Question

Using the following equation (Debye-Huckel), find the coefficient of activity of the following:

a) Fe³⁺ with I = 0.062M answer should be 0.22

b) Ce⁴⁺I = 0.070M answer should be ≈ 0.08

c) Pb²⁺  I = 0.042M

Note: if you attempt this question please solve all parts (a,b and c) or else your answer will be rated as wrong/reported.

Answer 1

Debye-Huckel equation,

log(Y+/-) = -1.824 x 10^6 (Z1.Z2) sq.rt.(I)/(eT)3/2

where,

Y+/- = mean activity coefficient

Z1 and Z2 = are charges

e = dielectric constant of solvent water [from literature]

T = temperature = 298 K

I = ionic strength

a) Fe3+ with I = 0.062 M

We have,

log(Y+/-) = -1.824 x 10^6 (Z1.Z2) sq.rt.(I)/(eT)3/2

               = -1.824 x 10^6 (3.1) sq.rt.(0.062)/(78.54 x 298)^3/2

               = -0.509 x 3 x sq.rt.(0.062)

Y+/- = 0.42 is the mean activity coefficicent

activity coefficient Fe3+ = 0.21

b) Ce4+ with I = 0.070

log(Y+/-) = -1.824 x 10^6 (Z1.Z2) sq.rt.(I)/(eT)3/2

               = -1.824 x 10^6 (4.1) sq.rt.(0.070)/(78.54 x 298)^3/2

               = -0.509 x 4 x sq.rt.(0.070)

Y+/- = 0.30 is the mean activity coefficicent

activity coefficient Ce4+ = 0.075

c) Pb2+ with I = 0.042 M

log(Y+/-) = -1.824 x 10^6 (Z1.Z2) sq.rt.(I)/(eT)3/2

               = -1.824 x 10^6 (2.1) sq.rt.(0.042)/(78.54 x 298)^3/2

               = -0.509 x 2 x sq.rt.(0.042)

Y+/- = 0.62 is the mean activity coefficient

activity coefficient Pb2+ = 0.062