Question

You can smell perfume very shortly after opening the bottle. To show that it is not reaching your nose by diffusion, calculate the average distance a perfume molecule moves in one second in air, given its diffusion constant (D) to be (1.00 times 10⁶ m²/s).

A) (0.01 m)
B) (0.03 m)
C) (0.1 m)
D) (0.3 m)

Answer 1

Using the equation for diffusion (Xrms = √(2Dt)), the average distance a perfume molecule travels by diffusion in one second in air is approximately 1.4 mm. This is much less than the distances provided in the options, showing that diffusion is not the sole means by which smell is detected quickly.

Step-by-step explanation:

To calculate the average distance a perfume molecule travels in one second in air by diffusion, we use the equation Xrms = √(2Dt), where D is the diffusion constant and t is the time in seconds. In this case, the diffusion constant D is given as 1.00 × 10-6 m2/s and the time t is 1 second. Plugging in these values, we get:

Xrms = √(2 × 1.00 × 10-6 m2/s × 1s)

Xrms = √(2 × 10-6 m2/s)

Xrms = √(2 × 10-6)

Xrms = √(2 × 10-6) m

Xrms = √(2 × 10-6) m ≈ 0.0014 m or 1.4 mm

This calculation shows that the average distance a perfume molecule travels by diffusion in one second is far less than any of the options given (A) 0.01 m, (B) 0.03 m, (C) 0.1 m, or (D) 0.3 m, indicating that smell is detected much more rapidly by a process other than diffusion over large distances.