A dozen Molar Mass Science 10 is a number of objects. A dozen eggs, a dozen cars, and a dozen people are all 12 objects. But a dozen cars has a much greater mass than a dozen eggs because the mass of each car is much greater than the mass of each egg. 1 2 Mass of atoms An Au atom contains 79 p + and 118 n. An H atom contains one p +. The mass of an Au atom is about 197 times greater than the mass of an H atom. A dozen A dozen Au atoms have a mass that is about 197 times greater than the mass of a dozen H atoms. But atoms are very small A gold atom has a mass of about 3 x 10-22 g or 0.0000000000000000000003 g 3 4
The mole Because atoms are so small it is not practical to talk about individual atoms. Chemists talk about moles of atoms. Like a dozen, a mole is a number of atoms. One mole of atoms is about 6.02 x 10 23 atoms. Avogadro s number Just like 12 eggs is called a dozen eggs, 6.02!x!10 23 atoms is a mole of atoms. 6.02 x 10 23 is known as Avogadro s number. 5 6 Power of the mole A mole of Au has 6.02 x 10 23 atoms. A mole of Mg has 6.02 x 10 23 atoms. The mole allows easy comparisons of amounts of atoms in the same way that the dozen allows easy comparisons of amounts of eggs. Why 6.02 x 10 23? An oxygen atom has 8 p + and 8 n. Its atomic mass number is 8 + 8 = 16. 6.02 x 10 23 oxygen atoms have a mass of 16!grams. 16 grams of oxygen atoms is a convenient amount of oxygen, whereas 16 atoms is impractical. 7 8
Molar mass is the mass of one mole of a substance. The atomic mass numbers of an element on the periodic table is the average mass, in grams, of one mole of that element s atoms. Example 1 What is the molar mass of Zn? 65.41 g/mol 9 10 Example 2 What is the molar mass of methane gas? Methane is CH4, meaning each molecule has one C atom and 4 H atoms. Each C: 12.01 g/mol Each H: 1.01 g/mol Total: 12.01 g/mol + (4 x 1.01 g/mol) = 16.05 g/mol Example 3 What is the molar mass of water? H2O: H: 2 x 1.01 g/mol = 2.02 g/mol O: 1 x 16.00 g/mol = 16.00 g/mol M = 18.02 g/mol 11 12
Example 4 What is the molar mass of iron (III) oxide? Your turn Page 108 practice questions Fe2O3: Fe: 2 x 55.85 g/mol = 111.70 g/mol O: 3 x 16.00 g/mol = 48.00 g/mol M = 159.70 g/mol 13 14 Number of moles One mole of Cu has a mass of 63.55 g. The molar mass (M) for Cu is 63.55 g/mol. 63.55 g of Cu would be composed of 6.02!x!10 23 atoms. 127.10 g of Cu would be two moles of Cu, or 2 x 6.02 x 10 23 = 1.204 x 10 24 atoms. Number of moles We can find the number of moles in a sample of any substance if we know (or can determine) the substance s molar mass, and we know the mass of the sample. We use the molar mass formula 15 16
Number of moles mass n= m (g) M Example 1 Find the number of moles in 2.00!g of helium. Find the molar mass: number of moles (mol) molar mass (g/mol) He: 1 x 4.00 g/mol = 4.00 g/mol M = 4.00 g/mol 17 18 Example 1 n= m M = 2.00!g 4.00!g/mol =!0.5!mol Example 1 What does 0.5 mol mean? one mol = 6.02 x 10 23 atoms 0.5 mol = 0.5 x 6.02 x 10 23 atoms 0.5 mol = 3.01 x 10 23 atoms 19 20
Example 2 Find the number of moles in 6.00 g of strontium chloride. Find the molar mass: SrCl2: Sr: 1 x 87.62 g/mol = 87.62 g/mol Cl: 2 x 35.45 g/mol = 70.90 g/mol M = 158.52 g/mol Example 2 n= m M = 6.00!g 158.52!g/mol =!0.03785011...!mol =!0.0379!mol 21 22 Significant Digits are a way of representing how accurate a measurement is. SD Rules The digits 1 through 9 are always significant. Leading zeros are not significant. All other zeros are significant. In scientific notation, the digits before the x!10 are significant. Exact numbers have unlimited significant digits. 23 24
1.23 0.123 0.0123 103 120 12.0 3 SD examples Examples of 2 SD 9.0 15 0.43 5.0 x 10 4 10 25 26 Exact Numbers These are exact numbers: 15 students $5.25 SD Rules Part 2 In multiplication or division calculations, the answer should be rounded to the least number of SD from the numbers used. 27 28
SD in Example n= m M = 6.00!g 158.52!g/mol =!0.03785011...!mol =!0.0379!mol 3 SD 3 SD Example 2 Find the number of moles in 9.50!g of ethanol. C2H5OH: C: 2 x 12.01 g/mol = 24.02 g/mol H: 6 x 1.01 g/mol = 6.06 g/mol O: 1 x 16.00 g/mol = 16.00 g/mol M = 46.08 g/mol 29 30 Example 2 Find the number of moles in 9.50!g of ethanol. n= m M = 9.50!g 46.08!g/mol =0.2061631...!mol =0.206!mol Example 3 Find the number of moles in 1.1!kg of gold (II) phosphate. Au3(PO4)2: Au: 3 x 196.97 g/mol = 590.91 g/mol P: 2 x 30.97 g/mol = 61.94 g/mol O: 8 x 16.00 g/mol = 128.00 g/mol M = 780.85 g/mol 31 32
Example 3 mol to mass Find the number of moles in 1.1!kg of gold (II) phosphate. n= m M = 1100!g 780.85!g/mol =1.4087212...!mol m=nm =1.4!mol 33 34 Example 4 Find the mass of 0.205 mol of sodium carbonate. Na2CO3: Na: 2 x 22.99 g/mol = 45.98 g/mol C: 1 x 12.01 g/mol = 12.01 g/mol O: 3 x 16.00 g/mol = 48.00 g/mol M = 105.99 g/mol Example 4 Find the mass of 0.205 mol of sodium carbonate. m=nm =0.205!mol!x!105.99!g/mol =21.72795!g =!21.7!g 35 36
Example 5 Find the mass of 0.015 mol of calcium chloride. CaCl2: Ca: 1 x 40.08 g/mol = 40.08 g/mol Cl: 2 x 35.45 g/mol = 70.90 g/mol M = 110.98 g/mol Example 5 Find the mass of 0.015 mol of calcium chloride. m=nm =0.015!mol!x!110.98!g/mol =!1.6647!g =!1.7!g 37 38