1. Introduction to Gas Laws 💨
Gas laws are fundamental principles that describe the relationship between the measurable properties of gases: pressure (P), volume (V), and temperature (T). These laws are based on observations of how gases behave when one or more of these properties are changed. The laws assume that gases are composed of tiny particles that are in constant, random motion and that there are no forces of attraction or repulsion between them (Ideal Gas behavior).
2. Boyle’s Law (Volume and Pressure) 🎈
Boyle’s Law states that at a constant temperature, the volume of a fixed mass of a gas is inversely proportional to its pressure.
- Mathematical Representation: V∝P1 or PV=k (a constant)
- Formula: For a gas at two different states, the relationship is P1V1=P2V2.
- Application: When you compress a gas (increase pressure), its volume decreases. For example, pushing down on the plunger of a syringe with the tip blocked causes the air inside to be compressed into a smaller volume.
3. Charles’s Law (Volume and Temperature) 🌡️
Charles’s Law states that at a constant pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature (Kelvin scale).
- Mathematical Representation: V∝T or TV=k (a constant)
- Formula: For a gas at two different states, the relationship is T1V1=T2V2.
- Absolute Zero: The law implies that if you cool a gas to a temperature of 0 Kelvin (−273.15∘C), its volume would theoretically become zero. This temperature is called absolute zero.
- Application: A balloon inflates on a hot day and shrinks on a cold day because the volume of the gas inside changes with temperature.
4. Pressure-Temperature Law (Gay-Lussac’s Law) 🔥
The Pressure-Temperature Law (also known as Gay-Lussac’s Law) states that at a constant volume, the pressure of a fixed mass of a gas is directly proportional to its absolute temperature.
- Mathematical Representation: P∝T or TP=k (a constant)
- Formula: For a gas at two different states, the relationship is T1P1=T2P2.
- Application: An aerosol can left in a hot car can explode because the pressure inside increases with the rising temperature.
5. Standard Temperature and Pressure (STP) 🧊
To compare the properties of different gases, a standard set of conditions is defined.
- Standard Temperature: 0∘C or 273 K.
- Standard Pressure: 1 atmosphere (atm) or 760 mm Hg or 76 cm Hg.
At STP, the molar volume of any ideal gas is approximately 22.4 liters.
6. The Combined Gas Law 🤝
The Combined Gas Law unifies Boyle’s Law, Charles’s Law, and the Pressure-Temperature Law. It relates the pressure, volume, and absolute temperature of a fixed amount of gas.
- Formula: T1P1V1=T2P2V2
- Application: This law is used to solve problems where all three properties of a gas change simultaneously.
The combined gas law can be easily derived from the individual gas laws.
- If T is constant, T1=T2, so the formula becomes P1V1=P2V2 (Boyle’s Law).
- If P is constant, P1=P2, so the formula becomes T1V1=T2V2 (Charles’s Law).
- If V is constant, V1=V2, so the formula becomes T1P1=T2P2 (Gay-Lussac’s Law).
Boyle’s Law (P₁V₁ = P₂V₂) 🎈
- A gas occupies 10 L at 2 atm pressure. What is its new volume if the pressure increases to 4 atm at a constant temperature?
- P1=2 atm,V1=10 L
- P2=4 atm,V2=?
- V2=P2P1V1=4 atm2 atm×10 L=5 L
- A balloon contains 500 mL of air at 760 mm Hg. If the pressure changes to 380 mm Hg, what will be the new volume?
- P1=760 mm Hg,V1=500 mL
- P2=380 mm Hg,V2=?
- V2=P2P1V1=380 mm Hg760 mm Hg×500 mL=1000 mL
Charles’s Law (V1/T1=V2/T2) 🌡️
Important: Remember to always convert the temperature to Kelvin (K) by adding 273 to the Celsius (°C) value.
- A gas occupies 2 L at 27 °C. What is its volume at 127 °C if the pressure is kept constant?
- V1=2 L
- T1=27°C+273=300 K
- T2=127°C+273=400 K
- V2=?
- V2=T1V1T2=300 K2 L×400 K=2.67 L
- A gas sample has a volume of 450 mL at 0 °C. At what temperature (in °C) will its volume be 600 mL at constant pressure?
- V1=450 mL
- T1=0°C+273=273 K
- V2=600 mL
- T2=?
- T2=V1V2T1=450 mL600 mL×273 K=364 K
- Temperature in °C = 364 K−273=91°C
Combined Gas Equation (T1P1V1=T2P2V2) 🤝
- A gas occupies 5 L at 2 atm and 27 °C. What is its new volume at STP (Standard Temperature and Pressure)?
- P1=2 atm,V1=5 L,T1=27°C+273=300 K
- At STP: P2=1 atm,T2=0°C+273=273 K
- V2=?
- V2=T1P2P1V1T2=300 K×1 atm2 atm×5 L×273 K=9.1 L
- A gas sample has a volume of 800 mL at 600 mm Hg and 17 °C. What will be its pressure at 400 mL and 27 °C?
- V1=800 mL,P1=600 mm Hg,T1=17°C+273=290 K
- V2=400 mL,P2=?,T2=27°C+273=300 K
- P2=T1V2P1V1T2=290 K×400 mL600 mm Hg×800 mL×300 K=1241.38 mm Hg
