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The Mole Concept

The Mole Concept. Goal: To develop the concept of the mole as a useful measurement and to apply this in calculations involving mass and volume. Objectives. 1. Define the mole in terms of Avogadro's number, formula mass or molecular mass.

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The Mole Concept

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  1. The Mole Concept Goal: To develop the concept of the mole as a useful measurement and to apply this in calculations involving mass and volume.

  2. Objectives • 1. Define the mole in terms of Avogadro's number, formula mass or molecular mass. • 2. Given the number of moles, determine the number of molecules of a covalent compound, formula units of an ionic compound or atoms of an element. • 3. Given the number of particles present in a sample, determine the number of moles. • 4. When given the formula, calculate the molecular mass of a covalent compound or the formula mass of an ionic compound. • 5. Given the number of moles in a substance, determine the mass of the substance. • 6. Given the mass of a substance, determine the number of moles of the substance. • 7. When given the formula, calculate the percentage composition of each of the elements in the compound.

  3. Molecular and Formula Mass • Molecular Mass is determined by the sum of the atomic masses of each element in a compound. • The atomic mass of hydrogen in atomic mass units is 1, and the atomic mass of oxygen is 16. • Therefore, the total mass of a water molecule, H2O, is 1+1+16, or 18 amu. • This name is incorrect when applied to an ionic substance. • E.g. Sodium chloride, NaCl, is an ionic substance which does not exist in molecular form. • A better name for the mass of ionic substances is formula mass. • Formula mass is determined by the sum of the atomic masses of all atoms in the formula unit of an ionic compound.

  4. EXAMPLE: Formula Mass • Find the formula mass of sodium sulfate, Na2SO4. • Solving process: • Add the atomic masses of all the atoms in the Na2SO4 unit. • 2 Na atoms, 2 x 23 = 46 amu • 1 S atom, 1 x 32 = 32 amu • 4 O atoms, 4 x 16 = 64 amu • The total formula mass = 142 amu

  5. EXAMPLE: Formula Mass • Find the formula mass of calcium nitrate, Ca(NO3)2 • Solving process: • Add the atomic masses of all the atoms in the Ca(NO3)2 formula unit. Remember that the subscript applies to the entire polyatomic ion. • 1 Ca atom, 1 x 40 = 40 amu • 2N atoms, 2 x 14 = 28 amu • 6 O atoms, 6 x 16 = 96 amu • Total formula mass is 164 amu

  6. Groups of Atoms • There is one problem in using the molecular and formula masses of substances. • These masses are in atomic mass units, which is only 1.66 x 10-24 g. • The mass of a single molecule is so small that it is impossible to measure it in the laboratory. • For everyday use in chemistry, a larger unit, such as a gram, is needed. • One helium atom has a mass of 4 amu, and one nitrogen atom has a mass of 14 amu. The ratio of the mass of one helium atom to one nitrogen atom is 4 to 14, or 2 to 7. • No matter what number of atoms we compare, equal numbers of helium and nitrogen atoms will have a mass ratio of 2 to 7. • In other words, the numbers in the atomic mass table give us the relative masses of the atoms of the elements.

  7. Avagadro’s Number • The standard laboratory unit of mass is the gram. • We would like to choose a number of atoms which would have a mass in grams equivalent to the mass of one atom in atomic mass units. • The same number would fit all elements since equal numbers of different atoms always have the same mass ratio. • Chemists have found that 6.02 x 1023 atoms of an element have a mass in grams equivalent to the mass of one atom in amu. • E.g. 1 hydrogen atom has a mass of 1.0079 amu • 6.02 x 1023 atoms of hydrogen have a mass of 1.0079 g. • This number, 6.02 x 1023 is called Avogadro's Number in honor of a 19th century Italian scientist.

