Ideal Gas Law Applications: Relationships and Graphs

Ideal Gas Law Applications

Introduction

The Ideal Gas Law is a fundamental equation in chemistry that describes the relationship between pressure, volume, temperature, and the number of moles of a gas. Understanding how these variables interact allows us to predict the behavior of gases under different conditions.

Ideal Gas Law Formula

• Formula: $PV = nRT$

• P = Pressure (usually in atm or Pa)

• V = Volume (usually in liters)

• n = Number of moles of gas

• R = Universal gas constant ($0.0821$ L·atm/(mol·K) or $8.314$ J/(mol·K))

• T = Temperature (in Kelvin)

Variable Relationships

By rearranging the Ideal Gas Law, we can determine how changing one variable affects another, assuming the rest are held constant.

Variables	Relationship
P & V	Inversely proportional
P & T	Directly proportional
V & T	Directly proportional
V & n	Directly proportional
P & n	Directly proportional

Variables Chart

The chart below summarizes how each variable changes when another is increased, assuming all other variables are held constant:

	P	V	n	T
P	-	down	up	up
V	down	-	up	up

Additional info: The chart shows that increasing the number of moles (n) or temperature (T) increases both pressure (P) and volume (V), while increasing pressure decreases volume and vice versa.

Example Problem

Question: If the number of moles (n) inside a container were tripled while keeping the pressure (P) constant, what will happen to the volume (V)?

• a) It will remain the same

• b) It will be cut by a third

• c) It will triple (correct answer)

• d) It will double

Explanation: According to the Ideal Gas Law, if pressure and temperature are constant, volume is directly proportional to the number of moles. Tripling the moles will triple the volume.

Graphical Relationships

The relationship between the partial pressure of a gas (P) and the number of moles of that gas (n) can be represented graphically. The correct graph shows a direct linear relationship:

• Graph A: Shows an inverse relationship (not correct for P vs. n)

• Graph B: Shows a direct linear relationship (correct for P vs. n)

• Graph C: Shows no relationship (not correct)

Correct graph: Graph B, where pressure increases linearly with the number of moles.

Key Terms

• Directly proportional: When one variable increases, the other increases at a constant rate.

• Inversely proportional: When one variable increases, the other decreases.

• Partial pressure: The pressure exerted by a single component of a gas mixture.