Under certain conditions, neon (Ne) gas diffuses at a rate of 7.0 centimeters per second. Under the same conditions, an unknown gas diffuses at a rate of 4.9 centimeters per second. What is the approximate molar mass of the unknown gas?

6.5 g/mol

11 g/mol

20 g/mol

41 g/mol

Are omitting the word cubic from cubic centimeters. 7 cm/sec and 7 cc/sec are two different rates.

41

To find the approximate molar mass of the unknown gas, you can use Graham's Law of Diffusion. This law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

Mathematically, Graham's Law can be represented as:

Rate₁/Rate₂ = √(Molar mass₂/Molar mass₁)

In this case, we are comparing the rate of diffusion of the unknown gas (Rate₂ = 4.9 cm/s) to the rate of diffusion of neon gas (Rate₁ = 7.0 cm/s).

So, plugging the given values into the equation, we get:

4.9/7.0 = √(Molar mass of Neon/Molar mass of the unknown gas)

Now, let's solve for the molar mass of the unknown gas:

(Molar mass of Neon/Molar mass of the unknown gas) = (4.9/7.0)²

Molar mass of the unknown gas = (Molar mass of Neon) / ((4.9/7.0)²)

Now, let's substitute the known values:

Molar mass of the unknown gas = (20.18 g/mol) / ((4.9/7.0)²)

Calculating this, we find:

Molar mass of the unknown gas ≈ 41 g/mol

Therefore, the approximate molar mass of the unknown gas is 41 g/mol.