Expt 027 -- Charles' Law

The volume of gases varies with changes in the temperature.

A sample of gas is trapped in the bulb of a plastic transfer pipet using a drop of colored liquid placed in the pipet stem. The gas is then heated by immersing it in water baths of known temperature, and the length which the trapped liquid moves in the pipet stem is measured.

Background

• The accepted temperature at which the volume of an ideal gas would be zero is -273.15 ºC.
• A temperature scale that starts at this temperature but has the same degree-size interval as the Celsius scale is called the absolute scale or Kelvin scale, and the degree intervals are called kelvins.
• When temperatures are expressed using this scale, Charles' Law can be written as:

  V = kT + constant, or V₁/T₁ = V₂/T₂

• Suppose a gas were contained in a vessel that could changes its volume while maintaining a constant pressure, (A syringe is a container like this -- the plunger moves to maintain constant pressure by adjusting the volume.) If a gas has a volume of 246 mL at 25 ºC, find its volume at 50 ºC.

  V₂ = V₁ x [T₂/T₁] = 246 mL x [(50 + 273)/(25 + 273)]

  = 267 mL

• An extremely important skill is to be able to predict whether the volume will increase or decrease. When heated, the volume increases, so the cool volume will be multiplied by a ratio larger than one (larger than unity) to find the warm volume. It is better to get this sense of how values will change than to try to memorize many formulas.

Safety

• There are no special safety precautions to follow for this experiment. Wear goggles and apron. Follow routine safety precautions.
• If mercury thermometers are used and a thermometer breaks during the experiment, notify the instructor immediately.

Procedure

1. Place some ice and water in a beaker to prepare an ice bath. Prepare a second cool water bath with cold water.
2. Fill the pipet completely with water. Tare a small beaker. Add the water from the pipet to the beaker. Determine the mass of water. Using 1.00 g/cm³ as the density of water, determine the volume of the water (pipet). Fill the stem of the pipet completely with water. Tare a small beaker. Add the water from the pipet stem to the beaker. Determine the mass of water. Using 1.00 g/cm³ as the density of water, determine the volume of the water (pipet stem). Measure the length of the pipet stem from tip of the bulb to the exit end, and record this length.
3. Squeeze all of the water from the pipet. Use a 250-mL beaker
4. filled with water and ice as a bath. Immerse the bulb in the ice bath. Allow a few minutes for equilibrium to be reached. Measure and record the temperature of the ice bath.

   !!!Click here to See Picture.

5. Fill a standard transfer pipet with some colored water. Insert the stem of this pipet into the larger pipet stem and move it to the bottom of that stem. Squeeze enough water from that pipet to place about 1 cm of colored water in the larger stem with the bottom edge exactly at end of the curvature of the pipet bulb. Quickly move the pipet from the ice bath to the cool water bath. Allow the bulb to reach equilibrium.

   !!!Click here to See Movie.

6. Measure carefully the distance from the top of the bulb to the bottom of the colored liquid in the stem. Record the temperature and the length.

   !!!Click here to See Picture.

7. Add some warm water to raise the temperature of the bath a few degrees (6-8 ºC). Allow the bulb to reach equilibrium. Measure carefully the distance from the top of the bulb to the bottom of the colored liquid in the stem. Record the temperature and the length. Repeat for several temperatures until the colored liquid is near the exit end of the pipet stem.
8. Discard the colored liquid from the pipet into a sink.

Data Analysis

For each temperature, determine the volume of the gas. Plot the volume of the gas (mL) as a function of the Celsius temperature.

Either:

1. Use computer software to plot the data, draw a best line through the points, and determine the slope and intercept,
   • or
2. Plot the points on graph paper. Draw the best possible line through the points. From the graph, determine the y-intercept and measure the slope.

Determine absolute zero, the temperature at which the apparent volume of the 'ideal' gas would be zero.

Questions

1. Suggest ways in which this experiment might be improved.
2. The volume of an 'ideal' gas sample is 242 mL at 23 ºC. Predict the volume of this gas at 0 ºC.
3. A balloon filled with air at room temperature is place on dry ice. Predict any changes that will be observed, and justify that prediction.

