Calculating "gas change" typically refers to determining how a property of a gas (like pressure, volume, temperature, or number of moles) changes under different conditions. The approach depends on what is changing and what is being held constant. We can use the Ideal Gas Law and its derivatives, along with the Combined Gas Law.
Here's a breakdown of how to approach different scenarios:
1. The Ideal Gas Law: A Foundation
The Ideal Gas Law provides the fundamental relationship:
PV = nRT
Where:
- P = Pressure
- V = Volume
- n = Number of moles of gas
- R = Ideal gas constant (approximately 0.0821 L atm / (mol K) or 8.314 J / (mol K), depending on the units used for pressure and volume)
- T = Temperature (in Kelvin)
This law is useful when you know the values of three of the variables (P, V, n, T) and need to find the fourth. Changes aren't directly addressed here, but it's the basis for understanding those changes.
2. The Combined Gas Law: When Conditions Change
When all the variables can change, but the amount of gas (n) is constant, the Combined Gas Law is useful:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
- P₁, V₁, T₁ = Initial pressure, volume, and temperature
- P₂, V₂, T₂ = Final pressure, volume, and temperature
This lets you calculate how one variable changes when others change.
Example: If you have a gas at an initial pressure of 1 atm, a volume of 10 L, and a temperature of 300 K, and then you increase the pressure to 2 atm and the temperature to 350 K, what is the new volume?
(1 atm * 10 L) / 300 K = (2 atm * V₂) / 350 K
Solving for V₂:
V₂ = (1 atm * 10 L * 350 K) / (300 K * 2 atm) = 5.83 L
3. Specific Gas Laws (Derived from the Combined Gas Law): When Some Variables are Constant
The Combined Gas Law simplifies when one of the variables remains constant:
- Boyle's Law (Constant Temperature): P₁V₁ = P₂V₂ (Pressure and volume are inversely proportional)
- Charles's Law (Constant Pressure): V₁/T₁ = V₂/T₂ (Volume and temperature are directly proportional)
- Gay-Lussac's Law (Constant Volume): P₁/T₁ = P₂/T₂ (Pressure and temperature are directly proportional)
4. Calculating Changes in Moles
If the number of moles (n) changes, you generally need to revert to the Ideal Gas Law and solve for 'n' in each state if the other variables are known. Or, if other variables are held constant:
-
If P, V, T are held constant:
n₁ = n₂(No change in the number of moles) -
If P, T are held constant, then
V₁/n₁ = V₂/n₂(Volume and number of moles are directly proportional). This is Avogadro's Law.
Steps to Solve Gas Change Problems:
- Identify the knowns and unknowns: What values are given, and what are you trying to find?
- Determine which variables are constant: This dictates which gas law to use (Ideal, Combined, or a specific law).
- Choose the appropriate formula: Select the gas law that applies to the situation.
- Rearrange the formula (if necessary): Solve for the unknown variable.
- Plug in the values and solve: Ensure all units are consistent. Temperature must be in Kelvin.
- Consider changes in n (number of moles): If the number of moles is changing, make sure to account for it in your calculations, usually by using the ideal gas law or Avogadro's law.
Example Problem
A balloon contains 5 L of air at 27°C and 1 atm. If the temperature is increased to 77°C and the pressure remains constant, what is the new volume of the balloon?
- Knowns: V₁ = 5 L, T₁ = 27°C = 300 K, P₁ = 1 atm, T₂ = 77°C = 350 K, P₂ = 1 atm. Unknown: V₂
- Constant: Pressure (P) and presumably the number of moles (n) are constant.
- Formula: Charles's Law: V₁/T₁ = V₂/T₂
- Rearrange: V₂ = (V₁ * T₂) / T₁
- Solve: V₂ = (5 L * 350 K) / 300 K = 5.83 L
The new volume of the balloon is 5.83 L.
