Unit 3: Chemistry Fundamentals

Given Conditions:
- Initial Temperature: T₁ = 25 °C
- Converted to Kelvin: T₁ = 25 + 273 = 298 K
- Initial Pressure: P₁ = 3 atm
Final Conditions:
- Final Temperature: T₂ = 845 °C
- Converted to Kelvin: T₂ = 845 + 273 = 1,118 K
- Final Pressure: P₂ = ?
Calculation Method:
- Use Gay-Lussac's Law, which states that pressure is directly proportional to temperature when volume is constant:
 $\frac{P1}{T1} = \frac{P2}{T2}$
- Rearranging gives us:
 $P2 = P1 \times \frac{T2}{T1}$
Plugging in values:
- Calculate P₂:
 $P2 = 3.0 \text{ atm} \times \frac{1,118 K}{298 K}$ $P2 = 11.23 \text{ atm}$

Problem Statement:
- The pressure of a gas in a cylinder when heated to a temperature of 250 K is 1.5 atm. What is the initial temperature of the gas if its initial pressure was 1.0 atm?
- Concept Applied: Use Gay-Lussac's Law to find initial temperature based on pressure change.
Practical Examples:
- List of items that obey Gay-Lussac's Law in daily life:
  - Pressurized cans (like deodorants)
  - Inflatable devices (like beach balls)
  - Balloon behavior with temperature changes
  - Automotive tires (pressure increase with temperature)

Concept Overview:
- A gas can experience simultaneous changes in temperature, pressure, and volume.
- It is essential to consider all three variables in a single equation to describe these changes accurately.
Combined Gas Law Equation:
- The combined gas law combines previously learned gas laws into one expression:
  $PV \alpha T$
- Rearranged mathematically:
  $\frac{PV}{T} = k$
- Where k is the proportionality constant, meaning:
- The ratio of pressure multiplied by volume to temperature will always produce the same constant k.
Final Formulation:
- Thus, for two sets of conditions, the law can be expressed as:
 $\frac{P1 V1}{T1} = \frac{P2 V2}{T2}$
- Where P₁, V₁, and T₁ are the initial pressure, volume, and temperature;
- P₂, V₂, and T₂ are the final pressure, volume, and temperature, respectively.