The Mole Q: how long would it take to spend a mole of $1 coins if they were being spent at a rate of 1 billion per second?

Background: atomic masses Look at the “atomic masses” on the periodic table. What do these represent? E.g. the atomic mass of C is 12 (atomic # is 6) We know there are 6 protons and 6 neutrons Protons and neutrons have roughly the same mass. So, C weighs 12 u (atomic mass units). What is the actual mass of a C atom? Answer: approx. 2 x 10-23 grams (protons and neutrons each weigh about 1.7 x10-24 grams) Two problems Atomic masses do not convert easily to grams They can’t be weighed (they are too small)

The Mole With these problems, why use atomic mass at all? Masses give information about # of p+, n0, e– It is useful to know relative mass E.g. Q - What ratio is needed to make H2O? A - 2:1 by atoms, but 2:16 by mass It is useful to associate atomic mass with a mass in grams. It has been found that 1 g H, 12 g C, or 23 g Na have 6.02 x 1023 atoms 6.02 x 1023 is a “mole” or “Avogadro’s number” “mol” is used in equations, “mole” is used in writing; one gram = 1 g, one mole = 1 mol. Do Q1-6. Challenge: 1st slide (use reasonable units)

Assignment 1. Why do we use the unit the mole? 2. What is a mole equal to? 3. Write out the number referred to a mole in expanded form. 4. How many particles would 3.00 moles of CO2 represent? How many total atoms is that? 5. How many particles would 0.500 moles represent? 6. a) If there is 1 dozen oranges in a box and a box weighs 1.43 kg, how much does each orange weigh? b) If 1.00 moles of hydrogen atoms are in a container. How much does each individual atom weigh?

The Mole: Answers A mole is a number (like a dozen). Having this number of atoms allows us to easily convert atomic masses to molar masses. 6.02 x 1023 602 000 000 000 000 000 000 000 3.00 x 6.02 x 1023 = 18.06 x 1023 or 1.81 x 1024 (note: there are 3 moles of atoms in one mole of CO2 molecules. In other words, there are 5.42 x 1024 atoms in 3.00 mol CO2) 3.01 x 1023 a) 1.43 kg  12 = 0.119 kg per orange b) 1.01 g  6.02 x 1023 = 1.68 x 10 –24 g

A: It would take 19 million years Mollionaire Q: how long would it take to spend a mole of $1 coins if they were being spent at a rate of 1 billion per second? A: $ 6.02 x 1023 / $1 000 000 000 = 6.02 x 1014 payments = 6.02 x 1014 seconds 6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes 1.003 x 1013 minutes / 60 = 1.672 x 1011 hours 1.672 x 1011 hours / 24 = 6.968 x 109 days 6.968 x 109 days / 365.25 = 1.908 x 107 years A: It would take 19 million years

Comparing sugar (C12H22O11) & H2O Same 1 gram each 1 mol each volume? No, they have dif. densities. No, molecules have dif. sizes. mass? Yes, that’s what grams are. No, molecules have dif. masses # of moles? No, they have dif. molar masses Yes. # of molecules? No, they have dif. molar masses Yes (6.02 x 1023 in each) # of atoms? No, sugar has more (45:3 ratio) No

Molar mass The mass of one mole is called “molar mass” E.g. 1 mol Li = 6.94 g Li This is expressed as 6.94 g/mol What are the following molar masses? S SO2 Cu3(BO3)2 32.06 g/mol 64.06 g/mol 308.27 g/mol Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3 O2 Pb3(PO4)2 C6H12O6 Cu x 3 = 63.55 x 3 = 190.65 B x 2 = 10.81 x 2 = 21.62 O x 6 = 16.00 x 6 = 96.00 308.27

Molar mass The mass of one mole is called “molar mass” E.g. 1 mol Li = 6.94 g Li This is expressed as 6.94 g/mol What are the following molar masses? S SO2 Cu3(BO3)2 32.06 g/mol 64.06 g/mol 308.27 g/mol Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3 O2 Pb3(PO4)2 C6H12O6 110.98 g/mol (Ca x 1, Cl x 2) 96.11 g/mol (N x 2, H x 8, C x 1, O x 3) 32.00 g/mol (O x 2) 811.54 g/mol (Pb x 3, P x 2, O x 8) 180.18 g/mol (C x 6, H x 12, O x 6)

Converting between grams and moles If we are given the # of grams of a compound we can determine the # of moles, & vise-versa In order to convert from one to the other you must first calculate molar mass g = mol x g/mol mol = g  g/mol This can be represented in an “equation triangle” g mol g/mol g= g/mol x mol 0.25 HCl 53.15 H2SO4 3.55 NaCl 1.27 Cu Equation mol (n) g g/mol Formula 36.46 9.1 98.08 0.5419 mol= g  g/mol 58.44 207 g= g/mol x mol 63.55 0.0200 mol= g  g/mol

Mass, Moles and Molar Mass n = m/mm m= n x mm mm= m/n n= number of moles m= mass in grams mm= molar mass in g/mol Some textbooks use M to symbolize molar mass as opposed to mm…I avoid M for molar mass since in the next unit M is used to symbolize molarity…two meaning for one letter… m n mm

Moles, # Entities, Avogadro’s # n = N/NA N= n x NA NA= N/n n= number of moles N= number of entities (atoms, molecules, particles, ions) NA= Avogadro’s number = 602 sextillion Since there is n in both triangles, the first and the second triangle link together. N n NA

Simplest and molecular formulae Consider NaCl (ionic) vs. H2O2 (covalent) Cl Na Cl H O Na H O H O Cl Cl Na Na Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular”. Ionic compounds are always expressed as simplest formulas. Covalent compounds can either be molecular formulas (I.e. H2O2) or simplest (e.g. HO) Q - Write simplest formulas for propene (C3H6), C2H2, glucose (C6H12O6), octane (C8H14) Q - Identify these as simplest formula, molecular formula, or both H2O, C4H10, CH, NaCl

Answers Q - Write simplest formulas for propene (C3H6), C2H2, glucose (C6H12O6), octane (C8H14) Q - Identify these as simplest formula, molecular formula, or both H2O, C4H10, CH, NaCl A - CH2 A - H2O is both simplest and molecular C4H10 is molecular (C2H5 would be simplest) CH is simplest (not molecular since CH can’t form a molecule - recall Lewis diagrams) NaCl is simplest (it’s ionic, thus it doesn’t form molecules; it has no molecular formula) CH CH2O C4H7