The Mole and Stoichiometry

understand the Avogadro number and mole (of particles) be able to carry out calculations involving quantities of substances expressed in moles be able express solution concentrations in mol dm-3 recall and understand the use of the ‘molar volume’ recall and be able to use the ideal gas equation know how to balance equations know how to balance ionic equations understand the purpose of, be able to carry out, and be able to carry out calculations involving, titration understand the use of empirical and molecular formulas be able to calculate empirical and molecular formulas be able to calculate theoretical yield and percentage yield of reactions understand and be able to calculate atom economy

Mr (Relative Molecular Mass) Ex. If we need 0.168 mole Ca3(PO4)2 for an experiment, how many grams do we need to weigh out? Calculate MM of Ca3(PO4)2 3 × mass Ca = 3 × 40.08 g = 120.24 g 2 × mass P = 2 × 30.97 g = 61.94 g 8 × mass O = 8 × 16.00 g = 128.00 g 1 mole Ca3(PO4)2 = 310.18 g Ca3(PO4)2 What do we want to determine? 0.168 g Ca3(PO4)2 = ? Mol Fe Start End

Learning Check: Using Molar Mass So, we need 0.168 = 52.11 g Ca3(PO4)2

Converting FIND MASS. from moles The expression relating mass and number of moles is: Mass of sample (g) = no. of moles (mol) × molar mass (gmol-1) Example Calculate the mass in grams in 0.75mol of sodium hydroxide, NaOH Step 1: Find the molar mass of the compound Na: 22.99 gmol-1 Mr: 40.00 gmol-1 O: 16.00 gmol-1 H: 1.008 gmol-1 Step 2: Substitute into the above expression Mass of sample = 0.75mol × 40.00 gmol-1 = 30g

Your Turn! How many grams of platinum (Pt) are in 0.475 mole Pt? 195 g Molar mass of Pt = 195.08 g/mol = 92.7 g Pt

Questions FIND MOLES Calculate the mass in grams present in: (a) 0.57mol of potassium permanganate (KMnO4) Answer: Molar mass KMnO4 = 158.03 gmol-1 Mass in grams = 0.57mol × 158.03 gmol-1 = 90.07 g (b) 1.16mol of oxalic acid (H2C2O4) Answer: Molar mass H2C2O4 = 90.04 gmol-1 Mass in grams = 1.16mol × 90.04 gmol-1 = 104.44 g (c) 2.36mol of calcium hydroxide (Ca(OH)2) Answer: Molar mass Ca(OH)2 = 74.1 gmol-1 Mass in grams = 2.36mol × 74.1 gmol-1 = 174.87 g

Converting between moles and mass Number of moles = mass of sample (g) molar mass (gmol-1) Example Convert 25.0g of KMnO4 to moles Step 1: Calculate the molar mass K Mn O 1 × 39.10 gmol-1 1 × 54.93 gmol-1 4 × 16.00 gmol-1 39.10 gmol-1 54.93 gmol-1 64.00 gmol-1 Mr = 158.03 gmol-1 Step 2: Substitute into above expression 25.0g . 158.03gmol-1 No. of moles = = 0.158 mol

Your Turn! = 0.227 mol CO2 How many moles of CO2 are there in 10.0 g? Molar mass of CO2 1 × 12.01 g = 12.01 g C 2 × 16.00 g = 32.00 g O 1 mol CO2 = 44.01 g CO2 = 0.227 mol CO2

Calculating the number of particles THE MOLE One mole of any object means 6.022 × 1023 units of those objects. For example, 1 mol of H2O contains 6.022 × 1023 molecules 1 mol of NaCl contains 6.022 × 1023 formula units Calculating the number of particles Avogadro’s number is used to convert between the number of moles and the number of atoms, ions or molecules. Example 0.450mol of iron contains how many atoms? Number of atoms = number of moles × Avogadro’s number (NA) Therefore No. of atoms = (0.450mol) × (6.022 × 1023) = 2.7 × 1023 atoms

Using Avogadro’s Number What is the mass, in grams, of one molecule of octane, C8H18? Molecules octane  mol octane  g octane 1. Calculate molar mass of octane Mass C = 8 × 12.01 g = 96.08 g Mass H = 18 × 1.008 g = 18.14 g 1 mol octane = 114.22 g octane 2. Convert 1 molecule of octane to grams = 1.897 × 10–22 g octane

The Mole How many atoms in 1 mole of 12C ? 1 mole of 12C = 6.022 × 1023 atoms = 12.011 g Avogadro’s number = 6.022 × 1023 atoms = NA 1 mole Xe = 6.022×1023 Xe atoms, I’ll round to 6 × 1023 1 mole NO2 = 6.022×1023 NO2 molecules. QUESTION: How many ATOMS does it, 1 mole of NO2, have? Ans: 18 × 1023 atoms Question: How many atoms are in 36.04g of water? Answer: 12 × 1023 or 1.2× 1024 Question: Given 2.4× 1025 atoms of diphosphorous pentoxide, how may moles is this? Answer : 5.70 mole

