Question

The diffusion coefficient for sodium ions crossing a biological membrane 12nm thick is 1.5 x10-18 m2/s. what flow rate of sodium ions would move across an area 12nm x 12 nm if the concentration difference across the membrane is 0.60 mol/dm3

Answer 1

Answer:

$-1.08\times 10^{23} mol/s$

Explanation:

We are given that

Diffusion coefficient,$D=1.5\times 10^{-18} m^2/s$

Thickness of membrane,$dx=12nm=12\times 10^{-9} m$

$1 nm=10^{-9} m$

Area,$A=12\times 12=144nm^2=144\times 10^{-18} m^2$

Concentration differences,$dc=0.60 mol/dm^3=0.60\times 1000=600mol/m^3$

We have to find the flow rate of sodium ions.

Flow rate,$\frac{dn}{dt}=-DA\frac{dc}{dx}$

Using the formula

$\frac{dn}{dt}=-\frac{1.5\times 10^{-18}\times (144\times 10^{-18})\times 600}{12\times 10^{-9}}=-1.08\times 10^{23} mol/s$

$\frac{dn}{dt}=-1.08\times 10^{23} mol/s$