Question

SO₂ and CH₄ are introduced in a vessel in the molar ratio 1:2 . The ratio of molecules of two gases present in the container when their rate of effusion becomes equal is :

A. 1:2
B. 2:1
C. 4:1
D. 1:4

Answer 1

Using Graham's Law of Effusion, the ratio of molecules of SO₂ to CH₄ when their rate of effusion becomes equal is determined to be 1:4, which corresponds to answer option D.

Step-by-step explanation:

The question involves the application of 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.

If SO₂ and CH₄ are introduced in a vessel in the molar ratio 1:2 and their rate of effusion becomes equal, we can set up the following proportion using Graham's Law:∙

(Rate of effusion of SO₂ / Rate of effusion of CH₄) = (√(Molar mass of CH₄) / √(Molar mass of SO₂))

Since the rates are equal, the ratio would be 1, and given that the molar mass of SO₂ (64 g/mol) and CH₄ (16 g/mol), the equation simplifies to:

1 = √(16 g/mol) / √(64 g/mol)

1 = (√16) / (√64)

1 = 4 / 8

1 = 1 / 2

Thus, for every one molecule of SO₂, there are two molecules of CH₄. Therefore, even though the molar ratio of introduction into the vessel was 1:2, the ratio of molecules when their rates of effusion become equal is actually 1:4. The correct option is D. 1:4.