Most chemical elements consist of mixtures of isotopes. The molar mass values we use are derived by using the concept of weighted averages. In this experiment, you will simulate one way that scientists can determine the relative amounts of different isotopes present in a sample of an element. For our imaginary element "pennium" we will use a mixture of pennies from pre-1982 and post-1982. These pennies have different compositions, and therefore different masses. These will represent the two isotopes of "pennium" in our mixture.

You will take a sealed bag containing a mixture of pre-1982 and post-1982 pennies. Your bag could contain any combination of the two "isotopes." Your task is to determine the isotope composition of the element pennium without opening the sealed bag.

The relationships can be represented mathematically by the following equality. Because this is a relationship, we will not use the units in our calculation.

The bag will contain 10 pennies of an unknown mixture. Let x = the number of pre-1982 pennies in the bag. Then, 10 - x = number of post-1992 pennies in the bag.

Also, the mass of all the pre-1982 pennies is equal to the number of pre-1982 pennies (x) multiplied by the mass of one pre-1982 penny. The mass of all the post-1982 pennies is equal to the number of post-1982 pennies (10 - x) times the mass of one post-1982 penny. We can write the relationship as:

Total mass of mixture of pennies = (x)(mass of pre-82 penny) + (10 - x)(mass of post-82 penny)

This equation can be solved for x after the three masses are known.

MATERIALS:

Several small manilla envelopes (Like fishhooks are sold in at the bait shop.)
11 pre-1982 pennies
11 post-1982 pennies
Balance

PROCEDURE:

1. Take a small envelope and find its mass to the nearest 0.01g (two decimal places). Record this mass on the DATA TABLE as mass of empty bag.

2. Give someone else (mom will do nicely) 10 of each kind of penny and the bag whose mass you found. Have them put a total of 10 pennies in the bag, but not tell you what combination of pre-82 and post-82 pennies they used. Have them seal it and give it to you.

3. Find the mass of the bag and pennies to the nearest 0.01g and record the mass on the DATA TABLE.

4. Find the mass of a pre-1982 penny and a post-1982 penny seperately, to the nearest 0.01g, and record the masses on the DATA TABLE.

DATA TABLE:

Mass of empty bag ________ g

Mass of bag and pennies ________ g

Mass of pre-1982 penny ________ g

Mass of post-1982 penny ________ g

CALCULATIONS:

5. Find the total mass of the pennies by subtracting the mass of the bag.

6. Calculate the value of x (the number of pre-1982 pennies) and 10 - x (the number of post-1982 pennies). Use the formula given in the introduction. Remember, do the multiplications, combine like terms, and solve for x.

Because we are using rounded numbers, the answer will not be a whole number. Remember that like atoms, we are using whole pennies, so round your answers for x and 10 - x to the nearest whole number.

7. Calculate the percent composition of the element "pennium" for both "isotopes" from your data.

% of isotope = The number of isotope present, divided by the total number (10), multiplied by 100

Now do it again with a different combination of the two pennies.

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