gas_module_reader - Chem 111-Gases by William Sweeney...

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1 Chem 111-Gases by William Sweeney Outline A problem set on how to obtain functional relationships from data ....................................... 1 Introduction to gases ............................................................................................................ 6 Kinetic molecular theory of gases ....................................................................................... 14 Applications ....................................................................................................................... 20 Poster exam information ..................................................................................................... 25
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2 GASES A problem set on how to obtain functional relationships from data In the first laboratory dealing with gas behavior you gathered (or will gather) experimental data on the relationship between pressure and volume. For a practicing scientist, experimentation is the first step on the path toward understanding as a system. Recall the five phases in the process of developing a good model: 1)gather experimental data 2)reduce the data 3)design a model 4)test the model 5)refine the model In this problem set we are concerned with the process of reducing your data. The goal is to convert a mass of data into a mathematical equation that the describes the relationship between your experimental variables. In the lab the variables you will deal with are pressure and volume, so you will be concerned with reducing that data into a functional relationship. The point of this problem set is to help you get a better understanding of that process. This goal of obtaining a functional relationship is useful for several reasons: It allows a quantitative interpretation of your data. For example, looking at your experimental data you might describe it by saying that the volume went down when the pressure went up. But actually your data can be interpreted much more quantitatively. If possible we would want to describe precisely how the volume changes when the pressure is altered. To do this you need to know the mathematical relationship between the variables. It provides a kind of averaging of your data. Every experiment has some error in it. When you fit your data to a linear function, you are using all your data to find that function. Thus the function represents a kind of averaging, a way to deal with fluctuations in your data due to experimental errors by looking at the overall trends. It allows a convenient and accurate way to interpolate between data points. We will approach the problem graphically, by finding some way to plot data linearly .
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3 Why try to find a linear plot? The goal is to find the functional relationship, and obtaining a linear plot is actually the easiest approach. For your pressure/volume data, you will use linearity to find the functional relationship. This is done by plotting P vs. some function of V (such as V, V 2 , 1/V 1/V 2 , ...) with the goal of finding a straight-line (i.e., linear) plot. Your eye can tell with good accuracy if the plot is linear. If you find a linear plot, you can use the equation for a straight line (y = mx + b) to determine the mathematical relationship between your variables. This can best be seen by looking at an example.
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