Chemistry Crunch #3.2: Name: KEY What Is a Mole? Why? 1) In the world around you, a variety of different measures are used to specify amounts. For example, at the store you might buy 10 apples or a 5 lb bag of apples. One measure is a counting unit and the other is a unit of weight. To compare the prices, you would probably want to know how many apples are in the 5 lb bag. Likewise, chemists use both number and mass to specify the amount of a substance. 2) Chemists work with chemical substances on a regular basis. However, they can t physically count the number of particles needed for a reaction, because they are so small and can t be seen individually! What they can do is mass a bunch of particles in grams. For elements, the particles are atoms. For covalent (molecular) compounds, the particle is called a molecule, and represents the actual number of each type of atom clumped together in a single molecule. For example, in sugar molecules, 24 atoms clump together to make one C 6 H 12 O 6 molecule. For ionic compounds, the particle is called a formula unit, and represents the simplest ratio of the ions in a crystal of that compound. For example, the formula for calcium chloride, CaCl 2, indicates that in a crystal of this compound, there are two chloride ions for every one calcium ion. 3) Chemists realize that chemical processes or changes happen via an exact recipe. The recipes are always followed using units of measure called moles. Learning Goals: Understand that fractions are sometimes used to represent equivalent measurements (conversion factors). Use dimensional analysis to solve problems. Figure out the mass of one mole of any element. Compare or calculate the number of moles of substances when given a chemical recipe. Prerequisites: Knowledge of atoms and isotopes Write the correct formula for any compound Knowledge of conversion factors 1
Model 1: Counting by Measuring Mass We know that certain words imply a certain number of things, like a gross happens to be 144 of something. A dozen is 12 of something. In your bag, you have 12 somethings. Mass them and record below. Get data from at least 2 other groups as well Your Data Group 1 Group 2 Composition (describe or draw) Mass of your 12 somethings (grams) Key Questions: 1. To calculate the mass of one of your somethings, without actually massing it, divide total mass by the number of somethings. grams/per 1 something 2. Based on the procedure you just followed, explain how you could obtain 385 somethings, without actually counting them out!! (Hint you would need a balance.) Take the mass of 1 something and multiply by 385 to get your goal mass; then keep adding somethings on the balance until you get this mass. 3. A dozen is 12 of an item. Even though your data for the 3 types of somethings in the data chart represents 12 items, the masses are different. Explain why, in terms of the composition of the items! Since their composition (what they re made of) is different, their masses are different. 4. What do you think the activity you just did has to do with counting atoms?? We can t count atoms because they re too small and we can t mass them individually so we have to figure out how many atoms we have by taking the mass of a large number of them... or in other words, by scaling it up. 2
Model 2: Making Sense of Units Information: Do you know the base units that you will be using? Circle or highlight mole and gram on the Table D. These are the units we will measure and convert in Unit 3! Everything listed on Table D is considered a base unit and can be represented by 10 0. In Unit 3, we will be converting between two base units, grams and moles, so we will not be using Table C. The mole, abbreviated mol, is a counting unit used to count large numbers of atoms. A mole is a number of things, like a pair (2) or a dozen (12). To determine the number of grams that is equal to 1 mole, you will look at the atomic mass listed on the Periodic Table. Examine the chart