Let's go through each statement carefully to determine its correctness:
Statement a:
"The rate at which gases diffuse is inversely proportional to the square root of their densities."
This is a correct statement and it refers to Graham's Law of Diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its density. Mathematically, it can be expressed as:
[tex]\[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{density}}} \][/tex]
Statement b:
"The rate of effusion of a gas is inversely proportional to the square root of either the density or the molar mass of the gas."
This is also correct and aligns with Graham's Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Since density and molar mass are related (density is mass per unit volume and molar mass is the mass of one mole of gas), the statement holds true. Mathematically, it is expressed as:
[tex]\[ \text{Rate of effusion} \propto \frac{1}{\sqrt{\text{molar mass}}} \][/tex]
Statement c:
"Light gases effuse or diffuse quickly and heavier gases effuse or diffuse slowly."
This is a correct observation and is a direct consequence of Graham’s Laws. Light gases, having lower molar mass and density, will diffuse and effuse more quickly than heavier gases. This is because the rate of diffusion and effusion is higher for gases with lower molar mass or density.
Statement d:
"All of the above."
Based on the analysis of statements a, b, and c, we see that each of them is correct.
Therefore, the correct choice is:
4 (d) All of the above.