Macroscopic to Microscopic How many silver atoms are in a 85.0 g silver bracelet? What do we know? 107.87 g Ag = 1 mol Ag 1 mol Ag = 6.022×1023 Ag atoms What do we want to determine? 85.0 g silver = ? atoms silver g Ag  mol Ag  atoms Ag = 4.7 × 1023 Ag atoms

Example: Determine the # of molecules How many molecules are there in 4 moles of hydrogen peroxide (H2O2)? No. of molecules = no. of moles × Avogadro’s number (NA) = 4mol × (6.022 × 1023 mol1) = 24 ×1023 molecules = 2.4 × 1024 molecules Questions How many atoms are there in 7.2 moles of gold (Au)? Answer: 4.3 × 1024 atoms The visible universe is estimated to contain 1022 stars. How many moles of stars are there? Answer: 1022 stars = 1022 = 0.17 mol. 6.022×1023

Example Calculate the mass of one molecule of ammonium carbonate [(NH4)2CO3] Step 1: Calculate the molar mass 2 Nitrogen atoms 8 Hydrogen atoms 1 Carbon atom 3 Oxygen atoms 2 × 14.01gmol-1 8 × 1.008 gmol-1 1 ×12.01gmol-1 3 × 16.00 gmol-1 = 28.02 gmol-1 = 8.064 gmol-1 = 12.01 gmol-1 = 48.00 gmol-1 Total = 96.09 gmol-1 Step 2: Employ Avogadro’s Number, NA Mass of one molecule = 96.09 gmol-1 . 6.022×1023mol-1 = 1.59 × 10-22g Questions Calculate the mass of one molecule of: Ethanoic acid (CH3COOH) Methane (CH4) Potassium dichromate (K2Cr2O7) 9.96 × 10-23 g 2.66 × 10-23 g 4.89 × 10-22 g

Learning Check: Mole Conversions Calculate the number of formula units of Na2CO3 in 1.29 moles of Na2CO3. How many moles of Na2CO3 are there in 1.15 x 105 formula units of Na2CO3 ? = 7.77×1023 particles Na2CO3 = 1.91×10–19 mol Na2CO3

Your Turn! How many atoms are in 1.00 x 10–9 g of U (1 ng)? Molar mass U = 238.03 g/mole. 6.02 x 1014 atoms 4.20 x 1011 atoms 2.53 x 1012 atoms 3.95 x 10–31 atoms 2.54 x 1021 atoms = 2.53 x 1012 atoms U

Mole-to-Mole Conversion Factors Can use chemical formula to relate amount of each atom to amount of compound In H2O there are 3 relationships: 2 mol H ⇔ 1 mol H2O 1 mol O ⇔ 1 mol H2O 2 mol H ⇔ 1 mol O Can also use these on atomic scale 2 atom H ⇔ 1 molecule H2O 1 atom O ⇔ 1 molecule H2O 2 atom H ⇔ 1 molecule O

Stoichiometric Equivalencies Within chemical compounds, moles of atoms always combine in the same ratio as the individual atoms themselves Ratios of atoms in chemical formulas must be whole numbers!! These ratios allow us to convert between moles of each quantity Ex. N2O5 2 mol N ⇔ 1 mol N2O5 5 mol O ⇔ 1 mol N2O5 2 mol N ⇔ 5 mol O

Your Turn! Calculate the number of moles of calcium in 2.53 moles of Ca3(PO4)2 2.53 mol Ca 0.432 mol Ca 3.00 mol Ca 7.59 mol Ca 0.843 mol Ca 2.53 moles of Ca3(PO4)2 = ? mol Ca 3 mol Ca  1 mol Ca3(PO4)2 = 7.59 mol Ca

Internal Mass-to-Mass Calculations Chlorophyll, the green pigment in leaves, has the formula C55H72MgN4O5. If 0.0011 g of Mg is available to a plant for chlorophyll synthesis, how many grams of carbon will be required to completely use up the magnesium? Analysis 0.0011 g Mg ⇔ ? g C 0.0011 g Mg → mol Mg → mol C → g C Assembling the tools 24.3050 g Mg = 1 mol Mg 1 mol Mg ⇔ 55 mol C 1 mol C = 12.011 g C

Ex. Mass-to-Mass Conversion 1 mol C ⇔ 12.0 g C 1 mol Mg ⇔ 24.3 g Mg 0.0011 g Mg → mol Mg → mol C → g C 1 mol Mg ⇔ 55 mol C = 0.030 g C