An Analogy for Atomic Mass

An analogy for atomic mass

Imagine that grains of rice and dried peas are an analogy for atoms. After all, they are small individual particles, each having their own unique mass. Suppose that someone gave you some grains of rice, and exactly the same number of dried peas. You don't need to know how many kernels of grain you have, but there must be the same number of each.

Why do you have to have the same number of grains?

It would be rather hard to find the mass of an individual grain of rice on a typical high school classroom balance, because the balance would not be sensitive enough. However, you could find the mass of a large number of grains, or peas. The following table shows the results you might get if you did this. Remember that we must put the same number of particles on the scale in each case.

Table 1
Rice isn't really the lightest stuff in the universe, but let's imagine it is for this analogy. Then we could compare other substances to it in r.m.u. - rice mass units! We can only do this because there were the same number of particles in each measurement. Nowhere in the calculation do we need to know how many that is. Try this experiment to prove to yourself that this works.

Here's the results of a similar experiment (using the same number of paper clips, thumbtacks, and stables):

Mass of paperclips	`4.30` g
Mass of staples	`0.35` g
Mass of thumb tacks	`2.30` g

To the correct number of significant digits, what is the relative mass of these objects?

Could we do the same thing with atoms? Yes, if we had some way of knowing that we had the same number of them to measure. It's hard enough to count individual grains of rice. The idea of counting individual molecules is preposterous. How can we possibly know that we have the same number of molecules, if we can't see them to count?

Fortunately we can do this if we believe in Avogadro's hypothesis that "equal volumes of gases at the same temperature and pressure contain equal numbers of molecules." Suppose that we take two equal sized flasks of gas, one filled with hydrogen at room temperature and atmospheric pressure, and the other filled with oxygen at the same conditions. Then we know that the number of particles in each container is the same, assuming of course that we believe Avogadro. We have no clue, how many that actually is, nor do we need to know. These are the results you might get if you did this experiment.

This time hydrogen really is the lightest substance so it makes sense to assign it a mass of 1.0. You can see that an oxygen atom is 16 times as heavy. It has a mass of 16 on a relative scale.

If the proper equipment is available, your teacher may demonstrate this experiment using Avogadro's hypothesis, and how it lets us calculate relative masses of gases.

Which of the following would you not need to know, in an experiment to measure the relative masses of gases? Assume that the flask will be repeatedly filled with different gasses.

The following measurements were made for a flask filled with oxygen, and then with an unknown gas. The temperature and pressure were kept constant. When empty, the flask weighed 142.56 g

Gas	Mass of flask and gas
Oxygen	`143.52` g
Gas X	`144.96` g

Compared to oxygen, what is the relative mass of the unknown gas?


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