Question

6. Consider the following: C2H6, SiF4, Cl2, and Ne.
   (a) Which one will diffuse the fastest?
   (b) What is the rms speed (m/s) of the slowest-moving atom or molecule at 25°C?

Answer 1

The expression for v_rms is:

v_rms = [3RT/M]^1/2 Here M is the molar mass of Gas and T is temperature

Since the rate of diffusion is directly proportional to v_rms. Since the temperature is same for all, The diffusion is inversely proportional to square root of the Molar mass.

Molar mass of C₂H₆ = 30

Molar mass of SiF₄ = 104

Molar mass of Cl₂ = 71

Molar mass of Ne = 20

Since Ne has the lowest molar mass it diffuses the fastest.

(b) Since we've determined that a higher molar mass leads to slower molecule, SiF₄ is the slowest in this set of gases. Using the expression for v_rms :

v_rms = [3RT/M]^1/2

= [3*8.314 * 298 / 104]^1/2 = 8.45 m/s