Combined Gas Law Calculator

What is the Combined Gas Law?

The Combined Gas Law is a fundamental principle in chemistry that describes the relationship between pressure, volume, and temperature of a fixed amount of gas. It combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single equation, allowing us to predict how these variables change when two or more of them are altered simultaneously.

How to Calculate Using the Combined Gas Law

To use the Combined Gas Law in calculations, follow these steps:

1. Identify the initial conditions (pressure, volume, and temperature)
2. Determine the final conditions (known and unknown variables)
3. Apply the Combined Gas Law equation
4. Solve for the unknown variable

Formula

The Combined Gas Law is expressed mathematically as:

\[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \]

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

Calculation Steps

Let's calculate the final volume when pressure and temperature change, given:

• Initial pressure (P₁) = 1.0 atm
• Initial volume (V₁) = 2.0 L
• Initial temperature (T₁) = 300 K
• Final pressure (P₂) = 2.0 atm
• Final temperature (T₂) = 400 K

1. Apply the Combined Gas Law equation: \[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \]
2. Substitute known values: \[ \frac{(1.0 \text{ atm})(2.0 \text{ L})}{300 \text{ K}} = \frac{(2.0 \text{ atm})V_2}{400 \text{ K}} \]
3. Solve for V₂: \[ V_2 = \frac{(1.0 \text{ atm})(2.0 \text{ L})(400 \text{ K})}{(2.0 \text{ atm})(300 \text{ K})} = 1.33 \text{ L} \]

Example and Visual Representation

Let's visualize the Combined Gas Law with our example:

This visual representation shows:

• The initial state with a larger volume, lower pressure, and lower temperature
• The final state with a smaller volume, higher pressure, and higher temperature
• The relationship between pressure, volume, and temperature as described by the Combined Gas Law

This example demonstrates how the Combined Gas Law governs the behavior of gases, showing how pressure, volume, and temperature are interrelated. When pressure increases and temperature rises, the volume decreases to maintain the equality of the Combined Gas Law equation.