THE MOLE CONCEPT I Quantifying the World of the Very Small ADEng. Programme Chemistry for Engineers Prepared by M. J. McNeil, MPhil.

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1 THE MOLE CONCEPT I Quantifying the World of the Very Small ADEng. Programme Chemistry for Engineers Prepared by M. J. McNeil, MPhil. Department of Pure and Applied Sciences Portmore Community College Main Campus SAVE PAPER AND INK!!! When you print out the notes on PowerPoint, print "Handouts" instead of "Slides" in the print setup. Also, turn off the backgrounds(tools>options>print>unchec k "Background Printing")! 1

LECTURE OBJECTIVES PART I Define the terms relative atomic and isotopic masses, based on the 12 C-isotope scale. Apply Avogadro s law. Define the term mole. Define the term molar mass.

2 LECTURE OBJECTIVES PART I Define the terms relative atomic and isotopic masses, based on the 12 C-isotope scale. Apply Avogadro s law. Define the term mole. Define the term molar mass. Perform calculations, including the use of the mole concept, involving: i. Reacting masses from formulae and equations. ii. iii. Volumes of gases (e.g. in the burning of hydrocarbons) Volumes and concentrations of solutions. Deduce stoichiometric relationship from calculations from i, ii and iii. PART II Reacting masses from equations. Calculate empirical and molecular formulae, using combustion data or composition by mass. Perform various titrimetric analyses: acid/base and redox types. 2

3 PREVIOUS KNOWLEDGE / MATERIALS Writing chemical formulae. A scientific calculator Writing molecular and ionic equations. Transform decimal notation to power of ten notations (standard form). A copy of the Chemistry Bible. Best side of your Solve simple algebraic equations etc. [BEST WAY TO EXPRESS CHEMICAL INFORMATION - #, formulas and equations] 3

4 REFERENCE WORKBOOK 4

5 16 O 24 Mg! THE MOLE CONCEPT - Let s Start at the Very Beginning. 5

6 a) A blind furry animal. WHAT IS A MOLE? b) A brown mark on your body. c) An important Chemistry concept. d) All of the above. 6

7 CRIME SCENE Amnesia How would you go about identifying the agent used at the murder scene? Develop a laundry additive (whiter clothing - simple to complex calculations) - Research Chemist. 7

8 FUNDAMENTAL PARTICLES OF MATTER ATOMS IONS MOLECULES 8

9 SAMPLE PARTICLES OF MATTER a. Network structure - ATOMS SiO 2 (silicon dioxide) - strong, rigid, high melting point) b. Network structure - IONS NaCl (strong, rigid, high melting point) c. Molecule groups C 12 H 22 O 11 (weak bonds, low melting point) 9

10 PERFORMANCE TASK Zinc Powder Water Table Salt Just how much A, I & M are present in the substances, respectively? 10

11 JUST HOW SMALL IS AN ATOM? Hydrogen makes up more than 90% of the atoms in the universe. The smallest (lightest) atom known is hydrogen (H). It is estimated that two million hydrogen atoms could fit on a full stop. The diameter of hydrogen is 7 x 10-8 m. Others such as oxygen and phosphorous, exist as groups of atoms called molecules. 11

THE MOLE DEMYSTIFIED Impossible to count; conveniently

But, what if a baker wants 120 eggs, how much dozen

It s easier to measure large objects by counting - cars,

It s easier to measure small objects by weight Suppose

12 THE MOLE DEMYSTIFIED Impossible to count; conveniently sold by mass. But, what if a baker wants 120 eggs, how much dozen cartons he needs? Other e.g. s of items are 12 How Many? Heavy? Big? Objects are measured by counting or by weight (mass). It s easier to measure large objects by counting - cars, eggs etc. It s easier to measure small objects by weight Suppose you had to count a vast number of coins (mass) - Nails, rice, What is the quickest method? If the mass of a certain number of coins is known, the total number can be weighed and then the amount can be calculated.

CALCULATIONS Chemist deal with matter on the macroscopic scale. Atomic mass unit (a.m.u.) - the relative masses of atoms of an element on the atomic mass scale.

13 CALCULATIONS Chemist deal with matter on the macroscopic scale. Atomic mass unit (a.m.u.) - the relative masses of atoms of an element on the atomic mass scale. Since all atoms are relative to one another, why not find a CONVERSION FACTOR that would translate the a.m.u. units into grams. Because the mass of one amu is so small (1. 66 x g), a more meaningful (larger) number is more desirable when working with chemicals 1 a.m.u) = x g (tiny) (impractical to use for calculations) If one C atom weighs 12 a.m.u. How many atoms weigh 12 g? 13

14 AVOGADROS NUMBER - THE ORIGIN If you weigh out exactly 12g of carbon-12, you will get 6.02x10 23 of carbon atoms. 14

? quadrillions trillions billions millions thousands 1 mole = 602213673600000000000000 or 6.

