Let's examine each option to determine which proportionality applies to Avogadro's law.
1. [tex]$V \propto \frac{1}{\rho}$[/tex]:
- This statement suggests that the volume (V) is inversely proportional to the density ([tex]$\rho$[/tex]).
- Avogadro's law does not deal with the relationship between volume and density.
2. [tex]$V \propto T$[/tex]:
- This statement suggests that the volume (V) is directly proportional to the temperature (T).
- This is actually Charles's law, which states that the volume of a gas is directly proportional to its temperature, provided the pressure remains constant.
3. [tex]$P \propto T$[/tex]:
- This statement suggests that the pressure (P) is directly proportional to the temperature (T).
- This is Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature, provided the volume remains constant.
4. [tex]$V \propto n$[/tex]:
- This statement suggests that the volume (V) is directly proportional to the number of moles of gas (n).
- Avogadro's law states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present. This means that if you increase the number of moles of gas, the volume will also increase, assuming the temperature and pressure remain constant.
Given these considerations, the correct proportionality according to Avogadro's law is:
[tex]\[ V \propto n \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{V \propto n} \][/tex]