below comparing these numbers: Element Weighted average mass of Mass of one mole of atoms (g) one atom (u) H 1.00 1.00 C 12.01 12.01 Fe 55.85 55.85 Hg 200.59 200.59 You do NOT need to know why the average mass of one atom, or in other words the atomic mass on the Periodic Table, equals the mass of one moles of atoms. (If you are interested, ask your teacher for the explanation.) What we are really focused on is that we can now use the atomic mass on the periodic table as a mass in grams. Notice that the numerical value of the weighted average atomic mass on the periodic table for an element is identical to the mass of one mole of atoms of that element. In other words, both values are represented by the same number, the only thing that is different is the units. For example: the weighted average mass of one atom of arsenic is 74.92 u, and the mass of one mole of arsenic atoms is 74.92 grams. The mass in grams of 1 mole of a substance is called molar mass. Key Questions: 1. What is a mole? A counting unit used to count/mass particles (similar to a dozen meaning 12 of something, a mole means 6 x 10 23 of something!) 2. What conversion factor correctly represents the relationship between kilograms and decigrams? a. 1 dg b. 10,000 dg 10,000 kg 1 kg 3
Model 3: Using Molar Mass to Create Conversion Factors for Elements Information: Mercury is a toxic substance that accumulates in the body and damages the central nervous system and other organs. Which do you think would be worse for you, 1 mole of mercury or 10 grams of mercury? To answer this question, it is necessary to understand the relationship between these two measures. To create the conversion factor that correctly represents this relationship, recall your work in Unit 1. You learned how to make conversion factors by making a fraction of two equivalent measures. For example, the correct conversion factor that correctly states the equivalent relationship between grams and milligrams is: 1 gram OR 1000 milligrams 1000 milligrams 1 gram Let s do this for grams and moles. Consider the element Ca. If you look on the Periodic Table, 1 mole (remember this just refers to a very specific and a really large # of atoms) of the element Ca has a mass of 40.08 grams. The correct factor or fraction that correctly states the equivalent relationship between grams and moles is: 1 mole Ca OR 40.08 grams Ca 40.08 grams Ca 1 mole Ca These values all express a ratio. Another ratio you are familiar with is miles per hour. If you were traveling at 65 miles per hour, there are many ways to express this: 65 miles per hour, 65 mph, 65 miles/1 hour, 65 miles/hour, _65 miles 1 hour 1 hour 65 miles For calcium, in means that there are 40.08 grams of Ca per every 1 mole, or notated differently: 40.08 grams/1 mole, 40.08 grams/mole (the 1 before mole is implied, just like miles/hour), or 40.08 g/mol. 1 mole of a different element, like B, would still be the same number of atoms, but since B atoms have a different composition of p +, n o and e -, they obviously have a different atomic mass. 1 mole of B has a mass of 10.81 grams. Exercises/Key Questions: 1. 1 mole of magnesium atoms has a mass of: 24.31_ g/ 1 mole 2. 1 mole of oxygen (O 2 ) molecules has a mass of: 32.00_ g/ 1 mole 3. State each of the above relationships as conversion factors: Mg: 24.31 g O 2 : 32.00 g 1 mol 1 mol 4. Which has more mass, 1 mole of copper atoms or 1 mole of arsenic atoms? 1 mole of arsenic atoms 5. Solve the original question posed: Mercury is a toxic substance that accumulates in the body and damages the central nervous system and other organs. Which do you think would be worse for you, 1 mole of mercury or 10 grams of mercury? 1 mole of mercury (~200g!) 4
