The Mole: The Start of Chemical Calculations

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Elvin Garrison
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1 The Mole: The Start of Chemical Calculations The creation of formulas and the finding of their molecular masses is only partially complete. What exactly does that number you have found for the molecular mass mean? Is it the mass of one molecule, or a million, or ten billlion? What unit is it measured in? The Carbon-12 Based Atomic Mass Scale In the years following Dalton's presentation of his atomic theory, chemists worked very hard at determining a complete set of relative masses for all the elements that were known. By knowing these relative masses the chemists were able to select amounts of elements in grams needed for any desired atom ratio. In establishing a table of atomic masses, it is necessary to have a reference point against which to compare the relative masses. Currently, the agreed-upon reference is the most abundant isotope of carbon, which is carbon-12. By definition, an atom of this isotope is defined as having the mass of exactly amu. (atomic mass units) In other words, an amu is defined as 1/12th of the mass of one atom of carbon-12. The definition of the size of the atomic mass unit was quite arbitrary. It could just as easily have been selected to be 1/24th of the mass of one atom of a carbon atom, or 1/10th the mass of a calcium atom, or any other value. Why 1/12th the mass of carbon-12? Carbon is a very common element, available to any scientist and by choosing the amu to be of this size, the atomic masses of nearly all the other elements are almost whole numbers, with the lightest atom having a mass of approximately 1. (hydrogen-1 has a mass of amu when carbon-12 is assigned a mass of exactly 12 amu.) The Mole Suppose we want to make molecules of carbon dioxide, CO 2, in such as way that there would be no extra carbon and oxygen atoms left. If we took ten atoms of carbon and twenty atoms of oxygen we would make 10 molecules of carbon dioxide. Suppose we wanted to make more, lets say 40,000 molecules of carbon dioxide. Once again, we could count out 40,000 atoms of carbon and 80,000 atoms of oxygen, let them react and we'd have 40,000 molecules of carbon dioxide. This sounds all very nice and neat unless you realize the trap. Have you ever seen an atom?

2 Atoms are too tiny to count individually. Saying they are tiny is even wrong because tiny can be seen. Even with the best scanning tunneling electron microscope ever invented the largest atoms known, look just like fuzzy cloud tops. We have never seen individual atoms. There are no lenses with the resolving power or balances fine enough to measure an individual atom. We get around this problem because each element has its own characteristic atomic mass and each formula has its own unique molecular mass. We know, that oxygen weighs in at 1.33 times that of carbon, because of this we get a ratio of their masses: 16.0 amu (for one atom of O) = amu (for one atom of C) = 1 If we take a sample of oxygen and carbon in a ratio of 1.33 to 1, we must obtain equal numbers of their atoms. That is, if we actually had a balance that could measure amu directly we could mass out 32 amu of oxygen and 12 amu's of carbon - a mass ratio of 2.66 to 1 - we would have exactly 2 atoms of oxygen for every atom of carbon and a 2 to 1 ratio by atoms. When we mass out a sample of an element such that its mass in grams is numerically equal to the element's atomic weight, we always obtain the same number of atoms no matter what element we choose. Thus 12.0 g of carbon has the same number of atoms as 16 grams of oxygen, or 32.6 g of sulphur, or 55.8 g or iron. This relationship also extends to compounds. The formula mass of water, H 2 O, is 18.0 amu. If we take 18.0 grams of water then it should have the same number of molecules as there were atoms in 12.0 grams of carbon. The carbon-12 isotope, which makes up 98.89% of all naturally occurring carbon, is the reference used by SI Metric in its definition of the base unit for a chemical substance, the mole, abbreviated mol. This mole concept is the most important in all of chemistry. Once this concept is grasped all the rest of chemistry will appear easy.

3 Avogadro's Number The mole is defined as 6.02 x 1023 units. It is called Avogadro's number in honour of Italian scientist, Amadeo Avogadro ( ). It is a pure number with a special name, just like so many others. For example: This number is not an odd number at all. It became inevitable once the amu was defined. The relationships needed are: Another useful relationship is that The mass in grams of a substance that equals one mole is often called its molar mass, and the units are grams/mol or g/mol. For example, aspirin has a molecular mass of 180 grams. Therefore if we massed out exactly 180 grams of aspirin we would have Avogadro's number of aspirin molecules. Using the Mole Concept One mole of any substance can be calculated from its formula mass. Since this is true it is absolutely essential that when you are using the mole concept that the correct formula be used. It is not enough to say "use 1 mole of nitrogen".

