The general gas equation $\frac{PV}{T}$ = K is a combination of

Step 1: Analyze the question The question asks which two gas laws combine to give the general gas equation PV/T = K (a constant).

Step 2: Explain the concepts

• Boyle's law: At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure. V ∝ 1/P, so PV = constant (when T is constant).

• Charles' law: At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. V ∝ T, so V/T = constant (when P is constant).

• Graham's law: The rate of diffusion of a gas is inversely proportional to the square root of its density (or molar mass). It deals with diffusion, not with P, V and T together.

• Dalton's law: The total pressure of a mixture of gases is the sum of the partial pressures of the individual gases. It deals with gas mixtures.

Step 3: Show the solution

Combine the two laws for a fixed mass of gas:

• From Boyle's law: V ∝ 1/P
• From Charles' law: V ∝ T

Joining the two proportionalities:

V ∝ T/P

Introducing a constant K:

V = K(T/P)

Rearranging:

PV/T = K

This is the combined (general) gas equation. Only Boyle's and Charles' laws are involved. Graham's and Dalton's laws have nothing to do with the relationship among P, V and T for a fixed mass of gas.

Step 4: Identify the answer The correct option is A. Boyle's and Charles' laws.

Step 5: Exam tip Remember that the general gas equation comes from the laws that involve P, V and T:

• Boyle: P and V
• Charles: V and T
• (Pressure law: P and T)

Whenever you see "Graham", think diffusion, and when you see "Dalton", think partial pressures. You can eliminate any option containing either of them straight away.