Gas Laws

To solve this problem, we will use Graham's Law of Diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, Graham's Law is expressed as:

where:

• and are the rates of diffusion of gases 1 and 2, respectively,
• and are the molar masses of gases 1 and 2, respectively.

Step 1: Identify the gases and their molar masses

• Gas 1: (sulfur dioxide), with molar mass .
• Gas 2: Another gas, with molar mass .

Step 2: Express the rates of diffusion The rate of diffusion is given by the volume of gas diffused per unit time:

where:

• is the volume of gas diffused,
• is the time taken for diffusion.

For :

For the other gas:

Step 3: Apply Graham's Law Using Graham's Law:

Substitute the expressions for and :

Simplify the left-hand side:

Simplify the right-hand side:

Thus:

Step 4: Solve for the ratio Cross-multiply:

Divide both sides by 2:

Rearrange to find the ratio :

Final Answer: The ratio of to is:

Henry's law states that the amount of gas that dissolves in a liquid is proportional to the partial pressure of the gas above the liquid, expressed as: Where: - is the concentration of the gas in the liquid,
- is the Henry’s law constant,
- is the partial pressure of the gas.
For gases dissolved in water, the Henry’s law constant is inversely proportional to the solubility of the gas in water. A higher Henry's law constant indicates that the gas is less soluble in water.
Among the given gases, helium ( ) has the highest Henry’s law constant because it is less soluble in water compared to the other gases listed (like , , and ).
Therefore, the correct answer is helium ( ).