The Ideal Gas Law is expressed mathematically as

Analyze the question: You're asked for the mathematical expression of the Ideal Gas Law, the equation that links pressure, volume, temperature and amount of gas in a single relationship.

Concept: The ideal gas law combines the individual gas laws:

• Boyle's law: P ∝ 1/V (at constant T and n)
• Charles's law: V ∝ T (at constant P and n)
• Pressure (Gay-Lussac's) law: P ∝ T (at constant V and n)
• Avogadro's law: V ∝ n (at constant P and T)

Combining these gives V ∝ nT/P, which becomes

PV = nRT

where:

• P = pressure
• V = volume
• n = number of moles
• R = universal gas constant (8.314 J mol⁻¹ K⁻¹)
• T = absolute temperature in kelvin

Checking each option:

• A. P₁/T₁ = P₂/T₂: This is the pressure (Gay-Lussac's) law, which holds at constant volume. It is not the general law.
• B. P₁/V₁ = P₂V₂: This is incorrect. Boyle's law is P₁V₁ = P₂V₂.
• C. PV = nRT: This is the Ideal Gas Law. ✔
• D. PV = KT: This is not the standard form. K would have to be nR, and the law is not normally written this way. It is only valid for a fixed amount of gas.
• E. V₁/T₁ = V₂/T₂: This is Charles's law, which holds at constant pressure.

Exam tip: Remember the phrase "PiVNRT" (like "pivnert"): P V = n R T. Also, when a question gives two sets of conditions, such as P₁, T₁ and P₂, T₂, it is usually a specific gas law. When it gives n and R, it is the Ideal Gas Law. Always convert temperature to kelvin (°C + 273) before calculating.