Gas Laws Application and Analysis: The Submarine and the Deep-Sea Dive Fix
Students will demonstrate knowledge and understanding of the gas laws (Boyle's, Charles's, Gay-Lussac's, Combined, and Ideal Gas Law) by solving problems and analyzing a real-world scientific scenario.
Group 1
Scenario: A deep-sea submersible, the Triton, is preparing for a record-breaking dive to the Challenger Deep. The submersible's internal atmosphere is carefully monitored, and its air tanks (containing a specific mixture of gases) must be managed to maintain safe pressure and volume for the crew. The dive introduces extreme conditions of pressure and temperature.
Instructions: Complete the following tasks, ensuring your responses are clear, well-supported, and use proper scientific notation and units.
Question 1a
Explain the underlying principles of the Kinetic Molecular Theory (KMT). In your explanation, detail how KMT provides a foundation for the observed relationships between pressure, volume, and temperature as described by the major gas laws (Boyle's, Charles's, and Gay-Lussac's).
Group 2
Part II: Problem-Solving in Familiar and Unfamiliar Situations (Criterion A, Strand ii)
Question 2a
Familiar Situation (Combined Gas Law): The Triton's primary air tank contains 500 L of a gas mixture at a surface temperature of 298 K and a pressure of 1.0 atm. When the submersible descends, the temperature inside the tank drops to 280 K, and the external pressure increases to 150 atm. Assuming the tank doesn't rupture, what is the new volume of the gas inside the tank? Show all work and state the final answer with correct units.
Question 2b
Unfamiliar Situation (Ideal Gas Law and Deep-Sea Chemistry): At the maximum depth, the submersible's cabin pressure is maintained at 3.0 atm, and the temperature is 295 K. The cabin has a volume of 8.0×10³ L. Calculate the total number of moles of gas present in the cabin at this depth. Use the Ideal Gas Constant, R=0.0821 mol·K⁻¹·atm⁻¹. Show all work and state the final answer with correct units.
Group 3
Part III: Analysis and Evaluation (Criterion A, Strand iii)
Question 3a
Analyze the relationship between the temperature and pressure in the log sheet, identifying the gas law represented.
Question 3b
Evaluate the data by plotting a graph of Pressure vs. Temperature (in Kelvin). Use the graph to extrapolate the approximate pressure of the cylinder if its temperature were to reach 100°C.
Question 3c
Make a scientifically supported judgment on the safety of this cylinder at 100°C if its maximum safe operating pressure is 175 atm.
Group 4
Assessment Rubric: Use this rubric to guide your responses and understand how your work will be evaluated.
Source 4.1
| Level | Strand i: Explaining Scientific Knowledge (Part I) | Strand ii: Applying Knowledge to Solve Problems (Part II) | Strand iii: Analyzing and Evaluating Information (Part III) | |-------|---------------------------------------------------|----------------------------------------------------------|-------------------------------------------------------------| | 7-8 | Explain the principles of the Kinetic Molecular Theory (KMT) and explicitly detail its relationship to all three proportional gas laws (Boyle's, Charles's, and Gay-Lussac's). | Solve problems set in familiar (Combined Gas Law) and unfamiliar (Ideal Gas Law/Partial Pressures) situations with clear, correct steps and units, and provide a thorough, justified explanation for the Heliox mixture switch. | Analyze the P-T data, evaluate the relationship graphically (converting to Kelvin), extrapolate the pressure at 100°C, and make a sophisticated, scientifically supported judgment on the cylinder's safety. | | 5-6 | Describe the principles of KMT and its relationship to two or more of the proportional gas laws. | Solve problems set in familiar situations (Combined Gas Law) with correct steps, and suggest solutions (e.g., correct setup with minor calculation/unit errors) for problems set in unfamiliar situations. | Analyze the P-T data (including creating a graph) and make a valid, scientifically supported judgment based on the analysis. | | 3-4 | Outline the principles of KMT or its relationship to one major proportional gas law. | Solve problems set in familiar situations (Combined Gas Law) but may include a significant calculation or unit error. | Interpret the P-T data to identify the general relationship and make a simple scientifically supported judgment. | | 1-2 | State one or two key concepts of KMT. | Suggest solutions to problems set in familiar situations (e.g., identifies the correct formula but makes errors in substitution or calculation). | Interpret the P-T data to make a simple judgment (e.g., states pressure increases with temperature). | | 0 | The student does not reach a standard identified by any of the descriptors below. | The student does not reach a standard identified by any of the descriptors below. | The student does not reach a standard identified by any of the descriptors below. |
CRITERION A RUBRIC: KNOWLEDGE AND UNDERSTANDING
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