Introductory Chemistry Lab 7: The Mole and Avogadro s Number
Objectives Understand the importance of Avogadro s Number Approximate the value of Avogadro s Number Introduction Avocados number: How many avocados and artichokes are there in a mole? A recipe calls for two avocados and two artichokes. Would you say that equal amounts of avocados and artichokes are used? The answer to that question depends on how you define the same amount. If you consider the quantity, yes, there are two of each. What if instead the recipe told you to use 250 grams of artichokes and avocados? There might be one and a half avocados used for every artichoke would you call this the same amount as well? One way to solve this problem would be to ask for more specific instructions. The phrase the same amount is being used to describe quantity (number) in one instance and mass in another. Similar situations come up in chemistry. If you are supposed to put the same mass of two different substances into a beaker, all you would have to do is weigh Figure 1: You can think of avocados and artichokes in this example as two different types of molecule each with a different molar mass. equal amounts using a scale. Things become more complicated, however, when the ratio of the total number of molecules or atoms is important in an experiment you might know the number of molecules in the reactants and products, but not the actual masses. How would you measure an exact number of NaCl molecules? The mole is an important unit in chemistry that you will use often. The modern definition of the mole is based around the carbon 12 ( 12 C) atom: 12 grams of 12 C is exactly one mole of substance. It turns out that 1 gram of 12 C has approximately 6.02 x 10 23 individual atoms a value called Avogadro s Number after the chemist Amedeo Avogadro. The mole is a similar concept to a dozen: one mole of a substance will always have 6.02 x 10 23 atoms or molecules. Atomic weight is a measurement of the mass of each element, and can be easily found on most periodic tables. Atoms that have a large number of protons and neutrons have more total mass than atoms with only a few protons and neutrons, and this difference is reflected by the atomic weight. Conveniently, the mole and atomic weight are defined so that one mole of a substance will have a mass equal to the atomic weight of that substance in grams. This number is called molar mass. For instance, the atomic weight of potassium (K) is 39.098. This means that one mole of potassium will have a mass equal to 39.098 grams. Calcium (Ca) is a larger atom than potassium, and has an atomic weight of 40.078. One mole of calcium will have the same number of atoms as a mole of potassium, but the Calcium will weigh more due to its larger atomic weight. See the next lab for more detail on atomic weigh and atomic mass. So how do you measure 1 mole of NaCl? We know that this molecule is made up of one sodium ion and one chlorine ion (chloride). Looking up sodium (Na) on the Periodic Table tells you its atomic weight is 22.99, meaning it has a molar mass of 22.99 g/mol. Chlorine, meanwhile, has a molar mass of 35.45 g/mol. Since one mole of sodium chloride consists of one mole sodium ions and one mole chlorine ions, we can add these together to find the molecular mass of NaCl. 67
1 Na = 22.99 g/mol + 1 Cl = 35.45 g/mol 58.44 g/mol of NaCl This is how to determine molar mass of a compound. 58.44 g NaCl 1 mol NaCl = 54. 88 grams NaCl 1 mol NaCl What if we weighed out 1.00 grams of NaCl how many molecules is this? We use the molar mass of NaCl, which we already know from above, to convert from mass to a number of moles. We can then use the fact that there are 6.02 x 10 23 molecules in a mole to find the number of molecules NaCl in one gram: 23 1 mol NaCl 6.02 10 molecules 22 1.00 g NaCl = 1.03 10 molecules NaCl 58.44 g NaCl 1 mol NaCl Notice how the molar mass is inverted in the second term. The value is the same, but we flip the fraction so that the gram units cancel. You can go through and cross out the units that cancel to verify that the resulting units are molecules. You can use similar calculations to convert between mass, moles, and the number of molecules fairly easily. Through this lab procedure, we will determine the experimental value for Avogadro s number. You will float cinnamon, evenly distributed, on the surface of water in a Petri dish. The dishwashing liquid you will use in this Lab is about 1% sodium stearate, and a solution with a known concentration of the liquid will be dropped onto the water. The sodium stearate molecules will form a single layer and spread out, pushing the cinnamon toward the edges of the Petri dish, allowing the surface area to be determined. We will assume that each molecule takes up 0.210 nm 2 of surface area, and that there is no space between the molecules. Pre lab Questions 1. How many grams of H 2 O do you need to weight out to have 1 mole of H 2 O? 68