15 FUNDAMENTAL PARTICLES IN A MOLE This number is named in honor of Amedeo Avogadros There is Avogadro's number (N A ) of particles in a mole of any substance.? quadrillions trillions billions millions thousands 1 mole = or x Wow that is a BIG number!! It is the number of particles present in exactly 12 grams of the isotope carbon

JUST HOW BIG IS A MOLE? You can have 6.02 x 10 23 (or a mole) of anything!

16 JUST HOW BIG IS A MOLE? You can have 6.02 x (or a mole) of anything! If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole. A mole of standard soft drink cans would cover the surface of the earth to a depth of over 200 miles! 16

A MOLE n IS A COUNTING UNIT The mole term is similar to the dozen term. just like: Just as a dozen represents 12 ; the mole represents 6.022 x 10 23. A very large amount.

17 A MOLE n IS A COUNTING UNIT The mole term is similar to the dozen term. just like: Just as a dozen represents 12 ; the mole represents x A very large amount. This is due to atoms & molecules being very small. The mole is also referred to as Avogadro s number, N A 1 mole = N A = n = x particles Particles could be atoms, molecules, ions, electrons, even eggs. Chemists must work with large groups of atoms due to their small size just as bakers work with groups of 12. Chemists called their group a mole (just as bakers call their group a dozen). 17

18 DEFINITION OF MOLE (mol) One mole is the amount of any substance that contains the same number of units as the number of atoms in exactly 12 grams of Carbon mole of any substance = 6.02 x units of that substance. (unit = molecules, formula units, or atoms) x is known as Avogadro s Number. 18

19 THE MOLE Mole is the same number regardless of the representative particle: atom, molecule, ion, electron. If you had a mole of H 2 O could you swim in it? NO! Water molecules are so small that a mole of H 2 O = 18ml 19

20 There are more atoms in one gram of salt than grains of sand on all the beaches of all the oceans in all the world. And a mole of Helium atoms is 4 times heavier than a mole of Hydrogen atoms. 20

21 Item WHAT IS MOLE? Unit used to count No. of items per unit for counting common objects Shoes pairs 2 Eggs dozens 12 Paper reams 500 Particles in Chemistry moles for counting particles like atoms, ions, molecules 21

22 A MOLE OF PARTICLES CONTANS HOW CAN THE CONCEPT OF A MOLE BE USED TO COUNT ATOMS? 1 mole C 6.02 x particles = 6.02 x C atoms 1 mole H 2 O 1 mole NaCl = 6.02 x H 2 O molecules = 6.02 x NaCl molecules (technically, ionics are compounds not molecules so they are called formula units) 6.02 x Na + ions and 6.02 x Cl ions 22

23 Remember... 1 mole = 6.02x10 23 atoms or molecules = g from the periodic table 23

24 USING THE MOLE CONCEPT TO COUNT ATOMS? 1 mole of carbon = 6.02 x atoms of carbon = 12 grams of carbon 1 mole of hydrogen = 6.02 x atoms of H = 1 gram of hydrogen 1 mole of aluminum = 6.02 x atoms = 27 grams Recall, in chemistry we don t work with individual atoms or molecules because they are too small to be weighed or measured We have to work with LOTS of atoms in order to measure them. THAT s WHERE THE MOLE COMES IN! 24

of chemical quantities and inter-conversions.

25 THE MOLE - WHAT S THE POINT? Important in the mathematics of chemistry - plays a central role in the relationships among a number of chemical quantities and inter-conversions. The mole helps measure atoms in a more manageable way because atoms are so small! One mole of silver contains 6.02 x atoms of silver, but those atoms can fit into a small beaker! 1 mol = Avogadro s Number = units 25

26 MEANING OF AVOGADROS NUMBER IN REAL LIFE The reason why Avogadro s number is so large is because the masses of atoms are extremely small. The term mole is similar to the word dozen refer to 12 of anything. 12 eggs, 12 cars, 12 atoms, 12 ions, 12 positive charges or 12 of anything else. The term mole can refer to 6.02 x eggs, 6.02 x cars, 6.02 x molecules, 6.02 x positive charges or 6.02 x of anything. 1 dozen cookies = 12 cookies 1 mole of cookies = 6.02 x cookies 1 dozen cars = 12 cars 1 mole of cars = 6.02 x cars 1 dozen Al atoms = 12 Al atoms 1 mole of Al atoms = 6.02 x atoms Note that the NUMBER is always the same, but the MASS is very different! Mole is abbreviated mol. Symbol for mole is n 26

to find their mass. RELATIVE SCALES R. A. M.

