The Ideal Gas Equation: Overview

Recall: Which set of fundamental gas laws is combined to derive the Ideal Gas Equation PV = nRT?

• Boyle’s, Charles’s, and Avogadro’s Laws

• Gay-Lussac’s, Dalton’s, and Graham’s Laws

• Henry’s, Raoult’s, and Le Chatelier’s Laws

Skill/Concept: Using the stated formula for molar mass from the Ideal Gas Law, what is the expression for molar mass M in terms of measured pressure P, volume V, temperature T, and number of moles n? Provide the exact form given.

Skill/Concept: According to the overview, which equation would you use to compute the density d of a gas from its pressure P, molar mass M, and temperature T? Choose the exact expression presented.

• d = PM/RT

• d = RT/PM

• d = PRT/M

Strategic Thinking: Explain why real gases deviate from ideal behavior at high pressures and low temperatures, and identify how the Van der Waals equation corrects for these deviations.

Recall/Application: Which statement best describes a real-life application of the Ideal Gas Law mentioned in the overview?

• Understanding air pressure in tires, scuba tanks, and LPG systems

• Predicting phase diagrams for solids

• Determining electron configurations in atoms

• Modeling nuclear decay chains

Refer to the four small graphs of gas laws: Boyle’s Law (P vs. V, hyperbolic), Charles’s Law (V vs. T, straight line), Gay-Lussac’s Law (P vs. T, straight line), and Avogadro’s Law (V vs. n, straight line). Which relationship is correctly described as an inverse relationship?

• Charles’s Law: volume vs. temperature

• Gay-Lussac’s Law: pressure vs. temperature

• Avogadro’s Law: volume vs. moles

• Boyle’s Law: pressure vs. volume

At constant pressure, the volume of a gas is directly proportional to its absolute temperature. Which equation form captures this statement using a proportionality constant?

• PV = k1

• V/T = k2

• P/T = k3

• Vn = k4

State the universal gas constant R commonly used with pressure in atm and volume in liters.

A 2.5 mol sample of an ideal gas occupies 10 L at 27°C. Using R = 0.0821 L·atm/mol·K, what is the pressure? Show your reasoning.

Which combination of fundamental gas-law proportionalities leads to V ∝ nT/P before introducing the constant R?

• P ∝ 1/V, V ∝ T, V ∝ n

• P ∝ V, V ∝ 1/T, V ∝ 1/n

• P ∝ T, V ∝ 1/T, n ∝ 1/P

• P ∝ 1/V only