Physical Chemistry Third Edition

10.2 Transport Processes 447

equal to 10−^9 m^2 s−^1  10 −^5 cm^2 s−^1. Diffusion coefficients for gases are somewhat

larger than this value and are more variable in size, and those for solids are much

smaller. Diffusion of one solid into another occurs only if the solids are soluble in each

other. For example, if finely machined blocks of gold and silver are clamped together

and left for several years at room temperature, a significant amount of each substance

will diffuse into the other.

EXAMPLE10.3

Calculate the value of the steady-state diffusion flux of sucrose in water at 25◦C if the

concentration of sucrose at the top of a cell of height 0.100 m is maintained at 0.060 mol L−^1

and at the bottom of the cell is maintained at 0.0300 mol L−^1.

Solution

From Table A.17 of Appendix A,

D 0. 5226 × 10 −^9 m^2 s−^1

JzD

∂c

∂z

≈D

∆c

∆z

(0. 5226 × 10 −^9 m^2 s−^1 )

(

0 .0300 mol L−^1

0 .100 m

)(

1000 L

1m^3

)

≈− 1. 57 × 10 −^7 mol m−^2 s−^1 − 1. 57 × 10 −^11 mol cm−^2 s−^1

The Equation of Continuity

We now derive a one-dimensional version of the equation of continuity. Consider a thin

horizontal slab in a fluid system in which properties depend on the vertical coordinate

zbut not onxory, as depicted in Figure 10.2.

System in which

diffusion occurs

“Slab”

bounded by

imaginary

planes

x

z

y

Figure 10.2 A Slab-Shaped Portion of a Fluid System.