27 However, atoms are very small and impossible to count out. In order to estimate the number of atoms in a sample of an element, it is necessary to find their mass. RELATIVE SCALES R. A. M. (A r )*** The mass of an atom is quantified in terms of relative atomic mass. R. I. M.*** Relative Isotopic Mass (Read up) R. M. M. (M r ) 27 R. F. M.

RELATIVE ATOMIC MASS The relative atomic mass (A r ) of an element is the mass of one of its atoms relative to 1/12 the mass of one atom of carbon-12. R. A. M. has no unit.

28 RELATIVE ATOMIC MASS The relative atomic mass (A r ) of an element is the mass of one of its atoms relative to 1/12 the mass of one atom of carbon-12. R. A. M. has no unit. relative atomic mass (A r ) = average mass of an atom 12 mass of one atom of carbon-12 Most elements have more than one isotope. The A r of the element is the average mass of the isotopes, taking into account the abundance of each isotope. This is why the A r of an element is frequently not a whole number.

29 RELATIVE MOLECULAR MASS The relative molecular mass (M r ) of a covalent substance is the mass of one molecule relative to 1/12 the mass of one atom of carbon-12. M r can be calculated by adding together the masses of each of the atoms in a molecule. R. M. M. has no unit. Example: what is the M r of H 2 SO 4? 1. Count number of atoms 2. Substitute the A r values 3. Add the values together (2 H) + (1 S) + (4 O) (2 1.0) + (1 32.1) + (4 16.0) = 98.1 The sum of all of the atomic weights in the compound in an ionic compound, it s the formula weight. In a covalent compound, it s the molecular weight.

30 RELATIVE FORMULA MASS The equivalent of relative molecular mass for an ionic substance is the relative formula mass. This is the mass of a formula unit relative to 1/12 the mass of one atom of carbon-12. It is calculated in the same way as relative molecular mass, and is represented by the same symbol, M r. R. F. M. has no unit. Example: what is the M r of CaCl 2? 1. Count number of atoms 2. Substitute the A r values 3. Add the values together (1 Ca) + (2 Cl) (1 40.1) + (2 35.5) = 111.1

31 MOLAR MASS For example: A mole of sodium = 23.0 grams/mole This means that if you could measure 6.02 x atoms of sodium (or one mole) into a beaker, it would weigh 23.0 grams! 31

32 MOLAR MASS The atomic mass of any substance (chemical element or chemical compound) expressed in grams is the molar mass (M) of that substance. The units of molar mass is grams/mole (g / mol) or g mol -1. For example: A mole of sodium = 23.0 grams/mole This means that if you could measure 6.02 x atoms of sodium (or one mole) into a beaker, it would weigh 23.0 grams! Recall, the atomic mass of sodium is 23.0 amu. Since oxygen occurs naturally as a diatomic, O 2, the molar mass of oxygen gas is 2 times g or g/mol. The atomic mass number under a symbol on the periodic table is also the molar mass of that element. C Molar Mass: grams Mole 32

33 CALCULATING MOLAR MASS What about a mole of water? A mole of water (or 6.02 x molecules) weighs 18.0 grams! You can determine the molar mass of any compound by adding the molar mass of each atom or multiples of atoms! What is the molar mass of magnesium nitrate? The sum of the atomic masses is: ( ) = (62.01) = amu The molar mass for Mg(NO 3 ) 2 is g/mol. 33

34 THE DOZEN ANALOGY Coin Mass of one coin Dozen Mass Number of Coins Penny 2 g 24 g 12 pennies Nickel 4 g 48 g 12 nickels Dime 1.5 g 18 g 12 dimes Quarter 7 g 84 g 12 quarters 34

35 MOLES CALCULATIONS Fill in the blank. A mole of oxygen atoms contain x 10 atoms and weighs grams. A mole of oxygen contains x molecules and atoms and weighs or grams. 2( (6.022 x ) A mole of fluorine atoms contain x atoms and weighs grams A mole of fluorine contains x molecules and x 10 atoms and 23 weighs grams. 35

36 QUANTITY AND MOLE RELATIONSHIPS Quantity of a chemical substance also can be stated in terms of (1) its mass (2) its volume (3) the number of particles in the sample. ALL OF THESE QUANTITES ARE RELATED TO ONE ANOTHER THROUGH THE MOLE. 36

