 THE MOLE & AVOGADRO Y11 DP Chemistry R. Slider Relative Atomic Mass As you know, atoms are very, very small Some single atom masses: single atom masses: -23 Li:Some 1.15217 x 10 g O: 2.65659 x 10-23-23 -23 O: 2.65659 x 10 g Li: 1.15217 x 10 g g 6.64605 x 10-24 g U: 3.95233 x 10-22 He: -24 -22 g He: 6.64605 x 10 g U: 3.95233 x 10 g are not terribly convenient to work with, so chemists These masses work with relative masses. The relative atomic masses of all the elements are based on the mass of C-12 (1.99X10-22 g), the most abundant isotope on the Earth. In fact: Relative atomic mass (Ar) is defined as the Relative atomic mass (Ar) is defined as the mass of an element relative to 1/12 of the mass of an

element relative to 1/12 of the mass of an atom of the Carbon-12 isotope. mass of an atom of the Carbon-12 isotope. These relative atomic masses are conveniently located on the Periodic Table and have no units since they are all relative. H: 1.01 P: 30.97 Br: 79.91 The Mole The mole is a unit used only in The mole that is a unit usedthe only in Chemistry denotes Chemistry that denotes amount of substance (n). the amount of substance (n). Since chemists had determined the Since chemists had determined the relative atomic masses of the relative atomic masses of thethat elements, it logically

followed elements, it logically followed that 1.01g of H had the same number of 1.01g of H had the same number atoms as 12.0g of C. And that sameof atoms as 12.0g of C. And that number of particles is equal to asame number of particles is equal to a mole of that substance. mole of that substance. This is also a mole The Mole is Mole is

The The number equal to the number of carbon atoms in exactly 12 The number12equal to the number of carbon atoms in exactly 12 grams of pure 12 C. (We once compared to H, the lightest element. grams of pure (We once compared to H, the lightest element. Now we use C-12,C. the most abundant) we use C-12, the Now 1 mole of anything = most 6.022abundant) 1023 units of that thing (atoms, 1 mole of anything = 6.022 1023 units of that thing (atoms, ions, molecules, grains of sand, etc.) ions, molecules, grains of sand, etc.) The Mole /Avogadro's number 12g of C-12 contains 6.022x1023 atoms. This is known as Avogadros Number (NA or L) and is equivalent to 1 mole of carbon atoms. 23 Avogadros Avogadros number

number = = 6.02x10 6.02x1023 = = 1mole 1mole Notice that the mass of 1 mole of C12 is the same value as the relative atomic mass for C-12 on the Periodic Table. In the same way, 1 mole of any element or compound is equivalent to its atomic, molecular or formula weight. We can now define the relative atomic masses from the periodic table as molar masses with the units g/mol. Substance carbon chlorine oxygen water Molar mass (g/mol) 12 35.5 16 18 Molar mass = mass of 1 Molar = mass of 1

molemass of any mole of any substance substance Calculations using moles From the previous example using C-12, we now have a mathematical relationship between mass and moles, which is: Mass of substance (g) Number of moles (n) = Molar mass (MM) (g/mol) Example: How many moles are in 25 g of CO? n CO = 25g CO/(12+16)g/mol = 0.89 moles Calculations using moles We can also convert between moles and We can also convert between moles and the thenumber numberof ofatoms atomsor ormolecules molecules using usingAvogadros

Avogadrosnumber number Number of atoms/molecules = moles (n) x NA Number of atoms/molecules = moles (n) x NA Example: How many atoms are there in a copper pipe that weighs 2.56g? n = 2.56/63.6 = 0.0403 moles number of Cu atoms = 0.0403 X 6.022X1023 = 2.43X1022 Calculations using moles We Wecan cannow nowuse usethe themole moleconcept conceptto to determine how much product to expect in determine how much product to expect in aachemical chemicalreaction. reaction.Take Takethe thefollowing following example: example: 2Fe2O3(s) + 3C(s) 4Fe(l) + 3COFe(l) + 3CO2(g) 2Fe2O3(s) + 3C(s) 4Fe(l) + 3COFe(l) + 3CO2(g)

The coefficients in front of each species provide us with useful The coefficients in front of each species provide us with useful ratios that we can use to calculate expected masses of ratios that we can use to calculate expected masses of products in a chemical reaction. We previously said that these products in a chemical reaction. We previously said that these were ratios based on the numbers of atoms. However, with were ratios based on the numbers of atoms. However, with Avogadros number, we can now say that these are molar Avogadros number, we can now say that these are molar ratios. ratios. We say, 2 moles of iron (III) oxide react with 3 moles of carbon to We say, 2 moles of iron (III) oxide react with 3 moles of carbon to produce 4 moles of iron and 3 moles of carbon dioxide gas. produce 4 moles of iron and 3 moles of carbon dioxide gas. Calculations using moles 2Fe2O3(s) + 3C(s) 4Fe(l) + 3COFe(l) + 3CO2(g) Example: How many grams of iron will we expect if we react 12g of iron (III) oxide as in the above reaction, assuming neither reactant is in excess? Convert to moles Convert to moles 12g Fe2O3 X 1 mol Fe2O3 159.8g Fe2O3 = 12 X 1 X 4 X 55.9 159.8 X 2 X 1 Convert to g

Convert to g of of unknown unknown Molar ratio Molar ratio X 4 mol Fe 2 mol Fe2O3 = 8.4 g Fe X 55.9g Fe 1 mol Fe Molecular Mass Molecular Molecularmass massisisthe thesum sumof ofthe theatomic atomic masses massesof ofthe theatoms atomsininaamolecular molecular formula.

formula. Example: Example: The molecular mass of sucrose (table sugar) The molecular mass of sucrose (table sugar) C12H22011 is calculated as: C12H22011 is calculated as: M.W. = (12XAC) + (22XAH) + (11XAO) M.W. = (12XAC) + (22XAH) + (11XAO) M.W. = (12X12.0) + (22X1.01) + (11X16.0) M.W. = (12X12.0) + (22X1.01) + (11X16.0) = 342.2 = 342.2 Formula Mass Formula mass is the sum of the atomic masses in Formula mass is the sum of the atomic masses in a compound which has no discreet molecules a compound which has no discreet molecules (e.g. ionic compounds). These describe the (e.g. ionic compounds). These describe the ratios of the atoms present (i.e. empirical ratios of the atoms present (i.e. empirical formulas), but are calculated the same way as formulas), but are calculated the same way as molecular masses. molecular masses. Example: Example: The formula mass of calcium phosphate Ca3(PO4)2 The formula mass of calcium phosphate Ca3(PO4)2 is calculated as: is calculated as: F.W. = (3XACa) + (2XAP) + (8XAO) F.W. = (3XACa) + (2XAP) + (8XAO) F.W. = (3X40.1) + (2X31.0) + (8X16.0) F.W. = (3X40.1) + (2X31.0) + (8X16.0) = 310.3

= 310.3 Exercises 1. 2. 3. What is the symbol for relative atomic mass? Write the relative atomic masses for O, Mg, S. Calculate the molecular mass of ethanol C2H5OH. 4. Calculate the molar mass of copper(II) sulfate CuSO4. 5. State the value and symbols of Avogadros Number. How many atoms are there in 3 moles of nitrogen atoms? 3 moles of ammonia? How many grams are there in 3 moles of nitrogen? 3 moles of ammonia? How many moles are there in 48g of water? 6. 7. 8.