Avogadro’s law — statement check: “Equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules.” Is this statement (Avogadro’s law) correct?

Introduction / Context:
Avogadro’s law underpins the concept of molar volume of gases and the equivalence between volume ratios and mole ratios under identical temperature and pressure. It is a cornerstone for stoichiometry and gas-mixture calculations.

Given Data / Assumptions:

• Ideal-gas behavior at the same temperature and pressure.
• Equal volumes are being compared.
• Fixed overall conditions across samples.

Concept / Approach:
If T and p are equal, the ideal-gas law pV = nRT shows V ∝ n. Therefore, equal volumes correspond to equal moles n, which implies equal numbers of molecules (since molecules = n * N_A, with N_A Avogadro’s number). This is the content of Avogadro’s law.

Step-by-Step Solution:
Write ideal-gas relation: pV = nRT with T and p equal for both samples.Rearrange: V = (nR/ p) * T ⇒ V ∝ n.Hence equal V implies equal n and therefore equal number of molecules.

Verification / Alternative check:
Molar volume at standard temperature and pressure (STP) is approximately 22.414 L per mole (idealized), illustrating the law’s practical use.

Why Other Options Are Wrong:
Marking “False” would contradict the ideal-gas model and widespread experimental validation under dilute conditions.

Common Pitfalls:
Extending the law to high-pressure or highly non-ideal regimes without corrections; forgetting it applies to gases, not liquids/solids.

Final Answer:
True