Chemistry 140

 

Please have the following pages ready before class on Wednesday, November 13. As usual, write an abstract and paper-clip it to the front of your individual writeup. The abstract and the carbon-copy pages of the write-up is due in class on Wednesday, November 20.

 

As you saw in the previous lab, graphs are an important part of an experiment; it allows you to visualize hypothetical situation. In this experiment, you will not get much more hypothetical: the determination of the value of absolute zero in degrees Celsius (°C)!

 

What you will do in this experiment is trap a small amount (3 to 5 mL) of “wet” air inside an overturned graduated cylinder immersed in a beaker of distilled water. You will measure the amount of this trapped “wet” air at different air temperatures by heating the water in the beaker to various temperatures. Please look at the experimental setup.

 

The ideal gas law states that PV = nRT, where P is the pressure of a gas, V is the volume the gas occupies, n is the number of moles of gas, R is the gas constant (available in various units on the inside back cover of the text) and T is the temperature of the gas. Note that the equation above can be recast as:

 

T = (1/k) V, where k is a combination of n, R and P. If we could guarantee that P and n did not change (and R won’t, since it is a constant), then k is a constant. This means that the equation is linear; in other words, T is proportional to V.

 

So, as the temperature of any ideal gas decreases, the volume of the gas decreases proportionally. Finally, at absolute zero (0 Kelvins), the volume of any ideal gas is therefore zero.

 

After you collect the data of the trapped gas in the inverted graduated cylinder, you will plot your data, with volume of trapped “dry” air along the x-axis and temperature of the air along the y-axis.

 

The astute among you noticed that the word before “trapped” changed from wet to dry. How does that work?

 

According to Dalton’s Law of Partial Pressures, the total pressure of the gas in the cylinder may be broken up as follows (note that the subscript “air” refers to dry air and that “total” refers to wet air, that is, air with water vapor in it):

 

Ptotal = Pair + Pwater vapor

 

or Pair = Ptotal - Pwater vapor

 

Using Boyle’s Law, then: (Vwater vapor)/(Pwater vapor) = Vtotal/ Ptotal

 

or Vwater vapor = Vtotal (Pwater vapor/Ptotal)

 

Finally, Vair = Vtotal – Vwater vapor

 

Combining the bold-faced equations, then,

 

Vair = Vtotal (Pair/Ptotal)

 

So we can calculate the volume of dry air in a sample of wet air (like the air in the inverted graduated cylinder) by measuring the total volume and the total pressure, and looking up the pressure of water vapor at the air temperature.

 

Making the assumption that water vapor is an ideal gas, then, we can use the ideal gas law:

 

Tair = (P/nR) Vair

 

and P/nR is a constant. So, if you plot Vair versus Tair, you should get a straight line. You should calculate r2, the correlation coefficient, to determine how linear your values are. You should also determine the equation of the best-fit line through those data points.

 

In this experiment, we are not getting anywhere close to absolute zero. In order to figure out the temperature at absolute zero, note that we can use the information that, at absolute zero, the volume of the gas is zero. This means that when Vair = 0, the value of Tair must be absolute zero. This is simply the y-intercept of your best-fit line (hey, don’t take my word for it; draw it and see!). This method of getting a number well beyond the range of your data points is called extrapolation. It is a useful and thus abused method; this is why the correlation coefficient is necessary — it tells you how much to believe your data points really do lie along a line.

 

That is how we are going to do the lab. Oh, and one more complication, I am not doing a step-by-step procedure for you. Between exercise 11 and your observation skills, I want you to write the procedure down, numbered step by numbered step, as you do the experiment.

 

For background material on gases, the text sections 5.3 and 5.5 may be helpful (especially pages 209 and 210).

 

                                                                                    Your name, your partner’s name, date of experiment

 


Lab 4:  Determination of absolute zero using the gas laws

   Part 1.  Purpose

 

The abstract for this lab’s reference may be found at:

 

http://jchemed.chem.wisc.edu/Journal/Issues/2001/Feb/abs238.html

Do not use this as your own abstract!

 

The reference is Kim, M-H., Kim, M. and Ly, S-Y (2001). A simple laboratory experiment for the determination of absolute zero. Journal of Chemical Education 78, 238-240.

 

The title of this lab is pretty self-explanatory about its purpose, but do state it as a sentence.

 

   Part 2. Materials and methods

 

Chemical list: Distilled water

 

Sketch the setup as you are using it and label the various pieces of equipment. This picture link may help.

   Part 3. Procedure

 

Goodness! Must I spell this out for you every time? In this experiment, you will write the steps as you go along. Write down everything. Number the steps. And use your experimental design sheet (exercise 11) as you go along!

 

1.

 

2.

 

3.

 

etc.

Waste disposal — No hazardous materials will be used in this experiment.

 

            Part 4.  Original data 

 

You should be able to develop the table, based on exercise 11, if nothing else.

 

 

Part 5.  Calculated results 

 

Show a sample calculation for one of the data points (how you derived Vair).

 

Using any spreadsheet/graphing program, make a plot of volume of dry air (x-axis) versus temperature of dry air (y-axis). Make sure the axes are labeled (along with units) and that the graph has a title, such as “Volume versus temperature of air for lab 4, Chemistry 140”. Attach the graph to the lab writeup.

 

Use the functions available on the program to draw the best-fit line through your data points. If it is possible to display the equation for the line, do so; in any case, determine the temperature (in °C) of the air when the volume of dry air is zero by extrapolation, and show your calculation.

 

Determine also the correlation coefficient (r2 or R2) of your data points.

 

 

 Part 6.  Group results

 

Once your group has obtained the value of absolute zero in °C by extrapolation of your data, write the maximum value on the board. Eliminate outliers, if necessary, and calculate a mean and standard deviation of the absolute zero in °C for the class.

 

Part 7.  Questions

 

1. What are you assuming about the temperature of the water and the temperature of the trapped air? Why might this assumption be faulty?

 

2. Why was it important to look up really accurate vapor pressures of water at different temperatures? In other words, why can’t you use a table of water vapor pressures, like some textbooks have, with only a few temperature entries? Hint: Look at how the vapor pressure of water changes at high temperatures. What would a small deviation here mean for the volume of water vapor calculated?

 

3. How many moles of air did you have trapped? Hint: You can calculate this number using the slope of your line. Show the details of your calculation.

 

4. Look at the on-line abstract for this experiment (given at the beginning of the lab) and compare our class mean and standard deviation for absolute zero with theirs. How do the two ranges compare (do they overlap significantly? at all?)? Is there any evidence for a systematic error, and, if so, what might its source be?

 

 

   Part 8.  Conclusion

 

First sentence: “We determined that the temperature of absolute zero using this experimental setup was ________ °C. “

 

Explain if our assumptions were reasonable (that water vapor is an ideal gas and the question 1 assumption).

 

Mention any significant random and/or systematic errors and how they could be fixed or not fixed next time. Question 4 might be of some help here.

 

Finally, mention: “The class mean for the temperature of absolute zero was _________ ± _________  °C, which is (consistent/inconsistent) with our partnership’s result and is (consistent/inconsistent) with the result of Kim et al. (2001).”

 

How confident are you of your result? The r2 value on your graph should help you answer this question, because your result is dependent on how linear your data points were.

 

   Abstract

 

As usual, a short (less than 100 word) summary of the major result of your experiment, and the method by which you achieved this result. Report both your own result and the class mean and standard deviation for the temperature of absolute zero. Report also the percent error between the class mean and the true value. Report the source of any significant errors in your own result.