4 Do we mean atomic elemental nitrogen or nitrogen gas? There is a difference! One mole of N consists of Avogadro's number of nitrogen atoms (and has a mass of g), whereas 1 mole of N 2 consists of Avogadro's number of molecules, each molecule having two nitrogen atoms. One mole of N 2 molecules would have a mass of 2 X g = g.

5 Converting Grams to Mole This is probably the single most used equation in chemistry. It is the one that allows the conversion of moles into grams and grams back into moles. Moles are a "theoretical value" which looks good on paper. Grams is the "practical value" that you take out of a stock bottle and place on the balance. Lab balances read in grams, not moles, and so in practical work all mole values have to first be converted. Moles to grams formula: Example: Sodium bicarbonate, NaHCO 3, is one ingredient of baking powder. How many grams of sodium bicarbonate are in moles? Step 1. Step 2. Use the equation: Step 3: Provide a written answer:

6 Grams to moles formula: Example: Potassium permanganate, KMnO 4, at one time was used for an anti-fungal agent. You could always tell someone who had just been treated because their feet were purple. The pharmacy gives you 250 grams of the stuff in a bottle. How many moles of it do you have? Step 1: Step 2: Use the equation: Step 3: Write a written answer. Finding the molecular mass In the above two examples you have had a molecular formula to work with. As long as you have a molecular formula, or name, from which you can make a formula up, you will always have a molecular mass. In order to find the molecular mass, without a name to go on, you need two pieces of information. The number of grams and the number of moles that it represents.

7 Example: A fellow student comes to you with a sample of an unknown chemical. They tell you that it has a mass of grams and that it is exactly 0.20 moles. What is the molecular mass of the substance? Step 1: Use the equation: Step 2: Write a sentence. The three formulas can be written using the math triangle:

8 Worksheet 3.1: Avogadro's Number, Grams, Moles and Molecular Mass 1. What are the units of molar mass? 2. The mass of 2.5 X 10 4 grapes is 50 kilograms, and that of an equal number of oranges is 1.2 X 10 3 kg. What is the mass ratio of a single grape to a single orange? 3. A mole of carbon atoms has a mass of 12 grams, and a mole of magnesium atoms, 24 grams. What is the mass ratio of a single carbon atom to a single magnesium atom? 4. Aluminum and oxygen combine in a mass ratio of 9.00 to If a flashbulb contains 5.4 X 10-3 grams of aluminum, what mass of oxygen must be present for complete combustion of the aluminum? 5. If there are 'x' atoms in 5 grams of carbon, how many atoms are there in 5 grams of silicon? 6. If 10 grams of iron contain 'y' atoms, how many grams of aluminum will contain 'y' atoms. 7. If 8 grams of oxygen contain 3.01 X atoms, calculate the number of atoms present in 2 grams of oxygen. 8. Using Avogadro's number, calculate the number of atoms in kilograms of carbon. 9. What is the mass of mol of each of the substances given below: (a) Sodium carbonate, Na 2 CO 3 (b) Ammonium tetraborate, (NH 4 ) 2 B 4 O 7 (c) Calcium cyclamate, Ca(C 6 H 12 NSO 3 ) How many moles of sodium nitrate are in 1.70 grams of sodium nitrate, NaNO 3, a substance used in fertilizers and to make gunpowder. 11. Ammonium sulphate, (NH 4 ) 2 SO 4, is a fertilizer used to supply both nitrogen and sulphur. How many grams of ammonium sulphate are in 35.8 moles of (NH 4 ) 2 SO A mol sample of table sugar, C 12 H 22 O 11, weighs how many grams? 13. A solution of zinc chloride, ZnCl 2, in water is used to soak the ends of wooden fenceposts to preserve them from rotting while they are stuck in the ground. One ratio used is 840 grams ZnCl 2 to 4 L water. How many moles of ZnCl 2 are in 840 grams of ZnCl 2? 14. In the early 1970s, thallium sulphate, Tl 2 SO 4, a powerful poison, was illegally used in poison baits to control predators such as coyotes on western rangelands. Hundreds of eagles died after taking these baits. A 1.00 kilogram can of Tl 2 SO 4 contains how many moles of this compound? 15. Borazon, one crystalline form of boron nitride, BN, is very likely the hardest of all substances. If one sample contains 3.02 X atoms of boron, how many atoms and how many grams of nitrogen are also in this sample? 16. If iodine is not in a person's diet, a thyroid condition called goitre develops. Iodized salt is all that it takes to prevent this disfiguring condition. Calcium iodate, Ca(IO 3 ) 2, is added to table salt to make iodized salt. How many atoms of iodine are in moles of Ca(IO 3 ) 2? How many grams of calcium iodate are needed to supply this much iodine?

