7.2: Lab - The Gas Laws
- Page ID
- 438411
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Equipment and Materials
Prepare 12 sets of equipment and materials for 24 students per class section. Include a few more for backup if needed. Each set should include
Equipment
- 12 Laptops with Logger Pro software installed
- 12 Vernier pressure sensors
- 12 Syringes with tube that can be connected to Vernier pressure sensors
- 12 Plastic bin (e.g. Sterilite 8 Qt or larger)
Materials
- Vinegar: 2 bottles of one-gallon vinegar
- Sodium bicarbonate: 12 packs of 8 oz baking soda (Arm & Hammer). An option is to place these in glass vials with lids.
- 6 boxes of 90-count snack-sized Ziploc bags
- Recognize the different gas laws such as Boyle’s law, Charles’s law and Avogadro’s laws.
- Determine the effect of pressure on volume of a gas.
- Determine the effect of temperature on volume of a gas.
- Determine the effect of amount (moles) on volume of a gas.
Laboratory Skill
- Practice using LabQuest gas pressure sensor.
- Practice measurements using electronic balance and graduated cylinder.
- Practice plotting graphs with given data sets.
Equipment and Materials
- Laptops with Logger Pro software installed
- Gas pressure sensors
- Funnel
- Scoopula
- 100-mL graduated cylinder
- Snack size Zipper or Ziploc bags
- 250-mL beaker
- Weigh boats
- Plastic bin (e.g. Sterilite 8 Qt)
- Vinegar
- Sodium bicarbonate powder
Safety and Hazard Information
- Wear gloves and safety goggles, except recommended by the instructor.
Background Information
Do you know that we are all submerged in a gigantic volume of mixed gases, just like aquatic life is submerged in a gigantic volume of ocean waters? It is important for us to understand the significance of the gases that surround us in our daily living. A person that drowns does so because of lack of air, particularly oxygen that is essential for life. Oxygen is a gas that is needed for essential reactions occurring in our body cells. Understanding the behavior of gases helps us understand the process through which oxygen in air finds its way into the lungs, and eventually into cells where it is needed. In general, the behavior of gases can be described using simple quantitative relationships called gas laws. Gas laws involve variables such as pressure (\(P\)), volume (\(V\)), temperature (\(T\)), and amount (\(n\)). Boyle’s law, Charles’s law, and Avogadro’s law are some of the gas laws that we will cover in this experiment.
Boyle’s Law
Boyle’s law states that when the pressure of a fixed amount of gas increases, its volume decreases provided temperature remains unchanged. This is an inverse relationship between pressure and volume because when one variable increases the other decreases.
Mathematically, Boyle’s law is stated as
\[ P_1V_1 = P_2V_2 \label{1}\]
where \(P_1\) and \(V_1\) are the pressure and volume of a gas, respectively at a given initial set of conditions, while \(P_2\) and \(V_2\) are the pressure and volume of the same gas under a new final set of conditions.
Oxygen in air is made available to the cells through the process of breathing and diffusion. In the process of breathing (see Figure \(\PageIndex{1}\)), the diaphragm which is a dome-shaped structure located below the lungs contracts and flattens out. Simultaneously, the rib muscles contract pulling the ribs upwards. These contractions cause the rib cage (thoracic cavity) to expand resulting in its pressure dropping below the outside atmospheric pressure – a representation of Boyle’s law! To counter the pressure drop, air from outside flows into the thoracic cavity. The movement of outside air into the thoracic cavity or lungs is called inhalation. When the diaphragm relaxes its contraction, it returns to its dome-shape by pushing up into the thoracic cavity. Simultaneously, the rib muscles relax allowing the ribs to move down. These relaxations of the diaphragm and rib muscles cause the rib cage (thoracic cavity) to contract resulting in its pressure rising above the outside atmospheric pressure – another representation of Boyle’s law! To relieve the pressure increase, air from the thoracic cavity flows out into the atmosphere. The movement of air from the lungs or thoracic cavity to the outside is called exhalation.
Charles’s Law
Usually when substances are heated or cooled they expand or contract, respectively. Solids and liquids show very minimal expansion and contraction when heated or cooled. However, heating and cooling of gases are usually accompanied by dramatic changes (either in pressure or in volume). According to Charles’s Law, the volume and absolute temperature of a given amount of gas are directly proportional provided pressure remains constant. This means that as the Kelvin temperature of a gas increases, its volume increases.
Mathematically, Charles’s law is stated as
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2}\]
where \(V_1\) and \(T_1\) are the initial volume and temperature and \(V_2\) and \(T_2\) are the final volume and temperature of gas, respectively.
