Question

The mobility (u) of an organic ammonium ion, [N(CxHy)4]+ in dilute aqueous solution is 5.51x10-8m2 s-1 V-1 at a temperature of 298 K. Estimate the radius of the ion, given that the viscosity of water at this temperature is 0.001 N s m-2. Express your answer in Å (Angstroms).

Answer 1

Ionic molbility of ammonium ion

using,

Ionic mobility (u) = z.e/6.pi.n.r = 5.5.1 x 10^-8

where,

n = visocity = 0.001 N s m^-2

r = radius of ion

z = elementary charge = 1.602 x 10^-19 C

e = 1

So,

ionic radius (r) = 1 x 1.602 x 10^-19/6 x 3.14 x 5.51 x 10^-8 x 0.001

                        = 1.54 x 10^-10 m = 1.54 Angstroms

So ionic radius of ammonium ion is 1.54 Angstroms.