9 17. Ammonium carbonate,(nh 4 ) 2 CO 3, is used as a fertilizer and to manufacture explosives. How many atoms of nitrogen are in moles of this substance? How many grams of ammonium nitrate supply this much nitrogen? 18. Sodium perborate, NaBO 3, is present in "oxygen bleach". It acts by releasing oxygen, which has bleaching ability. How many grams of sodium perborate are in 4.65 moles of NaBO 3? 19. Barium sulphate, BaSO 4, is given to patients as a thick slurry in flavoured water before X-rays are taken of the intestinal tract. The barium blocks the X-rays, and the tract therefore casts a shadow that is seen on the x-ray film. How many grams are in mole of barium sulphate. 20. Calculate the number of grams in mole of each of the following substances? (a) Water, H 2 O. (b) Glucose, C 6 H 12 O 6, a sugar in grape juice and honey. (c) Iron, Fe. (d) Methane, CH Calculate the number of moles of each substance in grams of each of the following samples: (a) Ammonia, NH 3 (b) Cholesterol, C 27 H 46 O (c) Gold, Au (d) Ethyl alcohol, C 2 H 6 O 22. Why does grams of ammonia, NH 3, have so many more moles than grams of cholesterol, C 27 H 46 O? 23. A sample of a compound with a mass of 204 grams consists of 1.00 x molecules. What is its formula weight?

10 Marvin Da Mole! Our Hero 1. Calculate the mass of a) 2.00 moles of water, H 2 O b) 4.38 moles of chlorine, Cl 2 c) moles of ammonia, NH 3 d) 1.8 moles of oxygen, O 2 2. Calculate the number of moles in a) 25 g of helium, He b) 12.5 g of methane, CH 4 c) g of iodine, I 2 d) 40.0 g of sodium, Na 3. Calculate the number of particles in a) 2.50 moles of Neon, Ne b) moles of iron, Fe 4. Calculate the number of moles in a) 9.03 X atoms of Cu b) 3.76 X molecules of SO 2 c) 8.6 X electrons 5. Calculate the number of molecules in a) 12.5 g of nitrogen, N 2 b) 0.76 g of ammonia, NH 3 c) 0.60 g of hydrogen, H 2 6. Calculate the mass of a) 4.25 X atoms of C b) 6.02 X molecules of H 2 O c) one trillion atoms of Zn d) one atom of U

11 Marvin Da Mole Strikes Again! 1. How many particles are there in one mole? 2. It is estimated that a sample of matter contains 1.38 X atoms. How many moles are present in the sample? 3. How many moles of barium are present in a sample having a mass of 22.3 grams? 4. A chemical reaction requires 3.7 moles of boron. What mass, in grams, of boron must be used in the reaction? 5. A sample of naturally occurring carbon has a mass of grams. Calculate the number of moles of carbon in this sample. 6. A chemical reaction results in 57.2 grams of the gas carbon dioxide, CO 2. How many molecules of gas were produced? 7. Calculate the mass of one trillion molecules of oxygen, O Calculate the number of moles in: a) 25 grams of oxygen, O 2 b) 0.27 g of ammonia, NH 3 c) 10.5 g of sodium, Na d) 347 g of ammonium nitrate, NH 4 NO 3 9. Calculate the mass, in grams, of: a) 1.24 moles of water, H 2 O b) moles of amonium chloride, NH 4 Cl c) 5.62 moles of sodium hydroxide, NaOH d) 2.35 moles of sodium sulphate, Na 2 SO Calculate the number of molecules in: a) 3.00 moles of chlorine, Cl 2 b) 3.00 moles of uranium hexafluoride, UF 6 c) 3.00 moles of hydrogen chloride gas, HCl d) 3.00 moles of any kind of molecule 11. Calculate the number of atoms in: a) 3.00 moles of chlorine, Cl 2 b) 3.00 moles of uranium hexafluoride, UF 6 c) 3.00 moles of hydrogen chloride gas, HCl d) 3.00 moles of ammonium sulphate, (NH 4 ) 2 SO 4

3. Atoms and Molecules. Mark (1) Mark (1) Mark (1) Mark (1) Mark (1) Mark (1) Marks (2)

3. Atoms and Molecules. Mark (1) Mark (1) Mark (1) Mark (1) Mark (1) Mark (1) Marks (2) 3. Atoms and Molecules Q 1 144 grams of pure water is decomposed by passing electricity. 16 grams of hydrogen and 128 grams of oxygen are obtained. Which chemical law is illustrated by this statement?