Model 4: Mole-Mole Ratios We can view chemical equations as recipes. The cool thing is, the recipes are written implying mole amounts: 1 C 3 H 8 + 5 O 2 3 CO 2 + 4 H 2 O When we balance the chemical reaction shown above, we can read it two ways: 1) For every 1 molecule of C 3 H 8 that reacts, 5 molecules of O 2 are needed, and then 3 molecules of CO 2 and 4 molecules of water will be produced. 2) For every 1 mole of C 3 H 8 molecules that reacts, 5 moles of O 2 molecules are needed, and then 3 moles of CO 2 molecules and 4 moles of water molecules will be produced. So We can view the balanced equation as a recipe written in amounts called moles : 1 C 3 H 8 + 5 O 2 3 CO 2 + 4 H 2 O 1 mole + 5 moles 3 moles + 4 moles Rememebr that conversion factors are relationships between equivalent values. We can also make conversion factors for equations. Here is the conversion factor for the reactants: 1 mole C 3 H 8 OR 5 mol O 2 5 mol O 2 1 mole C 3 H 8 Here is the conversion factor for the products: 3 mol CO 2 OR 4 mol H 2 O 4 mol H 2 O 3 mol CO 2 Other possible conversion factors: 1 mol C 3 H 8 3 mol CO 2 5 mol O 2 4 mol H 2 O 3 mol CO 2 5 mol O 2 4 mol H 2 O 1 mol C 3 H 8 The recipe can be scaled up or down, and is done so just like making a double batch of cookies all ingredient amounts are doubled in that case. 1 C 3 H 8 + 5 O 2 3 CO 2 + 4 H 2 O 1 mole + 5 moles 3 moles + 4 moles A double batch of the Chemical Recipe above: 2 moles + 10 moles 6 moles + 8 moles Key Questions: 1.) Fill in the amount of moles produced by the reaction if it were a 10x batch: 10 moles 50 moles _30 moles _80 moles 5
Model 5: Using Conversion Factors in Dimensional Analysis How are these conversion factors used?!? Step 1- Identify the Given and Needed Units To solve a problem you must first: Identify the given unit Identify the needed unit. Example: How many moles of CO 2 would be produced if you used 100 moles of C 3 H 8? The given unit is the initial unit. Given unit = moles C 3 H 8 The needed unit is the unit for the answer. Needed unit = moles CO 2 Practice: How many moles of C 3 H 8 would have reacted if you produced 1.7 moles of H 2 O? Identify the given and needed units given in this problem. Given unit = moles H 2 O Needed unit = moles C 3 H 8 _ Step 2- Problem Setup After you complete Step 1, make a t-chart and fill in the units. The given unit goes in the top left and the bottom right. The needed units go in the top right and as the label for the final answer. Example: How many moles of CO 2 would be produced if you used 100 moles of C 3 H 8? Given unit = moles C 3 H 8 Step 1 Needed unit = moles CO 2 Step 2 Needed Unit = Needed Unit mol C 3 H 8 mol CO 2 = moles CO 2 mol C 3 H 8 Practice: How many moles of C 3 H 8 would have reacted if you produced 1.7 moles of H 2 O? Given unit = moles H 2 O_ Step 1 Needed unit = moles C 3 H 8 _ Step 2 Needed Unit = Needed Unit mol H 2 O mol C 3 H 8 = moles C 3 H 8 mol H 2 O 6
Step 3- State the Conversion Factors Write the conversion factors that connect the units (from the original equation shown below). 1 C 3 H 8 + 5 O 2 3 CO 2 + 4 H 2 O Example: How many moles of CO 2 would be produced if you used 100 moles of C 3 H 8? Given unit = moles C 3 H 8 Step 1 Needed unit = moles CO 2 Step 2 Needed Unit = Needed Unit mol C 3 H 8 mol CO 2 = moles CO 2 mol C 3 H 8 Step 3 1 mol C 3 H 8 or 3 mol CO 2 3 mol CO 2 1 mol C 3 H 8 Practice: How many moles of C 3 H 8 would have reacted if you produced 1.7 moles of H 2 O? Step 1 Given unit = moles H 2 O_ Needed unit = moles C 3 H 8 _ Step 2 Needed Unit = Needed Unit mol H 2 O mol C 3 H 8 = moles C 3 H 8 mol H 2 O Step 3 1 mol C 3 H 8 or 4 mol H 2 O 4 mol H 2 O 1 mol C 3 H 8 7
Step 4- Set Up Problem and Calculate Answer a) Choose the correct conversion factor based on the units already in place in order to cancel the given unit and provide the needed unit. b) Solve by multiplying the numbers on the top of the t-chart together, then dividing by the number on the bottom. Example: How many moles of CO 2 would be produced if you used 100 moles of C 3 H 8? Given unit = moles C 3 H 8 Step 1 Needed unit = moles CO 2 Step 2 Needed Unit = Needed Unit mol C 3 H 8 mol CO 2 = moles CO 2 mol C 3 H 8 Step 3 1 mol C 3 H 8 or 3 mol CO 2 3 mol CO 2 1 mol C 3 H 8 Step 4 100 mol C 3 H 8 3 mol CO 2 = 300 moles CO 2 1 mol C 3 H 8 Practice: How many moles of C 3 H 8 would have reacted if you produced 1.7 moles of H 2 O? Step 1 Given unit = moles H 2 O_ Needed unit = moles C 3 H 8 _ Step 2 Needed Unit = Needed Unit mol H 2 O mol C 3 H 8 = moles C 3 H 8 mol H 2 O Step 3 1 mol C 3 H 8 or 4 mol H 2 O 4 mol H 2 O 1 mol C 3 H 8 Step 4 1.7 mol H 2 O 1 mol C 3 H 8 = _0.425 moles C 3 H 8 4 mol H 2 O 8
