Molecular Mayhem Gas Unit

The Particle Mass Effect

Compare your data for Heavy vs. Light particles. What are the key differences in how they respond to temperature changes?

Speeds

Pressure

The Limit of Motion

What happened to Pressure and Movement when temperature hit 0 K? Why do we call this "Absolute Zero"?

Do you think it is physically possible to reach absolute zero in a real-world lab? Explain your thinking.

Synthesis

Kinetic Molecular Theory Check

1. Motion Statement:

Gas particles are in

Constant

and

Random

motion.

*Use simulator observations to justify this statement.

Energy Transfer

Define "Elastic Collisions":

Temperature Scale

Which temperature scale measures average Energy?

Phase 01 // KMT Foundations

Molecular Simulator Mission Packet

The Mass Factor

Compare Heavy vs. Light particles. When exposed to the exact same conditions, how do their behaviors differ?

Similarities

Differences

The Zero Boundary

Describe what happened to Temperature, Pressure, and Movement when you cooled the container to 0 K.

Based on this information, how would you describe "Absolute Zero" to someone who is new to this class?

Post-Lab Synthesis

KMT Final Theory Check

1. Motion Statement (Circle the correct words):

Gas particles are in

Constant / Sporadic

and

Predictable / Random

motion.

Energy & Mass

Define "Elastic Collisions":

Temperature Scale

What can we use to measure energy?

Phase 01 // Kinetic Foundations

PhET Simulator Mission Packet

04

Rigid Heat (Gay-Lussac)

Study Guide: In a rigid container (fixed volume), Pressure (\( P \)) and Temperature (\( T \)) are directly related. Hotter particles move faster and hit walls harder.

Worked Example: \( 2.0 \, atm \) @ \( 300 \, K \) cooled to \( 150 \, K \).

Setup \( \frac{2.0}{300} = \frac{P_2}{150} \).
Solve \( P_2 = \frac{2.0 \times 150}{300} = 1.0 \, atm \).

A car tire is inflated to \( 32.0 \, psi \) at a temperature of \( 15^\circ C \). After driving on a hot highway, the air inside reaches \( 45^\circ C \). What is the new pressure in the tire?

05

The Triple Change (Combined Law)

Study Guide: Use this when \( P, V, \) and \( T \) all change. If one variable stays constant, just cross it out from: \( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \).

Worked Example: \( 5 \, L, 1 \, atm, 300 \, K \rightarrow ? \, L, 2 \, atm, 600 \, K \).

Formula \( \frac{(1)(5)}{300} = \frac{(2)(V_2)}{600} \).
Solve \( \frac{5}{300} = \frac{2V_2}{600} \rightarrow 0.0166 = 0.0033V_2 \rightarrow V_2 = 5.0 \, L \).

A \( 2.5 \, L \) sample of gas at \( 1.2 \, atm \) and \( 25^\circ C \) is compressed to \( 1.0 \, L \) while being heated to \( 100^\circ C \). Calculate the final pressure.

06

The Snapshot (\( PV = nRT \))

Study Guide: No "before and after" here. Use this for a single state. Units must match your R-constant! (atm/L/K/mol).

Worked Example: Moles in \( 22.4 \, L \) at \( 1 \, atm, 273 \, K \)?

Assign \( P=1, V=22.4, T=273, R=0.0821 \).
Solve \( (1)(22.4) = n(0.0821)(273) \rightarrow n = 22.4 / 22.41 = 1.0 \, mole \).

Calculate the volume occupied by \( 0.75 \, moles \) of Nitrogen gas at a pressure of \( 1.50 \, atm \) and a temperature of \( 35^\circ C \).

07

The Sum (Dalton's Law)

Study Guide: Total Pressure = sum of the pressures of each individual gas in the mix. They don't react, they just share space.

Worked Example: Tank with \( 2 \, atm \, O_2 \) and \( 5 \, atm \, N_2 \).

Logic \( P_{total} = P_{O_2} + P_{N_2} \).
Solve \( 2 + 5 = 7 \, atm \).

A mixture of Helium, Neon, and Argon has a total pressure of \( 950 \, mmHg \). If the partial pressure of Helium is \( 200 \, mmHg \) and Neon is \( 450 \, mmHg \), what is the partial pressure of Argon?

08

The Speed Gap (Graham's Law)

Study Guide: Effusion is escaping through a hole. Lighter = Faster. Ratio: \( \frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}} \). Note the flip in indices!

Worked Example: Speed ratio of \( He \, (4 \, g/mol) \) vs \( O_2 \, (32 \, g/mol) \)?

Setup Ratio \( = \sqrt{32 / 4} \).
Solve \( \sqrt{8} \approx 2.8 \) times faster.

An unknown gas diffuses \( 0.25 \) times as fast as Hydrogen gas (\( H_2, \, mass = 2.0 \, g/mol \)). What is the molar mass of the unknown gas?

09

Reality Check (Real Gases)

Study Guide: Ideal gases assume particles have NO volume and NO attraction. In reality, at High Pressure (particles too close) and Low Temp (particles too slow), these assumptions fail.

Worked Example: Why does steam condense when cooled?

KMT Link Lower KE means particles move slowly enough for intermolecular attractions to pull them together into a liquid.

Explain why Nitrogen gas behaves more like an ideal gas at \( 500 \, K \) than it does at \( 77 \, K \). Reference specific KMT postulates.

10

The Tanker Implosion

Study Guide: Multi-dimensional problems require connecting math to phenomena. Ask: "What variable is driving the change? What is the physical consequence?"

Worked Example: Heated aerosol can exploding.

Process \( T \uparrow \rightarrow P \uparrow \) (Gay-Lussac). When \( P \) exceeds the can's strength, it ruptures.

A railroad tanker is filled with steam at \( 100^\circ C \) and \( 1.0 \, atm \). It is sealed and then cooled rapidly to \( 20^\circ C \).
1. Calculate the final pressure inside.
2. Explain why the tanker implodes if the outside air pressure is \( 1.0 \, atm \).

Intel Leak: Verification Bank

Verify your numbers below. Numerical results are scrambled. Qualitative answers are not listed.

\( 50.0 \, L \)

\( 35.3 \, psi \)

\( 18.6 \, mL \)

\( 3.75 \, atm \)

\( 12.6 \, L \)

\( 300 \, mmHg \)

\( 32.0 \, g/mol \)

\( 0.785 \, atm \)

Collisions of particles with the container walls

The suction created by vacuum gaps between atoms

08

Why are gases so easily compressed compared to solids?

Gas particles are softer than solid particles

There is a lot of empty space between gas particles

Gas particles have no mass at all

Gravity does not affect gas particles

Molecular Mayhem Unit // Phase 01

Gas Dynamics & Theory Check

At \( 500 \, K \), particles have much higher Average Kinetic Energy. This high speed overcomes any intermolecular attractions (Postulate 3). At \( 77 \, K \) (very low), particles move slow enough for attractions to pull them together, violating the ideal assumption that attractions are negligible.

10

Synthesis: Tanker Implosion

Part 1 Math:

\( T_1 = 373 \, K, \, T_2 = 293 \, K \)
\( \frac{1.0}{373} = \frac{P_2}{293} \)
\( P_2 = \frac{293}{373} \approx 0.785 \)

\( P_2 = 0.785 \, atm \)

Part 2 Logic:

The internal pressure (\( 0.785 \, atm \)) is significantly lower than the external atmospheric pressure (\( 1.0 \, atm \)). This creates a massive pressure gradient. The outside air exerts a much greater force on the tanker walls than the internal gas, causing the structure to buckle inward (implode).

End of Assessment Key • Molecular Mayhem Unit