11: LAB 11 - BOYLE’S LAW [Pressure-Volume Relationship in Gases]
- Page ID
- 506219
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The purpose of this experiment is to:
- A gas pressure sensor and a gas syringe measure the pressure of an air sample at several different volumes.
- Determine the relationship between pressure and volume of the gas.
- Describe the relationship between gas pressure and volume in a mathematical equation.
- Use the results to predict the pressure at other volumes.
INTRODUCTION
British scientist Robert Boyle, in 1662, found that the pressure of a gas is inversely proportional to its volume, provided the number of moles of gas and the temperature remain constant. Mathematically, Boyle's law can be stated as:
P \(\propto\) 1/V Pressure is inversely proportional to the volume
Or
PV = k Pressure multiplied by volume equals some constant k
Where P is the pressure of the gas, V is the volume of the gas, and k is a constant.
Boyle's Law states that the product of pressure and volume is constant when the number of moles and temperature of a gas are held constant.
When comparing the same gas under two different sets of conditions of volume and pressure at constant temperature and number of moles, Boyle's law can also be expressed as:
P1V1 = P2V2
P1 and P2 are the initial changes in gas pressure at volumes V1 and V2, respectively.
The gas pressure can be expressed in different units, such as Atmospheres (atm), Millimeters of mercury (mm Hg), Torr, and Pascals. The standard unit of pressure is the atmosphere, and the SI unit is the pascal (Pa). A pascal is defined as a pressure of one newton per square meter. This unit is inconveniently small for many purposes, and kilopascal (kPa) is more commonly used.
1 atm = 760 mm Hg = 760 Torr = 101325 Pa = 101.3 kpa.
The volume of a gas can also be expressed in various units, such as liters (L), milliliters (mL), cubic meters (m³), and cubic centimeters (cm³).
In this experiment, you will measure the pressure of a sample of air at several different volumes. You will also graph pressure versus the reciprocal of volume (1/V) to demonstrate that pressure is inversely proportional to the volume of a gas. This indicates that as the volume increases, gas pressure decreases proportionally, and vice versa.
Figure 1: Syringe connected to the Vernier gas pressure sensor.
The primary objective of this experiment is to determine the relationship between the pressure and volume of a confined gas. We will use air confined to a syringe connected to a Gas Pressure Sensor.
When the volume of the syringe is changed by moving the piston, a change occurs in the pressure exerted by the confined gas. This pressure change will be monitored using a Gas Pressure Sensor. It is assumed that the temperature will be constant throughout the experiment. Pressure and volume data pairs will be collected and analyzed during this experiment. From the data and graph, you should be able to determine the mathematical relationship between the pressure and volume of the confined gas.
EQUIPMENT AND CHEMICALS NEEDED
Lab Quest interface or Vernier Computer interface with the Logger Pro software
Gas Pressure Sensor
20 mL gas syringe
* Images of equipment needed in this lab are in the appendix (the equipment may differ slightly or be subject to changes; follow your instructor’s directions).
1. Regular safety precautions, including wearing safety goggles and following proper lab procedures.
2. Be sure all equipment is returned to its proper place.
3. Clean the lab benches and check the laminated sheets to ensure all equipment is in your lab drawer before leaving.
4. Wash your hands once you leave the lab.
This lab experiment is adapted from Vernier and uses Logger Pro software, the LabQuest interface, and the Vernier gas pressure sensor.
EXPERIMENTAL PROCEDURE
1. Prepare the Gas Pressure Sensor and an air sample for data collection.
a. Obtain a LabQuest interface and turn it on by pressing the power button. The device opens on the LabQuest App screen.
b. Connect the Gas Pressure Sensor to it and choose New from the file menu.
c. Take the 20.0 mL syringe (not yet connected to the Gas Pressure Sensor and move the syringe's piston until the front edge of the inside black ring (indicated by the arrow in Figure 2) is positioned at the 10.0 mL mark.
d. Attach the 20.0 mL syringe to the valve of the Gas Pressure Sensor.
Figure 2: Syringe connected to the vernier gas pressure sensor, with an arrow pointing to 10.0 mL.
2. Set up the data-collection mode.
a. On the Meter screen, tap Mode. Change the mode to Events with Entry.
b. Enter the Name (Volume) and Units (mL). Select OK.
3. To obtain the best data possible, you must correct the volume readings from the syringe. Look at the syringe; its scale reports its internal volume. However, that volume is not the total volume of trapped air in your system, as there is a small space inside the pressure sensor.
To account for the extra volume in the system, you must add 0.8 mL to your syringe readings. For example, with a 5.0 mL syringe volume, the total volume would be 5.8 mL. You will need this total volume for the analysis.
4. You are now ready to collect pressure and volume data. It is easiest if one person handles the gas syringe and another enters the volumes.
a. Start data collection by clicking the green arrow.
b. Move the piston so the front edge of the inside black ring (see Figure 3) is positioned at the 5.0 mL line on the syringe. Hold the piston firmly in this position until the pressure value displayed on the screen stabilizes.
c. When the pressure reading has stabilized, click Keep. (The person holding the syringe can relax after Keep is clicked.) Type in the total gas volume (in this case, 5.8 mL) in the edit box. Remember, you are adding 0.8 mL to the syringe's total volume. Select OK to store this pressure-volume data pair.
Figure 3: Syringe connected to the Vernier gas pressure sensor, with an arrow pointing to 5.0 mL.
d. Move the piston to the 7.0 mL line. When the pressure reading has stabilized, click "Keep" and enter the total volume, 7.8 mL.
e. Continue this procedure using 10.0, 12.5, 15.0, 17.5, and 20.0 mL syringe volumes. Remember to add 0.8 mL to each syringe volume and enter the total volumes only.
f. Click the stop when you have finished collecting data.
