When we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding. Consider the diffusion constant that appears in Fick's first law:
J= -Ddn/dx
In this expression, J represents a flow of particles: number of particles per unit area per second, n represents a concentration of particles: number of particles per unit volume; and x represents a distance. We can assume that they have the following dimensionalities:
[J] = 1/L2T
[n] = 1/L3
[x] = L
Required:
From this, determine the dimensionality of D.
Answers: 1
![[J] = \frac{1}{L^2 T}](/tpl/images/0806/8188/0107d.png)
![[n] =\frac{1}{L^3}](/tpl/images/0806/8188/7ef2c.png)
![[x] = L](/tpl/images/0806/8188/a9174.png)
![\frac{1}{L^2 T} = -D \frac{d(\frac{1}{L^3})}{d[L]}](/tpl/images/0806/8188/f5d32.png)
![\frac{1}{L^2 T} = -D \frac{(\frac{1}{L^3})}{[L]}](/tpl/images/0806/8188/42ff8.png)
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