Apply Boyle S Law PV = K and P1V1 = P2V2

Boyle’s Law

Objectives

Determine the effect of volume on the pressure of a closed system containing a fixed amount of molecules at a constant temperature. Through this investigation students will

 Show that an inverse relationship exists between pressure and volume for a gas at a constant temperature.

 Apply Boyle’s law PV = k and P1V1 = P2V2.

 Differentiate between real and ideal gases.

Materials and Equipment For each student or group:

 data collection system  rubber tubing1, 1.5cm long  absolute pressure sensor  quick-release connector1  syringe1, 20mL  glycerin2, 2 drops

Background

The kinetic molecular theory explains that the particles in all forms of matter are in constant motion. In solids and liquids, the atoms or molecules are moving and are positioned very close to each other. In gases, the atoms or molecules are also moving, but they are positioned very far apart from each other and thus have properties very different from those of solids or liquids.

The kinetic molecular theory of gases makes a few basic assumptions. First, it assumes that gases are made up of small, hard particles that are very far apart from each other. Because the particles are so far apart, their volume is considered insignificant and there are no attractive or repulsive forces between the gas particles. The large amount of empty space between the gas particles explains why gases, unlike solids or liquids, are compressible. The lack of attractive or repulsive forces explains that gas particles take the shape and volume of containers they occupy.

The second assumption is that gas particles are in constant, random motion. The gas particles move independently from one another in straight lines and only change direction when they collide with other particles or the walls of a container. Gas pressure is related to how often and how hard gas molecules collide into surfaces.

The third, and final, assumption is that the collisions between gas particles are elastic. This means that no energy is lost when particles collide. The total kinetic energy remains the same before and after collisions. A gas that behaves according to all of the assumptions is called an ideal gas. Although there is no such thing as an ideal gas, at many conditions of temperature and pressure real gases behave ideally.

There are four variables that are used to describe a gas. These variables are volume (V), pressure (P), temperature (T) and number of moles (n).

Robert Boyle discovered the mathematical relationship between gas pressure and volume. Boyle’s law states that for a given number of gas molecules at constant temperature, the volume of the gas varies inversely with pressure. Because it is an inverse relationship, the product of the pressure (P) and volume (V) is constant (k); as one variable increases, the other must decrease. Boyle’s law can be represented by the following two equations:

1) PV = k

2) P1V1 = P2V2

When a given number of gas molecules at constant temperature are forced into a smaller volume the pressure will increase. The increase in pressure is due to an increase in collisions between the gas particles and the container. The number of collisions increases because it takes less time for the particles to travel across a smaller space.

Boyle’s law, like all the gas laws, holds true only for ideal gases. At higher pressures and lower volumes real gases behave less ideally and therefore do not follow Boyle’s law as well. This is because the assumption that gas particles are so far apart that their volume is considered insignificant no longer holds true. The closer the atoms are forced together, the more important their volume becomes. As the gas molecules become even closer, attractive forces also begin to take effect. This is what enables gases to condense into liquids.

Lab Safety

 Follow all standard laboratory safety procedures.

 Avoid over-compressing the air in the syringe in order to minimize the risk of injury or damage to the equipment.

Sequencing Challenge

Procedure with Guided Inquiry

Calculate the average pressure at Connect the each volume and While viewing a Record the absolute absolute pressure use the calculated Collect two data table display, pressure at 20mL, senor to the data averages to draw additional runs of connect a syringe 18mL, 16mL, collection system conclusions about absolute pressure with 20mL of air to 12mL, and set up manual the relationship data at each the absolute 10mL, 8mL, and sampling. between pressure volume. pressure sensor. and volume. 6mL.

After you complete a step (or answer a question), place a check mark in the box () next to that step.

Collect Data 8.  Make sure your data collection system is in manual mode and you are viewing the table display. Start a new data set.

