Which proportionality applies to Avogadro's law?


A$V \propto \frac{1}{P}$
B$V \propto T$
C$P \propto T$
D$V \propto n$

Verified Answer :

  • Avogadro's Law describes the relationship between the volume \(V\) and the number of moles \(n\) of a gas at constant temperature and pressure.
  • Comparing the given options: Boyle's Law is \(V \propto 1/P\), Charles's Law is \(V \propto T\), and Gay-Lussac's Law is \(P \propto T\).
  • Avogadro's Law is correctly stated as the direct proportionality \(V \propto n\).
  • The correct proportionality is \(\boxed{V \propto n}\).

Explanation

  1. Analysis of Avogadro's Law

Avogadro's law is a fundamental principle in chemistry that relates the volume of a gas to the amount of substance (number of moles) of that gas. The law states that, under constant temperature and pressure conditions, the volume \(V\) of a gas is directly proportional to the quantity of gas, expressed in moles \(n\). This can be mathematically represented as \(V \propto n\), or \(V = kn\) for some constant \(k\).

  1. Evaluation of Options

We evaluate the given options to identify which one corresponds to Avogadro's law:

  1. \(V \propto \frac{1}{P}\): This represents Boyle's Law, which states that at constant temperature, the volume of a given mass of gas is inversely proportional to its pressure.
  2. \(V \propto T\): This represents Charles's Law, which states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.
  3. \(P \propto T\): This represents Gay-Lussac's Law, which states that at constant volume, the pressure of a given mass of gas is directly proportional to its absolute temperature.
  4. \(V \propto n\): This represents Avogadro's Law, which relates the volume and the amount of substance (number of moles).
  1. Conclusion

Based on the definitions of the gas laws, the proportionality \(V \propto n\) is the correct representation of Avogadro's Law. Therefore, the final answer is \(V \propto n\).

Examples

Imagine you are inflating a balloon for a party. According to Avogadro's Law, as you breathe more air (more moles of gas molecules, \(n\)) into the balloon while the pressure and temperature remain relatively constant, the balloon expands to a larger volume (\(V\)). This direct relationship explains why adding more gas molecules consistently results in an increase in the volume occupied by the gas.