Avogadro’s Law
At constant temperature and pressure, the moles of a gas are directly proportional to volume. This is Avogadro’s law, which can be stated mathematically as
\[ \frac{V_1}{n_1} = \frac{V_2}{n_2}\]
where \(V_1\) and \(n_1\) are the initial volume and moles of gas and \(V_2\) and \(n_2\) are the final volume and moles of gas, respectively.
In this experiment, we will use a gas pressure sensor hooked up to a LabQuest Vernier or a laptop running Logger Pro software to monitor the effect of pressure on volume, similar to the effect of pressure on volume during breathing in and breathing out.
We will use a PhET simulation to collect and plot temperature-volume data to show how volume varies with temperature.
In this experiment, we will also investigate how the volume of a gas changes with the amount of gas. This will be conducted through a chemical reaction that results in a gas evolution. The reaction of sodium bicarbonate, a base, and acetic acid (a weak acid present in vinegar) results in the generation of carbon dioxide gas, water, and a salt. The equation for the reaction is
\[\ce{CH3COOH} (aq) + \ce{NaHCO3} (s) \rightarrow \ce{CH3COONa} (aq) + \ce{H2O} (l) + \ce{CO2} (g) \nonumber\]
In this reaction, we can generate more carbon dioxide gas by using more reactants, or less carbon dioxide gas by using less reactants. We will use one of the reactants in excess (acetic acid, \(\ce{CH3COOH}\)) and vary limiting amounts of the other reactant (\(\ce{NaHCO3}\)). This will generate varying amounts of gas (\(\ce{CO2}\)), which will be trapped in a plastic bag.
Special Instructions (if any)
N/A
Procedure
Part \(\PageIndex{1}\): Investigation of \(P\) & \(V\) using Vernier Gas Pressure Sensor
a. Turn on a laptop and connect a LabQuest gas pressure sensor to it using the Go! Link adapter. There should be a real-time reading of the pressure shown on the computer screen.
b. Set the initial volume to 20.0 mL to get a volume of air in the syringe. Then attach the syringe to the gas pressure sensor.
c. Record the initial pressure in atmospheres. If the gas pressure sensor does not read units of pressure in atmospheres (atm), then go to Experiment/Change Units/Go!Link/ and select atm.
d. Now, you will collect four ordered pairs of volume (mL) and pressure (atm) beginning with a volume of 20.0 mL. Record your data in Table \(\PageIndex{1}\) under experimental report. Continue to change the volume on the syringe and for each change, the new volume and corresponding pressure should also be recorded in Table \(\PageIndex{1}\).
e. Generate an Excel plot of Table \(\PageIndex{1}\) data. Place volume (mL) on the \(x\)-axis and pressure (atm) on the \(y\)-axis. Label the axes (including units).
f. Answer the questions that follow in this part.
Part \(\PageIndex{2}\): Investigation of \(T\) & \(V\) using PhET Simulation
Using the PhET simulation link provided, record temperature (K) and volume data on the table in part \(\PageIndex{2}\) of the report sheet, then plot the data set in the graph provided or using excel.
a. Launch simulation by clicking on the above link and clicking on Laws. Check the Width radio button on the displayed menu to display the width of the gas chamber in nm. For the purpose of this experiment, width = volume in that your adjustment of the width (nm) of the chamber will directly correlate with the volume of the chamber.
b. Click and move handle on gas changer all the way to the right until the volume (width) displays 5.0 nm.
c. Click and move the gas pump all the way up & down to deliver 3 full puffs of gas molecules into the chamber. This should display an initial pressure of approximately 35.0 atm, initial volume (width) of 5.0 nm, and an initial temperature of 300 K. Record the initial volume and temperature on Table \(\PageIndex{2}\) of the experimental report.
d. Hold pressure constant by clicking on the corresponding pressure radio button with \(V\) next to it. (Note: the handle of gas chamber should disappear.)
e. To heat the gas, click and move slide towards heat on the bucket at the bottom of the screen. The volume should change with heating/cooling. It is important to let the system equilibrate to the new condition before recording the final temperature.
f. Heat incrementally and record each volume and its corresponding temperature. Continue until you have recorded at least 5 readings of coordinated volume and temperature. Be careful because there is a limit to applying temperature to be cooled; you will receive an error message in this scenario.
g. Generate an excel plot of Table \(\PageIndex{2}\) data. Place temperature (K) on the \(x\)-axis and volume (nm) on the \(y\)-axis. Label the axes (including units).
h. Answer the questions that follow in this part.
