- What is the relationship between the pressure applied to a gas and the volume it occupies? In this experiment, a given quantity of gas will be trapped in a syringe. The pressure on the gas will then be increased by weights (books) on top of the plunger of the syringe. The total pressure acting on the gas consists of the weight of the books plus the weight of the atmosphere.
TOTAL PRESSURE = PRESSURE DUE TO BOOKS + PRESSURE DUE TO ATMOSPHERE

- The volume of the gas will be recorded for each of the pressures used. The data (values of pressure and volume) will be plotted on the graph in several ways in order to find a simple mathematical relationship between pressure and volume.
**MATERIALS NEEDED:**Ring stand 35 ml plastic syringe Utility clamp *Large rubber stopper 7-textbooks

(identical)**PRE-LAB PREP:*** Using the proper size cork-boring tool, bore a hole approximately 1 / 2 the length of the nipple on the syringe, into the small end of the large rubber stopper.

**PROCEDURE:**1. Set the plunger at the

**35.0 mL mark**of a dry syringe. Place the tip of the syringe into the rubber stopper. Clamp the syringe-stopper arrangement in an upright position, as shown in the drawing. Be sure not to tighten the clamp to tightly or the syringe will bind and your data will be affected.2. Carefully center a textbook on top of the plunger. One person will steady the books while the other reads the volumes. Read as precisely as possible the volume of gas trapped in the syringe when a load of one book is on the plunger. Record the volume of gas in milliliters, for one book (trial 1), in your

**DATA TABLE 1**.3. Now add another textbook and carefully determine the volume. Continue in this manner until a pressure of 6 or 7 books is obtained. Record your data in

**DATA TABLE 1**for**trial 1**. It is important to keep the books centered over the plunger so the apparatus does not tip.DO NOT WORRY IF THE SYRINGE DOES NOT RETURN TO THE ORIGINAL VOLUME WHEN THE BOOKS ARE REMOVED. THIS IS NOT DUE TO AIR LOSS, BUT TO FRICTION BETWEEN THE PLUNGER AND THE SYRINGE. DO NOT ATTEMPT TO CORRECT FOR IT.

4. repeat steps 1 through 3 two more times, and record your data in

**DATA TABLE 1**, for trials 2 and 3.**BE SURE TO REMOVE THE SYRINGE FROM THE CORK BETWEEN EACH TRIAL AND REFILL THE SYRINGE. THEN POSITION THE SYRINGE AS BEFORE**.**CALCULATIONS AND RESULTS:****Graphical relationships between pressure and volume.** - Review the procedure for drawing the
**best line of fit**.5. From the data in table one, calculate the

**AVERAGE**gas volume associated with each pressure in books. Record these average values in the appropriate column in**DATA TABLE 2**.6.

**On graph number one**, plot the pressure (in books) on the vertical (**Y**) axis and the average volume (in mL) on the horizontal (**X**) axis. Fit the best**smooth curve**line to your points.7. Find the

**reciprocal**of volume (**1/V**) for each of the values of average volume. Record your answers in**DATA TABLE 2**.8.

**On graph number two**, plot the pressure (in books) on the vertical (**Y**) axis. Put**y=0**up the graph high enough so that you will have enough room below it for at least**y= -4**. Plot the reciprocal (1/V) on the horizontal (**X**) axis. Be sure to start with**x=0**at the origin. Fit the best Straight line to your points. Be sure to use a straight edge, and extend your line to the "**Y**" axis.**Mathematical relationship between pressure and volume.** - The plot of graph 2 shows a straight-line relationship between pressure (in books) and 1/V. However, this line does not pass through the origin of the graph. How can this be? Surely a gas under zero pressure should occupy an infinite volume. The value of 1/V should be zero when no pressure is being exerted on the gas. The answer, of course, is that in addition to "book pressure", atmospheric pressure is also pushing on the gas.
9. Determine the value for atmospheric pressure in the following manner: Extend the pressure scale (in books) downward as far as is necessary to read the value of the

**Y-intercept**. The difference between the y-intercept and y=0 is the value for the atmospheric pressure (in books) pushing on the gas in addition to the "book pressure" that you measured.**Record the value of the atmospheric pressure in DATA TABLE 2**. This will be the same for each book line so simply repeat it 7 times in the table. DO NOT WORRY THAT THE VALUE FOR ATMOSPHERIC PRESSURE APPEARS TO HAVE A NEGATIVE SIGN. THIS SIMPLY SHOWS A RELATIONSHIP AND THE NEGATIVE SIGN NEEDS TO BE IGNORED.10. Find the mathematical relationship between pressure and volume in the following manner:

- Calculate the value for the
**TOTAL**pressure for each pressure in books that you have recorded. This is done by adding atmospheric pressure to each "book pressure". Enter these values in**DATA TABLE 2**.

- Find the product of pressure and volume by multiplying the
**TOTAL**pressure by the**AVERAGE**volume the gas occupied under that pressure. Use the correct number of significant figures. Record your answers in**DATA TABLE 2**, as**Total P x V**.**DATA TABLE 1:**Pressure and volume data.VOLUME OF GAS (mL) PRESSURE (books) TRIAL 1 TRIAL 2 TRIAL 3

1

2

3

4

5

6

7

**DATA TABLE 2:**Calculations for pressure (**P**) and volume (**V**).Graphical relationship between P and V Mathematical relationship between P and V

P

(books)

Average V

(mL)

Average

1/VP due to

Atmosphere

(books)

Total P

(books)

Total P x V

(books x mL)

1

2

3

4

5

6

7

11. What relationship is there between the mathematical products of**total pressure multiplied by volume**obtained in the last calculations?

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**SUGGESTIONS FOR FURTHER STUDY:**1. Repeat the experiment with a

**65 mL**syringe.2. You used air for your gas sample, which is a mixture of mostly nitrogen and oxygen. Repeat the experiment with a pure gas sample.

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GAS PRESSURE AND GAS VOLUME

**INTRODUCTION:**