UPCAT Chemistry — Gas Laws & ThermochemistryCheat Sheet
Gas Laws & Thermochemistry cheat sheet for UPCAT aspirants. If you could only take one sheet of paper into your review session, this is what it would look like. University of the Philippines's most-tested concepts, all in one place.
Exam context
On the UPCAT 2026, the Chemistry subtest carries a "Core" weight in University of the Philippines's pattern. Gas Laws & Thermochemistry lands at position 6th out of 7 in the standard review order. Target score is UPG ≤ 2.2 typical, and roughly 20 items come from Chemistry on a typical UPCAT paper.
Gas Laws & Thermochemistry - Cheat sheet
Your last-minute revision companion for Gas Laws & Thermochemistry - all formulas, key concepts, and exam tricks in one place.
Sections
Formulas
Formula
P₁V₁ = P₂V₂
Meaning
P = pressure, V = volume, subscripts 1 and 2 = initial and final states
Watch Out
Make sure pressure and volume units are consistent on both sides
When To Use
When temperature is constant and pressure/volume change
Section Title
Boyle's Law
Important Facts
- Only applies when temperature remains constant
- Inverse relationship: P↑ means V↓ and vice versa
- Graph of P vs V is a hyperbola
- Graph of P vs 1/V is a straight line
Key Definitions
Term
Boyle's Law
Example
Compressing a syringe decreases volume and increases pressure
Definition
At constant temperature, pressure and volume of a gas are inversely proportional
Diagrams To Know
- P vs V hyperbolic curve
- P vs 1/V linear graph
Formulas
Formula
V₁/T₁ = V₂/T₂
Meaning
V = volume, T = temperature in Kelvin
Watch Out
Temperature MUST be in Kelvin, not Celsius
When To Use
When pressure is constant and volume/temperature change
Common Values
Value
K = °C + 273.15
Symbol
T
Quantity
Kelvin conversion
Section Title
Charles's Law
Important Facts
- Only applies when pressure remains constant
- Direct relationship: T↑ means V↑ and vice versa
- Temperature must be in absolute scale (Kelvin)
- Graph of V vs T is a straight line passing through origin
Key Definitions
Term
Charles's Law
Example
Balloon expands when heated, contracts when cooled
Definition
At constant pressure, volume and temperature of a gas are directly proportional
Diagrams To Know
- V vs T linear graph
Formulas
Formula
P₁/T₁ = P₂/T₂
Meaning
P = pressure, T = temperature in Kelvin
Watch Out
Temperature must be in Kelvin for accurate calculations
When To Use
When volume is constant and pressure/temperature change
Section Title
Gay-Lussac's Law
Important Facts
- Only applies when volume remains constant
- Direct relationship: T↑ means P↑ and vice versa
- Also called Pressure-Temperature Law
- Graph of P vs T is a straight line
Key Definitions
Term
Gay-Lussac's Law
Example
Pressure cooker pressure increases with temperature
Definition
At constant volume, pressure and temperature of a gas are directly proportional
Diagrams To Know
- P vs T linear graph
Formulas
Formula
P₁V₁/T₁ = P₂V₂/T₂
Meaning
Combines all three individual gas laws
Watch Out
Cross out the variable that stays constant before solving
When To Use
When two or more gas properties change simultaneously
Section Title
Combined Gas Law
Important Facts
- Combines Boyle's, Charles's, and Gay-Lussac's laws
- Amount of gas (moles) must remain constant
- Can eliminate constant variables by crossing out
- Most versatile gas law equation
Key Definitions
Term
Combined Gas Law
Example
Weather balloon rising through atmosphere with changing P, V, T
Definition
Relationship between pressure, volume, and temperature when amount of gas is constant
Formulas
Formula
PV = nRT
Meaning
P = pressure (atm), V = volume (L), n = moles, R = gas constant, T = temperature (K)
Watch Out
Units must match R value: atm·L/(mol·K) or use appropriate R constant
When To Use
When you need to find moles or when dealing with different amounts of gas
Common Values
Value
0.0821 atm·L/(mol·K)
Symbol
R
Quantity
Universal Gas Constant
Section Title
Ideal Gas Law
Important Facts
- Most comprehensive gas law equation
- Works best at high temperature and low pressure
- Can calculate any variable if others are known
- Assumes no intermolecular forces
Key Definitions
Term
Ideal Gas
Example
Real gases behave like ideal gases at high T and low P
Definition
Hypothetical gas with no intermolecular forces and point particles
Common Values
Value
0°C = 273.15 K
Symbol
T
Quantity
Standard Temperature
Value
1 atm = 760 torr = 760 mmHg
Symbol
P
Quantity
Standard Pressure
Value
22.4 L/mol
Symbol
Vm
Quantity
Molar Volume at STP
Section Title
Standard Conditions
Important Facts
- STP: T = 0°C = 273.15 K, P = 1 atm = 760 torr = 760 mmHg
- At STP, 1 mole of any gas = 22.4 L
- Avogadro's Law: Equal volumes contain equal moles at same T and P
- Standard conditions are reference points for calculations
Key Definitions
Term
STP
Example
Used as reference conditions for gas calculations
Definition
Standard Temperature and Pressure: 0°C (273.15 K) and 1 atm
Term
Molar Volume
Example
22.4 L of any gas contains 6.022 × 10²³ molecules at STP
Definition
Volume occupied by 1 mole of any gas at STP
Must Remember
- Temperature must ALWAYS be in Kelvin for gas law calculations
- PV = nRT with R = 0.0821 atm·L/(mol·K)
- At STP: 1 mole gas = 22.4 L
- Boyle's Law: P₁V₁ = P₂V₂ (constant T)
- Charles's Law: V₁/T₁ = V₂/T₂ (constant P)
- Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂
- STP = 0°C (273.15 K) and 1 atm (760 torr)
- Direct relationship: both increase/decrease together
- Inverse relationship: one increases, other decreases
- Check units consistency in all calculations
Last Minute Tips
- Always convert Celsius to Kelvin first (add 273.15)
- For combined gas law problems, cross out the constant variable
- If pressure units don't match, convert to same units before calculating
- When given STP conditions, you can use 22.4 L = 1 mole shortcut
- Check if your answer makes physical sense (hot gas expands, compressed gas has higher pressure)
Comparison Tables
Rows
Values
- Temperature
- P ∝ 1/V
- P₁V₁ = P₂V₂
- P vs V hyperbola
Property
Boyle's Law
Values
- Pressure
- V ∝ T
- V₁/T₁ = V₂/T₂
- V vs T line
Property
Charles's Law
Values
- Volume
- P ∝ T
- P₁/T₁ = P₂/T₂
- P vs T line
Property
Gay-Lussac's Law
Values
- Amount (moles)
- All combined
- P₁V₁/T₁ = P₂V₂/T₂
- 3D surface
Property
Combined
Columns
- Law
- Constant Variable
- Relationship
- Formula
- Graph
Table Title
Gas Laws Comparison
Rows
Values
- V and T, P and T
- Other increases
- y = kx
Property
Direct
Values
- P and V
- Other decreases
- xy = k
Property
Inverse
Columns
- Type
- Variables
- When one increases
- Mathematical form
Table Title
Direct vs Inverse Relationships
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