L7.7
*Lesson 7: How can gas law calculations affect the Earth systems?
Question: How can gas law calculations predict the impact of rising temperatures on the Earth systems?
What did we learn last class about the way gasses behave?
How do you think gas behavior impacts sea level rise?
Complete the IMT for Lesson 6.
Part 1: Combining Gas Laws
Each of the gas laws investigated last class explored two variables at a time. This allows us to create simple models. In reality, our atmosphere is a complex system of gasses where all four gas variables interact simultaneously.
Let’s explore the four gas variables using the diagram above. Do google research to answer the following questions. Gas Variable, T: There is a temperature change between the stratosphere and the troposphere. Which is colder the stratosphere or the troposphere?
Gas Variable, P: There is a pressure change between the stratosphere and the troposphere. Which has a greater air pressure the stratosphere or the troposphere?
Gas Variable, V: There is a volume change between the stratosphere and the troposphere. Which has a greater volume the stratosphere or the troposphere?
Gas Variable, n: How are the number of particles increasing in the atmosphere?
Let’s review the relationships that we learned last class about how gases behave.
| Gas Law | Relationship amongst Variables | Equation |
|---|---|---|
| Boyles laws | V ∝ 1/P | P1V1 = P2V2 where PV = k Moles and Temperature are constant |
| Charles law | V ∝ T | V_1/T_1 = V_2/T_2 Moles and Pressure are constant |
| Lussacs Law | P ∝ T | P_1/T_1 = P_2/T_2 Moles and Volume are constant |
| Avogadros Law | V ∝ n | V_1/n_1 = v_2/n_2 Pressure and Volume are constant |
, where PT = k
, where Vn = k
What do the subscripts 1 and 2 represent in the equation?
Write all of the equations that represent a direct relationship.
Write all of the equations that represent an indirect relationship.
What would be the mathematical relationship if you combined Boyles and Charles law?
What would be the mathematical relationship if you combined all of the gas laws together?
As you can see from the answer to ‘e’, to understand gases, scientists are working with 8 variables. In working with gases, scientists must consider both the initial and final conditions of each of the base variables P, V, n, and T. One way that chemists simplify the calculation and their models are by combining the initial conditions to a set of standard conditions listed here. If n= 1 mole; P= 1 atm; V = 22.4 L; and T = 273 K; what is the numerical value of PVnT? Include all units.
R, 0.0821
This value is given the variable, R, and is called the Universal Gas Constant. The Universal Gas Constant combines all of the gas laws and can be used to describe the behavior of any gas. We can rewrite your answer to question ‘5e’ to be PV = nRT. Let’s practice using PV=nRT, where R = 0.0821 Latm/molK
A student last class placed 0.04 moles of air into the balloon that they massed. At SHP, the air pressure is usually 1.07 atm and the temperature was 297 K (24°C). What is the volume of the balloon? (R = 0.0821 Latm/molK)
0.921 Liters
At the top of Mount Everest, a balloon has a volume of 2.0 L, the air pressure is 0.30 atm, and a temperature of 264 K (-9°C). How many moles of gas are in the balloon? (R = 0.0821 Latm/molK)
Part 2: Using the Ideal Gas Law-Number of Gas Molecules in Your Breath Goal: The goal of this part of the lab is to determine the volume of one normal breath of air for each person in your group. The outline for a procedure is given below. Your group will need to decide how you will figure out the air volume.
Materials:
2 L plastic bottle with cap Large container tap water ~3 ft of flexible tubing Straw Marking Pen Blue tape
Procedure Use a thermometer to take the temperature in the room. Enter in the data table below. Calculate the temperature in Kelvin
| Temperature of air (oC) | 25 |
|---|---|
| Temperature of air (oK)Kelvin | 298 |
Fill a larger container or tub about half full with tap water. Fill a 2 L plastic bottle with tap water. Cover and/or put the cap on loosely. Carefully turn the bottle upside down into the half-full tub without spilling any water so that the mouth of the bottle is underwater. Remove the cap underwater. Feed the flexible tubing under the water so that one end goes inside the bottle. Put your straw into the other end of the tubing. Do not share straws. When it is your turn, exhale into the straw to collect the air of one normal breath. With a marking pen or piece of tape, mark the volume of air on the bottle. Figure out the volume of the air trapped inside the bottle. Record this volume. Repeat the procedure for each person in the group. Replace the straw for each new person. Volume data
| Initial Volume of Water (mL) | 2000 |
|---|---|
| Final Volume of Water (mL) | 0 |
| Volume of Air in 1 breath (mL) | 0 |
|---|---|
| Voulme of Air in 1 breath (L) | 2000 |
Finding the Pressure: Use your favorite internet search engine to find the barometric pressure in Atherton, Ca. Enter your finding into the Data table below. Be sure to use inches of mercury as your units for the first box. Convert the barometric pressure to atmospheres(atm) using the conversion factor below.
Pressure Data | Barometric Pressure (in. Hg) | 29.95 | | ---------------------------- | --- | | Convert in. of Hg to atm | 1 | (1atm = 29.92 in. Hg)
Part 3: Data Analysis To determine the number of molecules of air in one breath, use the volume you determined from the experiment and the ideal gas, PV = nRT where R = 0.082 L atm/mol K. Calculating Moles in a Breath at in Atherton at Sea Level. Based on the data collected and the volume of your breath, use the ideal gas law to determine the number of moles of air molecules in one breath.
n = PV/RT
\(n = \frac{1 * 2000}{0.0821 * 298}\)
n = 81.74 Moles
Calculating Moles in a Breath on a Mountaintop. Suppose you take a breath on a mountaintop at an altitude of 10,000 ft where the air pressure is 0.75 atm and the temperature is 20 °C (293 K). Use the ideal gas law to determine the number of moles of air molecules in one breath.
\(n = \frac{0.75 * 2000}{0.0821 * 293}\)
n = 62.35 moles
There are 602 sextillion, or 602,000,000,000,000,000,000,000, gas molecules in 1 mole. Calculate the number of gas molecules in a breath at sea level.
\(4.92*10^{25}\)
Calculate the number of gas molecules in a breath on a mountaintop.
\(3.75*10^{25}\)
Based on your calculations in Question 9, what is the difference between the number of molecules in one normal breath at sea level and the number at 10,000 ft?
\(1.17*10^{25}\)
Use the ideal gas law and your breath volume to figure out how many moles of air molecules would be in one breath at the top of Mount Everest. Air pressure at 29,000 ft is 0.30 atm. The temperature at the summit at the warmest time of the year is -19 °C.
Part 4: How can gas law calculations predict the impact of rising temperatures on Earth Systems? A student claims that the rising levels of carbon dioxide in the atmosphere are greatly impacting the pressure, volume, and temperature of the atmosphere. Do you agree or disagree with this claim? Explain your reasoning using the ideal gas law.
NEXT STEPS: Reflect on today’s question: How can gas law calculations affect the Earth systems?
Reflect on the unit question, how does today’s activity relate to the unit question? Open up the IMT for this unit, complete all boxes for lesson 7. Turn in lesson 6 & 7 for the IMT to the assignment post.
Make sure all parts of the L7.7 student sheet are complete & complete the check for understanding on Schoology.
Created: June 5, 2023