Isotopic Pennies PURPOSE: THEORY: atomic mass units isotopes average mass weighted average

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Janis Andrews
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1 Isotopic Pennies Name: Period: PURPOSE: To understand the concept of counting by weighing as well as how to calculate the mass of a naturally occurring element from information about its isotopes. THEORY: In class you have learned that each element has a mass in atomic mass units. This mass was determined by first discovering the ratio of the mass of the element to the mass of carbon-12. As carbon-12 is defined to have a mass of 12 amu s, the mass of the element in question can be found by taking the ratio of its mass to carbon-12 and multiplying by 12. However, that is not the whole story. Look for example at carbon. Although the mass of carbon-12 is defined to be 12 amu, the mass given on the periodic table is in fact Why? The reason for this apparent mistake is that each element typically exists as a mixture of several isotopes in nature. Now, the isotopes have no effect on the identity or chemical properties of the element, since the number protons and number and arrangement of electrons are the same. However, since the addition of neutrons adds mass, each isotope has a slightly different atomic weight. In nature, we find several isotopes of each element. Consequently, when you weigh out some carbon in lab, you are weighing out both carbon-12 and carbon-13. However, it is known that natural carbon is composed of 98.89% carbon-12 and 1.11% carbon-13. These percentages are always true for this compound. So let us say we obtained 10,000 carbon atoms. From the percentages, 9,889 of the atoms would be carbon-12 and 111 would be carbon-13. Hence the total mass of carbon would be (12)(9889) + (13)(111) = 120,111 amu s. But, we are more interested in the average mass, which would be 120,111 / = amu s, exactly what is on the periodic table! Hence, each elemental mass on the periodic table is a weighted average of the mass of each stable isotope of that element. To make this concept clearer, consider the following situation. Suppose you work in a hardware store and someone comes in and requests 600 nuts. You could count out the nuts, but this would be a slow process. You have a scale available, and you realize that weighing out the nuts would be a much faster way of counting them. What information do you need to count out the nuts by weighing them? The answer is the average mass. To determine the average mass of the nuts, you count out a sample of 10 and weigh them. Suppose the mass of the 10 nuts is 105 g. This means the average mass of a nut is 105/10 = 10.5 g/nut. Now, what sample size will contain 600 nuts? Its just 600 nuts x 10.5 g per nut, which would equal 6300 g. Therefore you weigh out a sample of 6.30 kg of nuts, put them in a bag, and assure the customer that the bag contains 600 hex nuts as requested. Note that counting by weighing works if you know the average mass of the units being counted. In the preceding example, it s possible that not one of the nuts had a mass of exactly 10.5 g. All that matters is that the average mass is 10.5 g. You are going to count by weighing today in lab. Instead of atoms, we will use pennies, because in 1982 the composition of the penny was changed from being one of nearly pure copper to that of a zinc center with a copper coating. Consequently, although the pennies look the same, their masses are significantly different. Thus, we will consider them as model isotopes for our lab.

2 MATERIALS: Weighing Boat with Pennies Centigram balance Empty film canister Film canister containing unknown numbers of pre-1982 and post-1982 pennies DATA DATA TABLE I: Masses of Pre-1982 and Post-1982 Pennies Weighing Boat Letter: Number of Pre-1982 Pennies: Mass of Pre-1982 Pennies (g) Number of Post-1982 Pennies: Mass of Post-1982 Pennies (g) Group Avg. Mass of Pre-1982 Pennies: Class Avg. Mass of Pre-1982 Pennies: Group Avg. Mass of Post-1982 Pennies: Class Avg. Mass of Post-1982 Pennies:

3 CALCULATIONS: 1) First start your calculations section be rewriting the class average mass of the pre and post-1982 pennies. Class average mass of pre-1982 pennies: Class average mass of post-1982 pennies: 2) Now use this information to determine the mass of 55 pre-1982 pennies. Show all work: 3) Now we will do an example of a counting by weight calculation. Determine the number of pre-1982 pennies present in 310. g of pre-1982 pennies. Show all work. 4) Using the same method as above, determine the mass of 75 post-1982 pennies: Show all work: 5) Now determine the number of post-1982 pennies present in 250. g. Show all work. Now let us see how the work you have done above can be applied to isotopes. You have learned that most elements have several isotopic forms. The various isotopes of an element all have the same number of protons and electrons (so they are chemically identical) but differ in the number of neutrons present. You have also discussed how the average atomic mass listed for a particular element on the periodic table represents a weighted average of the masses of all the isotopes of the element. By weighted average, we mean that the abundance of the element in nature is reflected in the average atomic mass You can see what we mean by weighted average using the data you have collected for the pre and post 1982 pennies above. Using your individual masses of all the pennies (both pre- and post-1982) calculate the average mass of a penny (without regard to the date it was minted). 6) Calculate the average mass of all pennies for your lab group:

