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🧪 Gas Laws: Complete Study Guide
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⚠️ Foundational Concepts
🔹 Properties of Gases:
* Pressure (P): Force gas exerts per unit area (measured in atm, mmHg, torr, kPa)
* Volume (V): Space a gas occupies (usually in liters, L)
* Temperature (T): Always in Kelvin for gas laws
K=°C+273\text{K} = \text{°C} + 273K=°C+273
* Amount of gas (n): In moles
moles=mass (g)molar mass\text{moles} = \frac{\text{mass (g)}}{\text{molar mass}}moles=molar massmass (g)
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⚙️ The Major Gas Laws
1. Boyle’s Law — Pressure vs. Volume
* Formula: P1V1=P2V2P_1 V_1 = P_2 V_2P1V1=P2V2
* Constant: Temperature, number of moles
* Relationship: Inverse
* When volume ↓, pressure ↑
* Use when: Temp is constant, P & V change
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2. Charles’s Law — Volume vs. Temperature
* Formula: V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}T1V1=T2V2
* Constant: Pressure, number of moles
* Temperature in Kelvin
* Relationship: Direct
* Temp ↑ ⇒ Volume ↑
* Use when: Pressure is constant, V & T change
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3. Gay-Lussac’s Law — Pressure vs. Temperature
* Formula: P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}T1P1=T2P2
* Constant: Volume, number of moles
* Relationship: Direct
* Temp ↑ ⇒ Pressure ↑
* Use when: Volume is constant, P & T change
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4. Combined Gas Law
* Formula:
P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}T1P1V1=T2P2V2
* Use when: P, V, and T all change
* Must use Kelvin and consistent units
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5. Ideal Gas Law
* Formula:
PV=nRTPV = nRTPV=nRT
* R (Gas constant): 0.0821 L·atm/mol·K
* Use when:
* Given or solving for moles, pressure, temp, volume
* Can also be rearranged:
* P=nRTVP = \frac{nRT}{V}P=VnRT
* V=nRTPV = \frac{nRT}{P}V=PnRT
* n=PVRTn = \frac{PV}{RT}n=RTPV
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6. Avogadro’s Law — Moles vs. Volume
* Formula:
V1n1=V2n2\frac{V_1}{n_1} = \frac{V_2}{n_2}n1V1=n2V2
* Relationship: Direct
* More moles = more volume (at same T & P)
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🧰 Conversions You’ll Need
Quantity
Convert to...
How
Temperature
Kelvin
°C + 273
Pressure
atm
1 atm = 760 mmHg = 101.3 kPa
Volume
Liters (L)
1000 mL = 1 L
Moles
from grams
mass / molar mass
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🧠 How to Know Which Law to Use
Problem Mentions...
Use This Law
Pressure & Volume change, temp constant
Boyle’s Law
Volume & Temp change, pressure constant
Charles’s Law
Pressure & Temp change, volume constant
Gay-Lussac’s Law
P, V, and T all changing
Combined Gas Law
Involves moles or gas amount
Ideal Gas Law
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🧪 Problem-Solving Strategy
1. Identify what's changing: P, V, T, or n?
2. Convert all units:
* Temp → Kelvin
* Volume → Liters
* Mass → Moles (if needed)
3. Choose correct gas law.
4. Plug values into formula.
5. Solve for unknown.
6. Check units & logic (volume shouldn’t be negative, etc.)
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📍 Example Problem
Q: A gas occupies 3.50 L at 1.00 atm and 300 K. What volume will it occupy at 2.00 atm and 400 K?
A: Use the Combined Gas Law
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📚 Practice Topics to Master:
* Interpreting graphs of pressure vs. volume (inverse)
* Recognizing when to use Kelvin
* Identifying whether relationships are direct or inverse
* Using molar mass to convert grams to moles
* Recognizing when a gas law question is a real-world scenario (e.g., balloons rising)