Summary: Let s put together our list of rules for using the t-chart. Step 1- Identify the Given and Needed Units Step 2- Problem Setup Make a t-chart and fill in the units. The given unit goes in the top left and the bottom right. The needed units go in the top right and as the label for the final answer. Step 3- State the Conversion Factors Write the conversion factors that connect the units (from the original information/equation). Step 4- Set Up Problem and Calculate Answer a) Choose the correct conversion factor based on the units already in place in order to cancel the given unit and provide the needed unit. b) Solve by multiplying the numbers on the top of the t-chart together, then dividing by the number on the bottom. ***NOTE: I know some of you could have figured this out another way. However, not all of the problems will be this simple; I want you to learn this method with simple problems first, so that you can use it correctly later when the numbers are more difficult and you have to use this method. For example: [From the 2001 APES Exam] Answer the following questions regarding the heating of a house in western New York State. Assume the following: The house has 2000 square feet of living space. 80,000 BTU s of heat per square foot are required to heat the house for the winter. Natural gas has a cost of $1.00 per hundred cubic feet. One cubic foot of natural gas supplies 1,000 BTU s of heat energy. The furnace is 80% efficient. Calculate the following, showing all the steps of your calculations, including units. a) The number of cubic feet of natural gas required to heat the house for one winter. b) The cost of heating the house for one winter. 9
Exercises: Complete the following using the t-chart method. 1. Based on the following chemical equation, how many moles of LiCl are needed to produce 2 moles of Cl 2? 2 LiCl 2 Li + Cl 2 2 mol Cl 2 2 mol LiCl = 4 mol LiCl 1 mol Cl 2 2. Based on the following chemical equation, how many moles of NaOH can be produced using 5 moles of Na? 2 Na + 2 H 2 O H 2 + 2 NaOH 5 mol Na 2 mol NaOH = 5 mol NaOH 2 mol Na 3. How many moles of CO 2 will form upon burning up 3.7 moles of C 2 H 2, based on the recipe for burning C 2 H 2 shown below? 2 C 2 H 2 + 5 O 2 2 H 2 O + 4 CO 2 3.7 mol C 2 H 2 4 mol CO 2 = 7.4 mol CO 2 2 mol C 2 H 2 10
Chem Crunch #3.2 Checkpoint Name: KEY 1. When a chemist talks about particles, they use different terms. a. For an element a chemist says: atom b. For an ionic compound a chemist says: formula unit c. For a molecular compound a chemist says: molecule 2. When a chemist says the word mole it implies (1) a molecule (3) a very large number of small particles (2) a mass (4) both (2) and (3) 3. What is the mass of a) 1 mole of barium atoms Reference Table-Periodic Table- Atomic Mass=137.33u =137.33 g b) 5 moles of Neon atoms 5 mol Ne 20.179g Ne = 100.90g Ne 1 mol Ne c) 1 mole of Cl 2 molecules 1 mol Cl 2 70.9 g Cl 2 (35.45gx2) = 70.9g Cl 2 1 mol Cl 2 4. Use this chemical recipe, or equation, to do the questions below using the t-chart method. This is for burning gasoline (C 8 H 18 ). 2 C 8 H 18 + 25 O 2 18 H 2 O + 16 CO 2 a) If 1 mole of C 8 H 18 is burned, how many moles of water will form? 1 mol C 8 H 18 18 mol H 2 O = 9 mol H 2 O 1 mol C 8 H 18 b) If 6 moles of C 8 H 18 are burned, how many moles of O 2 will be needed? 6 mol C 8 H 18 25 mol O 2 = 75 mol O 2 1 mol C 8 H 18 c) If 5.3 moles of C 8 H 18 are burned, how many moles of CO 2 will form? 5.3 mol C 8 H 18 16 mol CO 2 = 42.4 mol CO 2 2 mol C 8 H 18 11