Handout Makeup

Name ___________________________ Class ________

Teacher__________________________

SmallScale 027 Charles' Law

Watch the movies. Use the sample data to answer the questions.

• length of stem = 68 mm
• mass filled pipet = 4.533 g
• mass water in stem = 0.692 g

For each temperature, determine the volume of the gas. Plot the volume of the gas (mL) as a function of the Celsius temperature. See the data analysis section for more details. Attach your graph.

Curriculum-

Use this experiment when discussing gas laws and the properties of gases.

Safety-

• There are no special safety precautions to follow for this experiment. Wear goggles and apron. Follow routine safety precautions.
• If mercury thermometers are used, have a commercial mercury spill clean-up kit available in case a thermometer breaks.

Time-

Teacher Preparation: 20 minutes

Class Time: 50 minutes

Materials-

• food coloring
• water
• ice
• Add food coloring to the water.
• large stem plastic transfer pipet with constricted tip cut off
• standard plastic transfer pipet
• thermometer (prefer alcohol or metal thermometer; possible mercury spill kit)
• plastic ruler calibrated in millimeters
• 250-mL beaker
• 50-mL beaker
• balance

Lab Hints-

• The results from the experiment are not very good in terms of the extrapolated value for absolute zero. However, the simplicity of the apparatus makes clear the connection from Charles' Law: there is a relation between gas volume and temperature. Heated gases expand; cooled gases contract.
• The instructor may not want to have students calibrate the pipets. If not, the teacher can calibrate several pipets, average the results, and give the students a general equation for calculating volume from length. One such equation is:

  volume (mL) = 3.841 + [0.0102 x length (mm)]

Disposal-

Dispose of liquids at the sinks. Recycle plastics, or store them for reuse in later classes.

Data Table-

• length of stem = 68 mm
• mass filled pipet = 4.533 g
• mass water in stem = 0.692 g

Data Analysis-

• Record the mass of water in the stem, 0.692
• Determine the mass of water in the bulb = 4.533 - 0.692 = 3.841
• Determine the mass of water per mm of stem length =

  0.692 g/68 mm = 0.0102 g/mm

• Write a volume equation based upon length:

  Volume gas = 3.841 + (0.0102 x length)

Convert the lengths of gas into total volumes:

Temp (ºC)	Length (mm)	Volume (mL)
3	0	3.84
15	17	4.01
20	23	4.08
24.5	33	4.18
32	48	4.33
34	55	4.40

For the graph see below.

• These data were plotted using a graphing program (DeltaGraph^® Professional), and the line fit as follows:

  volume = 0.01665 x temperature + 3.773

• Solving for the temperature when the apparent volume is zero (the absolute zero), temperature = -3.773/0.01665 = -227
• This value for absolute zero is too high by over 40 ºC.

Answers-

Q1. Suggest ways in which this experiment might be improved.

A1. Use a more sensitive thermometer. Immerse the entire bulb in the temperature bath. Insulate the temperature bath (say by using Styrofoam cups).

Q2. The volume of an 'ideal' gas sample is 242 mL at 23 ºC. Predict the volume of this gas at 0 ºC.

A2. Vº = 242 mL x [(0 + 273)/(23 + 273)] = 223 mL

Q3. A balloon filled with air at room temperature is place on dry ice. Predict any changes that will be observed, and justify that prediction.

A3. A balloon does not have constant volume. Cooling the gas inside a balloon will cause the volume to decrease.

Computer Use-

This is an excellent experiment for analysis using a graphing program.

CoopLearn-

• This experiment can make good use of three workers in a team: a length reader, a temperature reader, and a recorder. The experiment is quick, but these tasks turn out to be fairly independent.
• The best analysis of errors comes from a pooling of class results based upon individual group's data sets.

Reference-

This experiment follows one developed by Robert Curtright and Dianne Epp and published in Chem 13 News, October 1992, Number 215.

Key Words 1-

gases, Charles' law, temperature, volume, graphical analysis, balance