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Match each gas law in List I with its correct mathematical expression(s) in List II. List I: (P) Boyle's law, (Q) Charles's law, (R) Avogadro's law, (S) Graham's law. List II: (1) (dP/dV)_T = -P/V, (2) (dV/dT)_P = V/T, (3) [d(PV)/dP]_T = 0, (4) (dV/dn)_(P,T) = RT/P, (5) -dP/dt = k / sqrt(d).

1. P -> 3; Q -> 1,2; R -> 5; S -> 4
2. P -> 2; Q -> 3,5; R -> 4; S -> 1
3. P -> 1,3; Q -> 2; R -> 4; S -> 5
4. P -> 3,5; Q -> 4; R -> 1; S -> 2

Correct answer: P -> 1,3; Q -> 2; R -> 4; S -> 5

Solution

P (Boyle): PV=C at const T. Differentiate: V+P(dV/dP)=0 => dP/dV=-P/V (expression 1). Also d(PV)/dP=0 (expression 3). P->1,3. Q (Charles): V=CT at const P => dV/dT=V/T (expression 2). Q->2. R (Avogadro): V=nRT/P => dV/dn=RT/P (expression 4). R->4. S (Graham): rate of effusion ∝ 1/sqrt(d), written as -dP/dt=k/sqrt(d) (expression 5). S->5. Answer: option C.

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