5.01 x 1024 g • d. 5.01 x 10-24 g 77 Review • D • 2. Which of these is true about the discovery of Millikan’s oil drop experiment – a. He discovered the electron – b. He discovered the mass of the neutron – c. He discovered the mass and the charge of the electron – d. He discovered the proton 78 Review • C • 3. What is CaSO4 ο· 5 H2O called? – a. calcium sulfate pentahydrate – b. calcium sulfate heptahydrate – c. calcium sulfate hydrate – d. calcium sulfate trihydrate 79 Review • A • 4. What is the mass of water in CaSO4 ο· 5 H2O? – a. 5 g – b. 90.0 g – c. 5.0 g – d. 18 g 80 Review • B • 5 mole H2O x 18.0 g/mole = 90.0 g • 5. Which of these would have the most water given off when heated? – a. calcium sulfate pentahydrate – b. calcium sulfate heptahydrate – c. calcium sulfate hydrate – d. calcium sulfate trihydrate 81 Review • B 82