Consider current flowing between two metal plates partially submerged in a solut

Question

Consider current flowing between two metal plates partially submerged in a solution containing sodium and chlorine ions (from table salt), as shown below. A 5 V battery drives a current, I, through the wire connecting the plates. Each plate has 250 cm2 of its area submerged in the ionic solution, and the plates are separated by a distance d = 5.0 cm.

Each second, 2.68×1016 Na+ ions reach the negatively-charged plate and 3.92×1016 Cl ions reach the positively charged plate. Calculate the resistivity, , of the ionic solution. (ans. 2.36×102 ·m)

Explanation / Answer

current i = (n1+n2)*e/t

n1 = number of Na+ ions

n2 = number of Cl- ions

t = time = 1s

current i = (2.68*10^16 + 3.92*10^16)*1.6*10^-19/1 = 0.01056 A

from ohms law

V = i*R

resistance R = V/i = 473.5 ohm

resistance R = rho*d/A

resistivity rho = R*A/d

A = area of plates

d = seperation between plates

resistivity rho = 473.5*250*10^-4/0.05 = 2.36*10^2 ohm m

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