The Combined Gas Law
The Combined Gas Law Calculator is an essential tool that simplifies calculations involving pressure, volume, and temperature changes of a gas. It allows you to find any unknown variable—whether it’s the initial or final volume, pressure, or temperature—when the other variables are known. The calculator also automatically converts any entered units to SI units before performing the calculation, ensuring accurate results in standard units.
What is the Combined Gas Law?
The Combined Gas Law combines three fundamental gas laws: Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law. It relates pressure, volume, and temperature of a fixed amount of gas, providing a way to predict how a gas behaves when subjected to changes in these conditions. The Combined Gas Law formula is expressed as:
\[\frac{P_1 \cdot V_1}{T_1} = \frac{P_2 \cdot V_2}{T_2}\]
where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( T_1 \) is the initial temperature,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume,
- \( T_2 \) is the final temperature.
How to Use the Combined Gas Law Calculator
- Enter Known Variables: Input the initial and/or final values for pressure, volume, and temperature as needed. The calculator supports different units for these inputs and will automatically convert them to SI units.
- Select the Unknown Variable: Choose which variable you want to solve for—whether it’s the final pressure \( P_2 \), final volume \( V_2 \), or another variable.
- Calculate: Click “Calculate” to get the result in SI units.
The calculator makes it easy to explore how changes in one factor, such as volume, will affect other factors like pressure or temperature.
Example Calculation Using the Combined Gas Law
Example Problem
Suppose a gas has an initial volume \( V_1 = 2.0 \, \text{L} \), an initial pressure \( P_1 = 1.0 \, \text{atm} \), and an initial temperature \( T_1 = 300 \, \text{K} \). The gas is then compressed to a final volume \( V_2 = 1.5 \, \text{L} \) at a final temperature of \( T_2 = 350 \, \text{K} \). What is the final pressure \( P_2 \) of the gas?
Solution
Using the Combined Gas Law:
\[\frac{P_1 \cdot V_1}{T_1} = \frac{P_2 \cdot V_2}{T_2}\]
Rearrange to solve for \( P_2 \):
\[P_2 = \frac{P_1 \cdot V_1 \cdot T_2}{V_2 \cdot T_1}\]
Substitute the values:
\[P_2 = \frac{1.0 \, \text{atm} \cdot 2.0 \, \text{L} \cdot 350 \, \text{K}}{1.5 \, \text{L} \cdot 300 \, \text{K}}\]
Calculating:
\[P_2 = \frac{700}{450} = 1.56 \, \text{atm}\]
So, the final pressure \( P_2 \) is 1.56 atm.
Practical Applications of the Combined Gas Law
The Combined Gas Law is widely used in situations where gases are stored under varying conditions or when they’re subjected to environmental changes. It’s commonly applied in fields such as:
- Chemistry: Studying reactions in closed systems with varying temperatures and pressures.
- Physics: Understanding the behavior of gases under different physical conditions.
- Engineering: Designing systems like pressurized containers, pneumatic devices, and HVAC systems.