4 You can arrive at the same average mass by another method of calculation using the average mass you calculated for each type of penny, rather than the individual masses of all the pennies. Consider the following example: A student has 5 pennies of average mass 3.11 g and 19 pennies of average mass of 2.49 g. The weighted average mass of these 24 pennies is given by [5(3.11 g) + 19(2.49 g)]/24 = [15.55 g g]/24 = 2.62 g The weighted average mass (2.62 g) is closer to 2.49 g than it is to 3.11 g because there were more pennies of the lower mass present in the sample: the weighted average has included the relative abundance of the two types of pennies. 6) Using the method outlined above, calculate the weighted average mass of a penny. Show all work. Question: Does this average mass correspond to the average you calculated above? DATA TABLE II: Masses of Empty and Filled Penny Canisters Average Mass of an Empty Canister: Number of Pennies in each Canister: 10 Mass of Penny Canister : Mass of Penny Canister : Mass of Penny Canister : Calculations for Part II Let us use the information we have obtained about the pennies to figure out how many of each type are in the unknown film canisters. Each canister contains 10 pennies, but we do not know how many of those are pre-1982 and how many are post However, this can be easily determined using the mass of the pennies in the canisters and the average mass of each penny.

5 8) First determine the mass of the pennies alone. To do so, you must subtract the mass of an empty canister from that of the filled canister. Show all work for your three canisters below. 9) Now let x be the number of pre-1982 pennies in each canister. Using the class average masses for the pre- and post 1982 pennies, we can write an expression for the total mass of the pennies as follows: (Class mass of pre-1982 pennies)(x) + (Class avg. mass of post-1982 pennies)(10-x) = mass of all pennies in the container. So again we can count the number of each type of penny in each unkown canister simply by knowing the average masses and weighing. Now for each of your unknown canisters, determine the numbers of pre- and post-1982 pennies in each. Show all work for the three canisters you chose below:

6 Complete the following table to finish off your part two calculations: Canister Label Number of pre-1982 pennies Number of post-1982 pennies. QUESTIONS 1) Assume the element Uus is synthesized and that it has the following stable isotopes 284 Uus (283.4 amu) 34.60% 265 Uus (284.7 amu) 21.20% 288 Uus (287.8 amu) 44.20% What is the average atomic mass for Uus that would be listed on the periodic table? 2) An element consists of 90.51% of an isotope with a mass of amu, 0,27% of an isotope with a mass of amu, and 9.22% of an isotope with a mass of amu. Calculate the average atomic mass and identify the element.

7 PROCEDURE: ISOTOPIC PENNIES 1) Obtain a labeled weighing boat filled with 25 pennies. 2) Look at each of the pennies and separate them into two piles: those that have dates through 1981, and those that have dates after If you find a penny with the date 1982, alert your teacher. Place each pile onto a labeled post-it note. Write down the number of each type of penny you have on your data table. 3) Weigh each of your pre-1982 pennies on the balance (to the nearest 0.01 g) and place this information on the data table. 4) Weigh each of your post-1982 pennies on the balance (to the nearest 0.01 g) and place this information on the data table. 5) Calculate the average mass of your pre-1982 and post-1982 pennies. 6) Have a member of the group go to the whiteboard and record the sample letter, the number of pre-1982 and post-1982 pennies, and the average mass of the pre-1982 and the post-1982 pennies. 7) Obtain three labeled film canisters, which are filled with 10 pennies. Record the letter and mass of each canister on the data table. 8) Return to your desk to begin calculations.

Drake Chemistry Isotopic Pennies Name: Atomic Structure Unit Isotopic Pennies

Drake Chemistry Isotopic Pennies Name: Atomic Structure Unit Isotopic Pennies Introduction At the beginning of the 19 th century, John Dalton proposed a new atomic theory all atoms of the same element are identical to one another and equal in mass. It was a simple yet revolutionary