Q.What is PV = nRT? Write it and prove it. OR Define the following:

PV = nRT (the ideal gas equation) combines three separate experimental gas laws — Boyle's law (V proportional to 1/P), Charles's law (V proportional to T), and Avogadro's law (V proportional to n) — into a single equation of state for an ideal gas.

PV = nRT relates the four macroscopic properties of a fixed sample of ideal gas: pressure P, volume V, number of moles n, and absolute temperature T, through the universal gas constant R.

Derivation (combining the individual gas laws):

Boyle's Law: at constant T and n, V is inversely proportional to P: V proportional to 1/P.

Charles's Law: at constant P and n, V is directly proportional to T: V proportional to T.

Avogadro's Law: at constant T and P, V is directly proportional to the number of moles n: V proportional to n.

Combining all three proportionalities (since each holds independently of the others):

V proportional to (n T / P)

Introducing a constant of proportionality R (the universal gas constant) to convert this into an equation:

V = R (n T / P)

Rearranging:

PV = nRT

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