Lab 8 Gas Laws and Kinetic Molecular Theory

Gas Lawsand Kinetic Molecular Theory

Introduction *

The behavior of ideal gases can be described by four parameters: the pressure (P), volume (V), temperature (T) and number of moles (n) of gas and how they are interrelated.   The Kinetic Molecular Model for an ideal gas describes the behavior of gas particles at the atomic/particle level based on a set of assumptions stated below.

• Particles of ideal gases are in continuous random motion.
• Gas particles move in straight lines, colliding frequently with one another and with the walls of the container.Pressure results from collisions between particles and the container walls.
• The volume of each particle is negligible compared with the large distance between gaseous particles. Particles of ideal gases are basically point masses occupying empty space.
• Particles do not exert forces on each other.No energy is lost by the collision; collisions areelastic.
• The average kinetic energy is proportional to temperature (K).Particles of all gases at the same temperature have the average kinetic energy.

In a gas sample, individual molecules have widely varying speeds; however, because of the vast number of molecules and collisions involved, the molecular speed distribution and average speed are constant. This molecular speed distribution is known as a Maxwell-Boltzmann distribution and it depicts the relative numbers of molecules in a bulk sample of gas that possesses a given speed.

In the kinetic molecular theory, the root mean square (RMS) velocity of a particle, u_rms, is defined as the square root of the average of the squares of the velocitieswith n = the number of particles:

The molecular speed distribution for oxygen gas at 300 K is shown on the right. Very few molecules move at either very low or very high speeds. The number of molecules with intermediate speeds increases rapidly up to a maximum, which is the most probable speed, then drops off rapidly. Note that the most probable speed, ν_p, is a little less than 400 m/s, while the root mean square speed, u_rms, is closer to 500 m/s.

In this lab, you will investigate the tow of gas laws, Charles’ lawand Graham’s Law of Effusion, using the computer simulation. You will determine the relationship in ideal gases between volume and temperature, and average speed and molar mass.

Procedure

Copy this in your web browser.  https://media.pearsoncmg.com/bc/bc_0media_chem/chem_sim/kmt/KMT.php

After going over Overview and Learning Outcomes, Click the tab “Experiment” and you will see this on the screen:

Choose “Run Demonstration” to learn how to use this virtual simulation. You will explore the relationship between pressure and temperature (Amonton’s Law) and kinetic molecular theory in the Demonstration.

Once you run through the demonstration, you will be led to run experiments.

You can toggle between macroscopic and submicroscopic views any time.

The main components of the macroscopic view in the simulation:

• Piston, glass container, and hotplate
• Controls to change the conditions of the experiment t(pressure, volume, temperature, and number of moles of the gas) and to record each change.
• Signify the responding variable by moving the Rspd button beside it. You then manipulate the controlling variables by sliding the slider bars.
• Ability to plot recorded data in graphical representations to view different relationships
• Ability to export the recorded data to CSV files for future reference.

Always record valueswhen you run an experiment to refer back to make observations, analyze data, make predictions, and answer questions.

Part I Charles’s Law (V and T)

You will study Charles’s Law with the default gas sample, 0.05 mole Helium.

• If you changed any values, click the Reset button to return to the default setting for the gas sample. Slide the Rspd button to make the responding variable Volume

2. Adjust the temperature to 400 K by moving the temperature slider. Click on the record button after the temperature is set.
3. Record six more temperature between 50K and 400K. Don’t forget to click on the Record button to each temperature.
4. There is now a list of seven value sets in the data table. Plot the data on the graph adjacent to the data table. The drop-down menus are set to Pressure of the y-axis and to Temperature for the x-axis (controlling variable). Switch the y –axis to Volume (responding variable). Click on Graph Data button.
5. Take a screen shot of the experiment, including both data table and graph. Submitted with your lab report.
6. Answer questions asked in the section of Discussion Part I.

Part II Graham’s Law (average speed and molar mass)

1. Click the Reset button to return to the default setting for the gas sample.
2. Now click the Submicroscopic tab to look inside the molecular container and the graph and observe the motion of the gas particles.
3. In the submicroscopic view, you will observe any changes in the behavior of the gas particles in the molecular container. You can also observe any changes in the velocity graph. For example, click on the Track button to observe an individual particle.
4. To select a different particle to track, click on the Pause button to pause the simulation. Now click on a different particle in the molecular container. Then click on the Resume button. If you do not want to track an individual particle, you can always click on the Untrack button. Based on your observations, answer questions asked in the section of Discussion Part II.
5. The default gas sample is 0.05 mole of Helium. Click the Untrack button if you tracted any gas particle. The room mean square (RMS) speed of gas molecules is displayed on the graph. Record the RMS speed of helium on Discussion®Part II→Table 1.
6. Adjust the mole of He with the slider bar and observe if any change occurs to the RMS speed. Then removing all helium by decreasing its mole to zero using the slider bar. And add 0.05 mole of neon into the container. Observe and record the RMS speed of neon on Discussion®Part II→Table 1.
7. Remove all neon by decreasing its mole to zero using the slider bar. And add 0.05 mole of argon into the container. Observe and record the RMS speed of argon on Discussion®Part II→Table 1.

Discussion:

Part I Charles’s Law (V and T)-Macroscopic View

1. In the experiment you preformed which variables are kept constant? Circle all that apply.

P, V, n, the substance, T

2. In the experiment you just preformed which of the following statements best describes the relationship between volume and temperature of a gas sample? Check all that apply.
3. The volume decreased as the temperature increased.
4. The volume increased as the temperature increased.
5. The volume remained constant as the temperature increased.
6. The volume is directly proportional to the temperature.
7. The volume is inversely proportional to the temperature.
8. Which of the following statements best describes the shape of the volume versus temperature graph?
9. A straight line with positive slope
10. A straight line with a negative slope
11. A curved line
12. Which of the following algebraic equations best represents the pattern of your data?
13. V=T
14. V=cT (where c is a constant)
15. V=cT^– (where c is a constant)
16. V=cT² (where c is a constant)
17. What is the best value for c in the equation selected in the previous question? Report your answers to two significant figures. _______ L /K
18. Calculate the volume exerted by the gas sample at 500.0 K to two significant figures.

_________ L

Part IIGraham’s Law (average speed and molar mass) – Submicroscopic View

Your observation

1. The speed of the particles is (circle one)
2. Constant b. Variable                 c. same
3. The particles move in a __________ between collisions.
4. straight –line b. curved path
5. The speed of the particles changes following the collision with ________
6. another particle
7. the wall of the container
8. both the wall of the container and another particle .

Use the Track function explained earlier to help answer this question.

4. Collisions between particles or the walls of the container are ________elastic or not elastic.
5. The particles _________ attractions to other particles.
6. experience b. don not experience
7. The RMS speed of helium is ____________ as the mole of helium changes.

                                a. constant                  b. variable

7. Record the RMS speeds of different gases in the following table.

8. 8. Is your observation of RMS speeds consistent the Graham’s law of effusion, which states that rates of gases are inversely proportional to the square roots of their molecular masses?

Show your calculations below.

 Post Lab Assignment

1. Upload your screen shot of the data tableand the graph of volume vs. temperature, andyour completed Discussion section to Canvas.