37 MOLES INTERCONVERSIONS 1. Moles to Moles 2. Moles to Mole Ratio 3. Moles to Mass and vice-versa 4. Moles to Volume and vice-versa 5. Moles to Particles and vice-versa 37

MOLES TO MOLES CONVERSION Stoichiometric coefficient refers to the number that is placed infront of a reactant or product of a chemical equation to indicate how many moles are involved in the

38 MOLES TO MOLES CONVERSION Stoichiometric coefficient refers to the number that is placed infront of a reactant or product of a chemical equation to indicate how many moles are involved in the reaction. Construct an equation for the reaction between copper and silver nitrate. Identify the relationships among all the reactants and products in terms of moles. How many moles of copper are needed to react with 3.50 moles of silver nitrate? 4 Fe + 3 O 2 2Fe 2 O 3 How many moles of Fe 2 O 3 are produced when 6.0 moles O 2 react? How many moles of Fe are needed to react with 12.0 mole of O 2? How many grams of O 2 are needed to produce mole of Fe 2 O 3? 38

MOLE TO MOLE RATIO Cheapium + Thriftium Dearium.

rests on the principles of the conservation of matter.

39 MOLE TO MOLE RATIO Cheapium + Thriftium Dearium. (Buy cheap and sell dear) CONVERSION The study of the quantitative aspects of chemistry (stoichiometry) It rests on the principles of the conservation of matter. Mole ratio - is the ratio that compares the number of moles of different substances in a balanced chemical equation. Stoichiometry is a measurement of the relative quantities of chemical reactants and products in a chemical reaction. 2 Al(s) + 3 Br 2 (liq) Al 2 Br 6 (s) When conducting a chemical reaction, it is often important to mix reactants in the correct proportions. This prevents contamination of the products by wasted reactants. 39

40 WRITING MOLE FACTORS 4 Fe + 3 O 2 2 Fe 2 O 3 Fe and O 4 mole Fe and 3 mole O 2 3 mole O 2 4 mole Fe Fe and Fe 2 O 3 4 mole Fe and 2 mole Fe 2 O 3 2 mole Fe 2 O 3 4 mole Fe O 2 and Fe 2 O 3 3 mole O 2 and 2 mole Fe 2 O 3 2 mole Fe 2 O 3 3 mole O 2 40

41 WRITING MOLE FACTORS 3 H 2 (g) + N 2 (g) 2 NH 3 (g) A. A mole factor for H 2 and N 2 is 1) 3 mole N 2 2) 1 mole N 2 3) 1 mole N 2 1 mole H 2 3 mole H 2 2 mole H 2 B. A mole factor for NH 3 and H 2 is 1) 1 mole H 2 2) 2 mole NH 3 3) 3 mole N 2 2 mole NH 3 3 mole H 2 2 mole NH 3 41

42 WRITING MOLE FACTORS 3 H 2 (g) + N 2 (g) 2 NH 3 (g) A. A mole factor for H 2 and N 2 is 2) 1 mole N 2 3 mole H 2 B. A mole factor for NH 3 and H 2 is 2) 2 mole NH 3 3 mole H 2 42

CONVERTING MOLES TO MASS Using molar mass (CONVERSION FACTOR) of an element/compound to convert between grams of a substance and moles. How many grams in 3.

43 CONVERTING MOLES TO MASS Using molar mass (CONVERSION FACTOR) of an element/compound to convert between grams of a substance and moles. How many grams in 3.5 moles of water? Proportionality Principle over the Triangular Mnemonic Concept Try these What is the mass of mole of sodium atoms, 2. 8 moles of iron atoms? 43

44 CONVERTING MASS TO MOLES Using molar mass (CONVERSION FACTOR) of an element/compound to convert. State the amount of substance in moles in g NaCl g Na 2 CO g of copper(ii) sulphate- 5-water, CuSO4.5H 2 O 44

CONVERTING MOLES TO PARTICLES Particles are atoms, ions (formula units) and molecules. How many atoms are there in 0.5 mol of S. 6.

