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?

(rate1/rate2) = sqrt(M2/M1)

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

The equation for Graham's Law is:

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

In this case, we are given the rates of diffusion for neon (Rate1 = 7.0 cm/s) and the unknown gas (Rate2 = 4.9 cm/s). We are looking for the molar mass of the unknown gas (Molar mass2).

Now let's rearrange the equation to solve for Molar mass2:

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

Squaring both sides of the equation:

(Molar mass2 / Molar mass1) = (Rate1 / Rate2)^2

Now we can substitute the values into the equation:

(Molar mass2 / Molar mass neon) = (7.0 cm/s / 4.9 cm/s)^2

Simplifying the equation:

(Molar mass2 / 20.18 g/mol) = (1.43)^2

(Molar mass2 / 20.18 g/mol) = 2.0449

Now we can solve for Molar mass2:

Molar mass2 = 2.0449 * 20.18 g/mol

Molar mass2 ≈ 41.15 g/mol

Therefore, the approximate molar mass of the unknown gas is approximately 41.15 g/mol.