Avogadro's law states that under constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas.

What is the relationship consistent with this statement?

Question

Avogadro's law states that under constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas.

What is the relationship consistent with this statement?

BlackTom AI · Accepted Answer

Question restatement: Avogadro's law says that, at constant temperature and pressure, the volume of a gas is directly proportional to the amount (moles) of gas, n. Which relationship among the options is consistent with this statement?

Option 1: T1V1 = T2V2. This equation mixes temperature and volume in a way that suggests a direct product of T and V remaining constant, which is not a standard expression of Avogadro’s law. It resembles a misapplied form of a gas-law relationship and does not isolate the dependence on n alone at fixed T and P.

Option 2: V1T1 = V2T2. Here, volume times temperature is stated to be conserved across two states. This would imply a specific coupling between V and T, but Avogadro’s law keeps T fixed, and the key proportionality is between V and n, not V and T. Therefore, this option does not capture the idea that V scales with n when T and P are constant.

Option 3: P1V1 = P2V2. This is Boyle’s law, which holds n constant and relates pressure and volume at fixed temperature. It directly contradicts Avogadro’s condition, since Avogadro’s law requires variation with n at constant T and P, not a fixed n scenario with P and V trade-off.

Option 4: P1V1 = P2V2. As written, this repeats Boyle’s law and similarly fails to express the V-n proportionality under constant T and P. It does not reflect that increasing moles at the same T and P should increase V rather than keep the product P·V constant for a changing n.

Option 5: n1V1 = n2V2. This form asserts that the product of n and V remains proportional across two states, which is a rearrangement of V ∝ n when T and P are fixed. It conveys that increasing the number of moles leads to a proportional increase in volume, aligning with Avogadro’s law.

Option 6: n1V1 = n2V2. This is the same relationship as Option 5, just presented with a different typographical rendering. Since it expresses the same proportionality between n and V under constant T and P, it is also consistent with Avogadro’s law.

In summary, the options that reflect the core idea of Avogadro’s law are those that tie volume directly to the amount of substance n when temperature and pressure are held constant. The options invoking temperature–volume products or Boyle’s law describe different gas relationships and do not match the Avogadro principle. The two n1V1 = n2V2 formulations both express the intended proportionality between V and n under fixed T and P, while the others mischaracterize the dependence or describe a different gas law.

Avogadro's law states that under constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. What is the relationship consistent with this statement?单项选择题

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