Question

A gas diffuse 1/5 times as fast as hydrogen its molecular weight is?

Answer 1

The molecular weight of a gas that diffuses 1/5 times as fast as hydrogen, with a molecular weight of 2.0 g/mol, is 50.0 g/mol according to Graham's Law of Effusion.

Step-by-step explanation:

The question relates to 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. Applying this law, we can determine the molecular weight of a gas that diffuses 1/5 times as fast as hydrogen (H₂) whose molecular weight is approximately 2.0 g/mol. Using the formula:

Rate of Gas1 / Rate of Gas2 = SQRT(Molecular Weight of Gas2 / Molecular Weight of Gas1)

If Gas1 is hydrogen and Gas2 is the unknown gas, we can plug in the known values:

(1/1) / (1/5) = SQRT(Molecular Weight of Gas2 / 2.0)

This simplifies to:

5 = SQRT(Molecular Weight of Gas2 / 2.0)

Squaring both sides gives us:

25 = Molecular Weight of Gas2 / 2.0

Therefore, the Molecular Weight of Gas2 = 25 * 2.0 = 50.0 g/mol.

Answer 2

Using Graham's law of effusion, the molecular weight of a gas that diffuses 1/5 times as fast as hydrogen is found to be 50.0 g/mol.

Step-by-step explanation:

The student's question involves finding the molecular weight of a gas that diffuses 1/5 times as fast as hydrogen. We can use Graham's law of effusion to solve this problem:

Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this can be represented as:

Rate of effusion of Gas 1 / Rate of effusion of Gas 2 = sqrt(Molar mass of Gas 2 / Molar mass of Gas 1)

If the unknown gas diffuses 1/5 as fast as hydrogen, and the molar mass of hydrogen (¹H₂) is 2.0 g/mol, then:

(1/5) = sqrt(Molar mass of unknown gas / 2.0 g/mol)

Squaring both sides, we get:

(1/25) = Molar mass of unknown gas / 2.0 g/mol

Thus, the molar mass of the unknown gas is 2.0 g/mol × 25, which equals to 50.0 g/mol.

Therefore, the molecular weight of the gas that diffuses 1/5 times as fast as hydrogen is 50.0 g/mol.