Question

A common small-molecular weight (and therefore fast diffusing for an organic molecule) ingredient in perfumes is vanillin, the primary component of vanilla bean extract (molecular weight = 152). the d for vanillin in air is 0.114 cm2/s. if i open a bottle of vanilla on the other side of the room 3 meters away, and the air is still so there is no convection, about how long would i have to wait before i could expect to smell the vanilla?

Answer 1

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Answer 2

Answer:

2.54 seconds

Explanation:

Gathering the data:

let molecular weight = 152 g/mol

diffusion coefficient = 0.114 cm²/s

Distance = 3 meters

The most important thing to know is Fick's Law of diffusion. The law states that the flux is directly proportional to the concentration gradient. In other words

where dc = change in concentration

            D = diffusion coefficient

            Dx = change in the distance, cm

solving:

j = dc/3 (-0.114)

 this gives t = 2.54 seconds