Part \(\PageIndex{3}\): Inflating Plastic Bags
In this part of the experiment we will combine acetic acid (vinegar) and sodium bicarbonate in a snack-size Ziploc\(\circledR\) or zippered bag. A gas will be generated, and students should ensure that all the gas is trapped, with none leaking out. You will report your results on Table \(\PageIndex{3}\) of the experimental report.
a. Obtain three snack-size Ziploc bags and label them 1 – 3.
b. Measure about 0.700 g, 1.400 g, and 4.200 g of sodium bicarbonate (\(\ce{NaHCO3}\)) and place each portion in separate Ziploc bags, 1, 2, and 3, respectively. Record each measured quantity (in grams) on Table \(\PageIndex{3}\) of the experimental report. Without causing a mess in the bag, place each portion of the sodium bicarbonate powder at the far end (on one side) inside its own bag.
c. You will add the required amount of vinegar into each bag. See Table \(\PageIndex{3}\) for amounts. Pinch the Ziploc bag to hold the powder on one side and carefully add the vinegar using a funnel in the opposite end of the bag. Seal the bag and ensure it is tight before allowing its content to mix. Gently shake bag to mix content. It is recommended that each bag is shaken and then placed in a plastic bin to make observations. Record the final observation after the reaction is visibly complete. Repeat this process for all bags and record their corresponding observations.
Experimental Report
Part \(\PageIndex{1}\): Investigation of \(P\) & \(V\) using Vernier Gas Pressure Sensor
Table \(\PageIndex{1}\): Pressure and volume of a gas
| Reading | Volume (mL) | Pressure (atm) |
|---|---|---|
| 1 | 20.0 | |
| 2 | ||
| 3 | ||
| 4 |
Generate an excel plot of Table \(\PageIndex{1}\) data. Place volume (mL) on the \(x\)-axis and pressure (atm) on the \(y\)-axis. Label the axes (including units). Use one of the options below to present your plot.
Option 1: Under Plot \(\PageIndex{1}\), delete the graphing space provided and replace it with the excel plot (copy and paste the excel plot).
Option 2: Sketch the excel plot you just generated on the Plot \(\PageIndex{1}\) graphing space provided.
Plot \(\PageIndex{1}\): Pressure volume relationship
1. Using the plot, explain the effect of pressure on volume.
2. Which gas law does the above behavior describe?
3. Given that an adult man who has fully exhaled during normal breathing has a thoracic volume of 3.3 L at 1.0 atm. In preparation for inhalation, the man’s diaphragm contracts to increases the thoracic volume to 3.8 L. Assuming that this volume change doesn’t result in air inhalation, what is the new thoracic pressure? Show the calculation.
Part \(\PageIndex{2}\): Investigation of T & V using PhET Simulation
Table \(\PageIndex{2}\): Temperature and volume of gas
| Reading |
Temperature (K) |
Volume (width) (nm) |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
Generate an excel plot of Table \(\PageIndex{2}\) data. Place temperature (K) on the \(x\)-axis and volume (nm) on the \(y\)-axis. Label the axes (including units). Use one of the options below to present your plot.
Option 1: Under Plot \(\PageIndex{2}\), delete the graphing space provided and replace it with the excel plot (copy and paste the excel plot).
Option 2: Sketch the excel plot you just generated on the Plot \(\PageIndex{2}\) graphing space provided.
Plot \(\PageIndex{2}\): Temperature-volume relationship
1. State the relationship between temperature and volume:
2. What gas law is described by this data? ____________________________________________________
3. What variables are held constant? __________________________________________________________
4. What is the volume of gas at temperature of 600 K? _______________________________________
5. What is the temperature (K) when the gas volume is corresponding to 12.5 nm? _________
Part \(\PageIndex{3}\): Inflating Plastic Bags
Table \(\PageIndex{3}\): Sodium bicarbonate and vinegar measurements per bag
| Bag Number | Mass of \(\ce{NaHCO3}\) (g) | Volume of vinegar (mL) | Observation |
| 1 | 20.0 | ||
| 2 | 20.0 | ||
| 3 | 60.0 |
This is the time to explain your reported observations with the three bags.
1. What is the gas that is causing the changes you observe in the Ziploc bags? _____________
2. How do bags 1 and 2 compare and why?
3. Which bag demonstrated the most dramatic change and why?
4. Given that the molar mass of \(\ce{NaHCO3}\) is 84.01 g/mol, calculate the number of moles of \(\ce{NaHCO3}\) that reacted in bag 2.
5. If all the \(\ce{NaHCO3}\) in bag 2 reacted, calculate the number of moles of gas produced?