To determine which proportionality applies to Avogadro's law, we need to understand Avogadro's law and its implications.
Avogadro's law states that, for a given mass of an ideal gas at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of the gas. In mathematical terms, this law is expressed as:
[tex]\[ V \propto n \][/tex]
Here's the breakdown of the options given:
1. [tex]\( V \propto \frac{1}{\rho} \)[/tex]:
This suggests that the volume is inversely proportional to the density of the gas. This is not a statement of Avogadro's law.
2. [tex]\( V \propto T \)[/tex]:
This suggests that the volume is directly proportional to the temperature of the gas. This is related to Charles's law, not Avogadro's law.
3. [tex]\( P \propto T \)[/tex]:
This implies that the pressure is directly proportional to the temperature. This is related to Gay-Lussac's law, not Avogadro's law.
4. [tex]\( V \propto n \)[/tex]:
This means that the volume is directly proportional to the number of moles of gas. This is precisely the statement of Avogadro's law.
Given these options, the correct proportionality that applies to Avogadro's law is:
[tex]\[ V \propto n \][/tex]
Therefore, the correct answer is:
[tex]\[ 4 \][/tex]