45 CONVERTING MOLES TO PARTICLES Particles are atoms, ions (formula units) and molecules. How many atoms are there in 0.5 mol of S particles = 1 mol (= molar mass) How many molecules in 3.5 moles of water? Using the Avogadros # (N A ) (CONVERSION FACTOR) to convert between moles and particles (A, I, M) How many particles are found in 18 g of table salt. 45

46 CONVERTING PARTICLES TO Using the Avogadros # (N A ) (CONVERSION FACTOR) to convert from particles (A, I, M) to moles. MOLES How many moles are in 6 x atoms of S? How many moles in 3.61 x molecules of laughing gas. 46

47 COVERTING PARTICLES TO If we want to convert particles to mass, we could first convert particles to moles and than we can convert moles to mass. MASS Use Avogadro s number and the molar mass of Pb Calculate the mass of 6 x iron atoms. We want grams, we have atoms of lead. 47

48 COVERTING PARTICLES TO How many O 2 molecules are present in g of oxygen gas? MASS We want molecules O 2, we have grams O 2. Use Avogadro s number and the molar mass of O molecules O 2 48

49 GROUP ACTIVITY Complete the table. SUBSTANCE MASS R.F.M. No. of MOLES No. of PARTICLES Water 18 Nitrogen dioxide Copper(II) Sulphate Sulphur trioxide 1.20 x Sodium 49

CONVERSION FROM MOLES TO VOLUME Sometimes an element exist as molecules (often gases). Elements which are gases at r.t.p are often diatomic. Gases are not very dense.

50 CONVERSION FROM MOLES TO VOLUME Sometimes an element exist as molecules (often gases). Elements which are gases at r.t.p are often diatomic. Gases are not very dense. The average pop bottle contains 1 litre of pop. One liter of air weighs just over 1 g size (a paper clip) If the conversion factor for the translation for moles to mass and vice-versa is Molar Mass, The conversion factor from moles to volume is therefore? Chemists have shown by experiment that: If we want to find the number of moles of a gas, we can do this by measuring the volume rather than the mass. 50

51 WHAT IS THE MOLAR VOLUME OF GASES? Depends on T & P Two sets of conditions Volume occupied by one mole of molecules of a gas. Gases are mostly empty space so they ALL have the same volume despite different mass 51

52 MOLAR VOLUME OF GASES Molar Volume (V of 1 mole at STP or RTP) 22.4 dm dm 3 at K dm& 3 1 atm (Standard temp & pressure / S.T.P.) at 273 K & 1 atm (Standard temp & pressure / S.T.P.) at 298 K & 1 atm (Room temp & pressure / R.T.P.) at 273 K & 1 atm (Standard temp & pressure / S.T.P.) 52

53 Gas Molar mass/g Molar volume at R.T.P./dm 3 Molar volume at S.T.P./dm 3 O N H He CO Not constant ~ 24 ~

54 AVOGADROS LAW Equal volumes of ALL gases at the same temperature and pressure contain the same number of moles of molecules. Mole Relationship of Selected Gases At fixed T & P, V = molar volume 54

55 CONVERTING MOLES Calculate the volume required to produce 0.5 moles of ammonia at r.t.p. TO VOLUME 55

56 CONVERTING VOLUME TO MOLES A sample of methane, CH 4, occupies 4.50 L at STP. How many moles of methane are present? Try this now How many molecules of hydrogen gas, H 2, occupy L at RTP? We want moles, we have volume. Use molar volume of a gas: 1 mol = 22.4 L molecules H 2 56

57 MOLE CONVERSION FACTORS We now have three interpretations for the mole: 1 mol = particles 1 mol = molar mass 1 mol = 22.4 L at STP for a gas This gives us 3 unit factors to use to convert between moles, particles, mass, and volume. 57

58 THE MOLE BRIDGE Everything must go through Moles!!! 58

59 EXTENSION EXCERCISE 1. What is the molar mass of Ba(NO 3 ) 2.4H 2 O a) b) c) d) How many moles are contained in 54.78g of Cu(NO 3 ) 2? a) mol b) 3.424mol c) 187.5mol d) Which contains the larger number of molecules? a) g HCl b) 15.0 g C 6 H 12 O 6 c) g of I 2 4. How many grams of silver are contained in mol of AgNO 3? a) g b) 81.3 g c) 128g d) 170g g of nitrogen (N 2 ) contains a) 7.0 atoms of N c) 3.0 x atoms of N b) 0.25 mole of N d) 7.0 atomic masses of N 6. How many atoms are in 56.9 g of potassium nitrite? 7. If g of calcium chloride reacted with g of sodium carbonate, how many moles of each will be reacting? 59

60 INDEPENDENT PRACTICE ACTIVITY 60

61 Good luck! Remember the best practice is practice! THE MOLE CONCEPT PART TWO IS NEXT 61

IGCSE Double Award Extended Coordinated Science

IGCSE Double Award Extended Coordinated Science Chemistry 4.1 - The Mole Concept The Atomic Mass Unit You need to know the atomic mass unit and the relative atomic mass. In Unit C3.3, 1 atomic mass unit