2. How many molecules of water are there in one mole of H 2 O? 3. How many moles of H 2 O are there in 1.0 g of H 2 O? 4. How many molecules of H 2 O are there in 1.0 g of H 2 O? 69
Experiment: Avogadro s Number Materials Safety Equipment: Eye goggles, gloves Ground cinnamon Dishwashing liquid Dropper Petri dish (bottom) Ruler 100 ml Graduated cylinder 10 ml Graduated cylinder Stirring rod 50 ml beaker Wash bottle Distilled water* *You must provide Procedure Part 1: Preparing the Sodium Stearate Solution 1. Measure exactly 1.50 ml of dishwashing liquid into a 10 ml graduated cylinder. 2. Fill a wash bottle with distilled water. Gently rinse the 1.50 ml of dishwashing liquid with distilled water and pour it into a 100 ml graduated cylinder. Rinse the 10 ml graduated cylinder several times to make sure all the dishwashing liquid has been transferred to the 100 ml graduated cylinder. HINT: Try not to create suds. 3. Add enough additional distilled water to get to the 100.0 ml. 4. Gently stir the solution with a stirring rod until it is mixed well. Part 2: Calibrating a Dropper 1. Fill a 50 ml beaker half full with distilled water. Use your dropper to fill a 10 ml graduated cylinder to 1.00 ml with water. HINT: Make sure the 10 ml graduated cylinder is clean of dishwashing liquid. 2. Next, draw up water from the 50 ml beaker into the dropper. Add water dropwise into the graduated cylinder. Hold the dropper consistently at a 45 o angle and drop at a rate of about one drop per second. Count the drops it takes to reach the 2.00 ml mark. HINT: It should take about 25 drops. If you feel that your measurement is incorrect, repeat until you achieve consistent readings. 3. Record in the Data section the number of the drops it takes to add 1 ml water to the graduated cylinder. 4. Repeat calibration for a second trial, and record the number of drops in the Data section. Average the two results. Part 3: Calculating the Number of Molecules 1. Rinse and then fill a petri dish with 20 ml distilled water. Allow the water to settle and remain motionless. 2. Lightly sprinkle cinnamon onto the surface of the water in the Petri dish. HINT: Add just enough to barely cover the water. 70
3. Draw up the dishwashing liquid solution with the calibrated dropper. Hold the dropper at a 45 o angle about 1 inch above the center of the Petri dish. Slowly deliver one drop of the solution. HINT: A clear circle should form, spreading the cinnamon outward. 4. Quickly use a ruler to measure the diameter of the cleared circle in cm. 5. Record the diameter in the Data section. Wash out the Petri dish. Data Part 2: Calibrating a Dropper 1. The number of drops in 1 ml water (drops used to move from the 1.00 ml to 2.00 ml mark): Trial 1: Trial 2: 2. The number of drops on average per one milliliter: Part 3: Calculating the Number of Molecules 1. The diameter of the circle formed (cm): Calculations 1. Calculate the surface area of the circle formed ( πd 2 /4 ) : Surface area = 2. Calculate the number of molecules on the top layer. We must convert the surface area in centimeters squared to nanometers squared and then multiply that by the surface area of a sodium stearate molecule. Convert the surface area of the circle formed (#1) to molecules per layer: Top layer SA (Question 1) cm 2 1 m 2 1 x 10 18 nm 2 1 molecule 10,000 cm 2 1 m 2 0.210 nm 2 = molecules top layer 71
3. Calculate the concentration of grams of sodium stearate per milliliter of diluted solution. To do this, multiply the concentration of sodium stearate in the dishwashing liquid by the dilution of the solution (1.50 ml dishwashing liquid per 100 ml solution). 1 g sodium stearate 1.50 ml dish liquid 100 ml dish liquid 100 ml diluted solution = g /ml 4. Calculate the number of moles of sodium stearate in a single layer. To do this, first take the number of drops used to achieve the monolayer (1 drop) and convert it to ml using the calibrated number of drops per ml. Then multiply the number of grams of sodium stearate per milliliter of solution. Finally, convert to moles through the molar mass of sodium stearate. HINT: The molar mass of sodium stearate is 296.4 g/mol. 1 drop (added to dish) 1 ml dish liquid solution g sodium stearate (from #3 calculation) 1 mol top layer drops (avg # calibrated per ml from Data Part 2) 1 ml dish liquid solution 296.4 g (molar mass of sodium stearate) = mol / top layer 5. Finally, we can calculate the Avogadro s number through the comparison of molecules of sodium stearate in the top single layer to the moles of sodium stearate in the monolayer. Avogadro s number (experimental) = # molecules / top layer (#2) # moles / top layer (#4) = molecules mole 72
Post lab Questions 1. Why do you think that Avogadro s number, 6.02 x 10 23, was probably not the exact number you obtained? Was your experimental value close to the actual value (i.e., was your experimental value on the order of 10 23 molecules)? 2. How many moles are in 0.289 g of methane (CH 4 )? 3. How many moles are in 1,000,000,000 molecules of H 2 0 2? 4. What is the mass in grams of 1,000,000,000 (10 9 ) molecules of H 2 O 2? 73