9.  Set syringe volume to 20mL and record the pressure in the column labeled “run 1” in the table below.

10.  Repeat step 9, but set the syringe volumes to 18mL, 16mL, 14mL, 12mL, 10mL, 8mL, and 6mL.

Data Table

Volume Pressure (kPa)

run 1 run 2 run3

11.  Stop the data collection.

12.  Remove the syringe from the absolute pressure sensor using the quick-release connector. Set the syringe plunger to 20mL and re-connect the syringe to the absolute pressure sensor. Start a new data set and record the pressure at each of the indicated volumes in the next run column in the table above.

13.  Stop the data set. Repeat step 12 so that you have three sets of collected data.

14.  Explain when and why it becomes difficult to depress the syringe.

______

15. Why is it important to collect more than one set of data?

______

16.  Save your data file and clean up your lab station according to the teacher’s instructions.

Data Analysis

Note to Editor: Erase the teacher tips in the student versions.

1. Calculate the average pressure for each volume. Use the average pressure to calculate the constant “k” for each run of data (PV=k). Use the table below to show your work.

Volume × Pressure = k V P P P ▬ ▬ Run Run Run P V×P= k 1 2 3 (Average) (kPa•mL) (kPa) (kPa) (kPa) (kPa)

2. What is the average value of “k” for all volumes? 3. Graph average pressure versus volume.

This graph should be titled average pressure versus volume. The x-axis should be labeled volume (mL) and the y-axis should be labeled average pressure (kPa).

4. What does this graph tell you?

Analysis Questions

1. Are pressure and volume directly proportional or inversely proportional? How do you know?

2. Does your data support Boyle’s law that PV = k (pressure × volume = constant)? Explain any discrepancies in your data.

3. What region of the pressure versus volume graph does air behave like an ideal gas? Like a real gas? What is the difference between an ideal and a real gas?

4. What is the constant (k) for air? (hint: look at question #2 above)

5. Calculate the pressure you would expect at 15.0 mL. Show your work.

Synthesis Questions

1. Explain why it is possible to write Boyle’s law as both PV = k and P1V1 = P2V2.

2. How could you change the experimental design to get results more consistent with an ideal gas?

3. A helium balloon is released into the atmosphere. As it rises, atmospheric pressure decreases. What do you expect will happen to the volume of the balloon?

4. A cylinder containing 250 mL of a gas has a pressure of 350 kPa. If the gas was compressed to a volume of 45 mL what would the pressure change to?

Multiple Choice Questions

Select the best answer or completion to each of the questions or incomplete statements below.

1. What conditions will cause the volume of a gas to decrease?

A. An increase in the amount of gas. B. An increase in temperature. C. An increase in pressure. D. A decrease in pressure.

2. At constant temperature the relationship between the volume (V) of a gas and its pressure (P) is

A. V= (constant)P. B. P = (constant)V. C. PV = constant D. V/P = constant

3. Which graph shows the relationship between the pressure and volume of nitrogen gas at a constant temperature?

4. At room temperature, air behaves like an ideal gas at

A. low pressures B. high pressures C. all pressures D. air never behaves ideally

5. A gas contained in a 3.0 L cylinder has a pressure of 120 kPa. What will the new volume be if the pressure is increased to 240 kPa?

A. 1.5 L B. 3.0 L C. 4.5 L D. 6.0 L

Key Term Challenge

Fill in the blanks from the list of randomly ordered words in the Key Term Challenge Answers section.

Gases are able to be ______into smaller volumes because there is ______space between gas particles. Solids and liquid, on the other hand, have fixed ______and cannot be compressed. When a fixed amount of gas is forced into a smaller volume the pressure of the gas will ______. This happens because volume is ______proportional to pressure. This relationship is known as ______law. An ideal gas is composed of a collection of perfectly hard ______that are so far apart that their ______is assumed to be insignificant. The gas particles move in constant ______motion and only change direction when they ______with another particle or the walls of the container. The collision of gas particles with a surface creates ______. Real gases can behave ideally at certain temperatures and pressures. However, real gases are not ideal because they actually do have volume. Their volume cannot be considered insignificant at ______pressures.

Key Term Challenge Word Bank Paragraph 1 Paragraph 2 a lot of high very little low Boyle’s spheres Avogadro’s pressure volumes volume increase temperature decrease ordered indirectly random directly collide compressed