Mastering the Combined Gas Law: A Comprehensive Guide with Solved Examples
The combined gas law is a crucial concept in chemistry, bringing together the relationships between pressure, volume, and temperature of a gas. Understanding this law is essential for predicting how gases will behave under changing conditions. This guide provides a comprehensive overview of the combined gas law, including its formula, application, and solved examples to help you confidently tackle any worksheet.
Understanding the Combined Gas Law
The combined gas law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single, powerful equation. It states that the ratio of the product of pressure and volume to the absolute temperature of a gas remains constant. Mathematically, it's represented as:
(P₁V₁)/T₁ = (P₂V₂)/T₂
Where:
- P₁ = Initial pressure
- V₁ = Initial volume
- T₁ = Initial absolute temperature (in Kelvin)
- P₂ = Final pressure
- V₂ = Final volume
- T₂ = Final absolute temperature (in Kelvin)
Important Note: Always remember to convert temperatures from Celsius to Kelvin using the formula: K = °C + 273.15. Failing to do this will lead to inaccurate calculations.
Why is the combined gas law important?
The combined gas law is essential because it allows us to predict the behavior of gases under various conditions. This is crucial in numerous applications, including:
- Meteorology: Predicting weather patterns based on changes in atmospheric pressure, temperature, and volume.
- Engineering: Designing systems involving gas compression or expansion, such as engines and refrigeration systems.
- Chemistry: Understanding reaction rates and equilibrium conditions involving gaseous reactants and products.
How to use the combined gas law formula?
Solving problems using the combined gas law involves identifying the known variables and solving for the unknown variable. Here's a step-by-step approach:
- Identify the known variables: Determine the values of P₁, V₁, T₁, P₂, V₂, and T₂ from the problem statement.
- Convert temperatures to Kelvin: If temperatures are given in Celsius, convert them to Kelvin.
- Substitute the known values into the combined gas law formula: Plug the known values into the equation (P₁V₁)/T₁ = (P₂V₂)/T₂.
- Solve for the unknown variable: Rearrange the equation to isolate the unknown variable and solve.
What are some common mistakes to avoid when using the combined gas law?
- Not converting to Kelvin: Always remember to convert temperatures to Kelvin.
- Incorrect unit conversions: Ensure consistent units throughout the calculation (e.g., Pascals for pressure, Liters for volume).
- Algebraic errors: Double-check your algebraic manipulations when rearranging the equation.
Solved Examples:
Let's work through a couple of examples to solidify your understanding.
Example 1: A gas sample has a volume of 2.00 L at a pressure of 1.00 atm and a temperature of 25°C. What will be its volume if the pressure is increased to 2.00 atm and the temperature is increased to 50°C?
-
Known variables:
- P₁ = 1.00 atm
- V₁ = 2.00 L
- T₁ = 25°C + 273.15 = 298.15 K
- P₂ = 2.00 atm
- T₂ = 50°C + 273.15 = 323.15 K
- V₂ = ?
-
Solve for V₂: Rearranging the combined gas law equation to solve for V₂, we get:
V₂ = (P₁V₁T₂)/(P₂T₁) = (1.00 atm * 2.00 L * 323.15 K) / (2.00 atm * 298.15 K) = 1.08 L
Therefore, the final volume will be approximately 1.08 L.
Example 2: A gas occupies 5.00 L at 20°C and 1.5 atm. If the temperature is changed to 40°C and the volume to 10.0 L, what will the new pressure be?
This example is left as an exercise for the reader. Try solving it using the steps outlined above. Remember to convert temperatures to Kelvin. The answer should be approximately 0.75 atm.
By understanding the combined gas law and practicing with examples, you can confidently tackle any worksheet or real-world problem involving the behavior of gases. Remember to always pay attention to units and temperature conversions!