5. When data collection is complete, a graph of pressure vs. volume will be displayed. Tap any data point to examine the data pairs displayed in the graph. As you tap each data point, the pressure and volume values are displayed to the right of the graph. Record the pressure and volume data values in your data table.
6. Based on the graph of pressure vs. volume, decide what kind of mathematical relationship exists between these two variables, direct or inverse. To see if you made the right choice:
a. Choose Curve Fit from the Analyze menu.
b. Select Power as the Fit Equation. The curve fit statistics for these two data columns are displayed as an equation.
y = Ax^B
where x is volume, y is pressure, A is a proportionality constant, and B is the exponent of x (volume). Note: The relationship between pressure and volume can be determined from the value and sign of the exponent, B.
c. If you have correctly determined the mathematical relationship, the regression line should nearly fit the points on the graph (that is, pass through or near the plotted points).
d. Select OK.
7. Once you have confirmed that the graph represents either a direct or inverse relationship, email or print a copy of the graph, with the graph of pressure vs. volume and its best-fit curve displayed, to include in your lab report.
8. A graph of pressure vs. the reciprocal of volume (1/volume) may also be plotted to confirm an inverse relationship between pressure and volume. To do this, it is necessary to create a new column of data, reciprocal of volume, based on your original volume data:
a. Tap the Table tab to display the data table.
b. Choose New Calculated Column from the Table menu.
c. Enter the Name (1/Volume) and Units (1/mL). Select the equation, A/X. Use Volume as the Column for X, and one as the value for A. Select OK.
9. Follow this procedure to calculate regression statistics and to plot a best-fit regression line on your graph of pressure vs. 1/volume:
a. Choose Graph Options from the Graph menu.
b. Select Auto scale from 0 and select OK.
c. Choose Curve Fit from the Analyze menu.
d. Select Linear as the Fit Equation. The linear-regression statistics for these two data columns are displayed in the form: y = mx + b
where x is 1/volume, y is pressure, m is a proportionality constant, and b is the y-intercept.
e. Select OK. If the relationship between P and V is inverse, the graph of pressure vs. 1/volume should be direct; that is, the curve should be linear and pass through (or near) the origin. Examine your graph to see if this is true for your data. Print or email a copy of the graph to your lab report.
10. Go to graph one or run one and proceed directly to the Processing the Data section with the displayed best-fit curve.
PRE-LAB QUESTIONS
Name: ___________________
- State Boyle’s Law and state the relationship between Pressure and Volume of a gas at constant temperature and moles of gas.
- Students, while conducting Boyle’s law experiment, measure that a gas syringe at STP (Standard Temperature and Pressure ≡ 1.0 atm; 273 K) has a volume of 20.0 ml if they push the plunger to 10.0 ml, what would be the pressure exerted by the air in the syringe (no change in the amount of air trapped in the syringe and the temperature)(Show your work)
- Convert the following: (Show your work)
a) 0.85 atm = _______________ kPa
b) 650 mmHg = _______________ atm = _______________ torr = _______________ kpa
c) 0.250 L =_______________mL = _______________ cm3
DATA, OBSERVATIONS, AND CALCULATIONS
Name _____________________ Lab Partner(s) __________________________
Volume (mL) |
Pressure (kPa) |
Constant, k
|
|---|---|---|
* One way to determine if a relationship between pressure, P, and volume, V, is inverse or direct is to find a proportionality constant, k, from the data. If this relationship is direct, k = P/V. If it is inverse, k = P•V.
The report should include two graphs, P vs V and P vs 1/V, along with the above data, calculations, and data analysis questions below.
DATA ANALYSIS AND POST-LAB QUESTIONS
- With the best-fit curve still displayed on graph one or run one graph, choose Interpolate from the Analyze menu. A vertical cursor now appears on the graph. The cursor’s volume and pressure coordinates are displayed in the floating box. Move the cursor along the regression line until the volume value is 5.0 mL. Note the corresponding pressure value. Move the cursor until the volume value is doubled (10.0 mL). What does your data show happened to the pressure when the volume is doubled? Mention the actual pressure values in your answer.
- Using the same technique as in Question 1, what does your data show happens to the pressure if the volume is halved from 20.0 mL to 10.0 mL? Mention the actual pressure values in your answer.
- Using the same technique as in Question 1, what does your data show happens to the pressure if the volume is tripled from 5.0 mL to 15.0 mL? Mention the actual pressure values in your answer.
- From your answers to the first three questions and the shape of the curve in the plot of pressure vs. volume, do you think the relationship between the pressure and volume of a confined gas is direct or inverse? Explain your answer.
- Based on your data, what would you expect the pressure to be if the syringe volume were increased to 40.0 mL? Explain or show work to support your answer.
- Based on your data, what would you expect the pressure to be if the syringe volume were decreased to 2.5 mL? Explain or show work to support your answer.
- What experimental factors are assumed to be constant in this experiment?
- One way to determine if a relationship is inverse or direct is to find a proportionality constant, k, from the data. If this relationship is direct, k = P/V. If it is inverse, k = P•V. Based on your answer to Question 4, choose one of these formulas and calculate k for the seven ordered pairs in your data table (divide or multiply the P and V values). Mention which relationship you are using and show the answers in the third column of the Data and Calculations table.
- How constant were the values for k that you obtained in Question 8? Good data may show some minor variation, but the values for k should be relatively constant.
- Write an equation representing Boyle's law using P, V, and k. Write a verbal statement that correctly expresses Boyle’s law.
Please click here to access the Pre-Lab, Data Tables, and Post-Lab in Word or PDF format. Complete them and upload according to your instructor's instructions.