  8. What is the Mole? • 6.02x1023atoms of an element = 1 mole of that element • E.g. 6.02x1023atoms of Na = 1 mole of Na • 6.02x1023molecules of a compound = 1 mole of that compound • E.g. 6.02x1023molecules of NaCl = 1 mole of NaCl

  9. Mole Trivia • If there were a mole of rice grains, all the land area in the whole world would be covered with rice to a depth of about 75 meters. • One mole of rice grains is more grains than all the grain that has been grown since the beginning of time. (1) • One mole of rice would occupy a cube about 120 miles on an edge! (1)

  10. Mole Trivia • A mole of marshmallows would cover the United States to a depth of 600 miles (3) • In order to put a mole of rain drops in a 30 meter (about 100 feet) diameter tank, the sides of the tank would have to be 280 times the distance from the Earth to the Sun. (4) • A mole of hockey pucks would be equal to the mass of the Moon.

  11. Mole Trivia • Assuming that each human being has 60 trillion body cells (6.0 x 1013) and the Earth's population is 6 billion (6 x 109), the total number of living human body cells on the Earth at the present time is 3.6 x 1023 or a little over half of a mole.

  12. Mole Trivia • If one mole of pennies were divided up among the Earth's population, each person would receive 1 x 1014 pennies.  • Personal spending at the rate of one million dollars a day would use up each persons wealth in about three thousand years.  • Life would not be comfortable because the surface of the Earth would be covered in copper coins to a depth of at least 400 meters.

  13. Mole Trivia • If you had a mole of pennies and wanted to buy kite string at the rate of a million dollars per inch, you would get your money's worth. • After stretching your string around the Earth one million times, and to the Moon and back twenty-five times, you would have enough string left over to sell back at a dollar an inch (a decided loss) to gain enough money to buy every man, woman and child in the US a $50,000 automobile and enough gasoline to run it at 55 mph for a year.  • After those purchases, you would still have enough money left over to give every man, woman, and child in the whole world about $5000.

  14. Mole Trivia • Basis for calculations: • Earth's circumference = 25,000 miles                • Distance to moon = 240,000 miles • Cost of gasoline = $2.50 per gallon • Gasoline mileage = 20 miles per gallon • U.S. population =220,000,000 • World population = 6,000,000,000

  15. Calculating Molecular Mass • 1. Calculate the molecular or formula masses of the following compounds, all in amu (g/mol): • a. C2H6 • Amu=30 • b. SiCl4 • Amu=170 • c. MgCO3 • Amu=84 • d. Ca3(P04)2 • Amu=310

  16. Calculating Molecular Mass • Calculate the molecular or formula masses of the following compounds, all in amu (g/mol): • K2S • Amu=110 • CH2CHCH2OH • Amu=58 • Pb3(As04)2 • Amu=899 • C12H22011 • Amu=342

  17. Conversions • Make the following conversions: • 1.00 x 1026 molecules of SnCl2 to moles. • Ans: 1.66 X 102 mol. • 0.400 moles of H2O to molecules. • Ans: 2.41 X 1023 molecules. • 76.0 grams CaBr2 to moles. • Ans: 0.380 mol. Or 3.80 X 10-1 mol. • 18.0 grams HBr to moles. • Ans: 0.222 mol. Or 2.22 X 10-1 mol.

  18. Conversions • Make the following conversions: • 9.30 moles SiH4 to molecules. • Ans: 5.60 X 1024 molecules. • Find the mass of one atom of Na. • Ans: 3.82 X 10-23g. • Find the mass of one molecule of H2SO4. • Ans: 1.63 X 10-22 g.

  19. Conversions • Make the following conversions: • 9.30 moles SiH4 to grams. • Ans: 298 g. • Find the mass of 1.405 mole of Na2SO4. • Ans: 199.5 g. • Find the mass of one molecule of H2SO4. • Ans: 1.63 X 10-22 g.

  20. Percent Composition • 1 mole of NaCl is comprised of equal parts Na and Cl • But Na and Cl have 23 g/mol and 35.45 g/mol, respectively! • So they have differing percent composition • The percent composition of Na is (molar mass Na) x 100 molar mass NaCl Molar mass NaCl= 23+35.45= 58 g/mol %Na= (23) x 100 (58) %Na= 40% %Cl= (35) x 100 (58) %Cl=60% • So, while NaCl is equal parts NaCl by molar ratios, by mass, it’s a 60/40 split.

  21. Percent Composition • Find the percentage composition of the following: • CsF • Ans: 87.5%; 12.5%. • Bi203 • Ans: 89.7%, 10.3%. • BaH2 • Ans: 98.6%, 1.44%.

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