Ionic Strength | Ionic Strength Formula

Ionic Strength | Ionic Strength Formula

Ionic Strength | Ionic Strength Formula

The interionic attraction in an electrolyte depends on the valencies and concentrations of the ions. These two factors are combined in a single term, called ionic strength.
Ionic strength is a measure of the concentration of ions in ionic solution. It was defined by Lewis and Randall in 1921 and it is based on the dissociation that suffers salts, acid and bases when are in an aqueous solution.
The ionic strength is expressed in Moles per litre (molL-1) or Moles per kg (mol kg-1) depending upon the units taken for the concentration of the ions.


Ionic Strength Formula

The ionic strength of a solution is a function of the concentration of all ions present in a solution-

Ionic Strength (I) = 1/2∑miz2i

Here, mi and zi are the molar concentration and the charge of ion 'i'. The sum is taken over all ions in the solution. Due to the square of zi, multivalent ions contribute strongly to the ionic strength.
The evaluation of ionic strength in the case of electrolytes of a few valence types is given below-

1-1 Type electrolyte
Example- NaCl
Let molality = m
m+ and m = m
z+ = z = 1
So, I = 1/2(m + m) = m
Thus, for a 1-1 type of electrolyte, the ionic strength is the same as molality.


2-2 Type electrolyte
Example- CuSO4
Let molality = m
m+ and m = m
z+ = z = 2
So, I = 1/2(m.22 + m.22) = 4m
Thus, for a 2-2 type of electrolyte, the ionic strength is four time of the molality.

3-3 Type electrolyte
Example- AlPO4
Let molality = m
m+ and m = m
z+ = z = 3
So, I = 1/2(m.32 + m.32) = 9m
Thus, for a 3-3 type of electrolyte, the ionic strength is nine time of the molality.


1-2 Type electrolyte
Example- Na2SO4
Let molality = m
m+ = 2m and m = m
z+ = 1 and z = 2
So, I = 1/2(2m + m.22) = 3m
Thus, for a 1-2 type of electrolyte, the ionic strength is three time of the molality.

2-1 Type electrolyte
Example- CaCl2
Let molality = m
m+ = m and m = 2m
z+ = 2 and z = 1
So, I = 1/2(m.22 + 2m) = 3m
Thus, for a 2-1 type of electrolyte, the ionic strength is three time of the molality.


1-3 Type electrolyte

Example- Na3PO4
Let molality = m
m+ = 3m and m = m
z+ = 1 and z = 3
So, I = 1/2(3m + m.32) = 6m
Thus, for a 1-3 type of electrolyte, the ionic strength is six time of the molality.

3-1 Type electrolyte

Example- La(NO3)3
Let molality = m
m+ = m and m = 3m
z+ = 3 and z = 1
So, I = 1/2(m.32 + 3m) = 6m
Thus, for a 3-1 type of electrolyte, the ionic strength is six time of the molality.


Summary of Ionic Strength

Type of Electrolyte Ionic Strength Example
1-1 Type1mNaCl
2-2 Type4mCuSO4
3-3 Type9mAlPO4
1-2 Type3mNa2SO4
2-1 Type3mCaCl2
1-3 Type6mNa3PO4
3-1 Type6mLa(NO3)3

Calculate the ionic strength of 3M potassium chloride.

potassium chloride dissociates as-
KCl → K+ + Cl.
Each ion's concentration is the same as the concentration of the salt is 3 mol/L.
z+ = +1 and z = −1
so, the ionic strength-
I = 1/2 [(3)(+1)2 + (3)(-1)2] = 3
So, the ionic strength is 3M.

Calculate the ionic strength of solution made by mixing equal volumes of 0.1 M NaCl and 0.01 M CaCl2.

mNa+ = 0.1
zNa+ = +1
mCa+2 = 0.01
zCa+2 = +2
mCl−1 = 0.1 + 0.02 = 0.12
zCl−1 = −1
so, the ionic strength-
I = 1/2 [0.1 + 0.04 + 0.12]
or, I = [0.26] = 0.13 So, the ionic strength is 0.13M.


Determine the ionic strength of a solution containing 0.050M BaCl2 and 0.10M Na2SO4.

Hints: I = 1/2[0.050 x 22 + 0.10 x (−12) + 0.20 x 12 + 0.10 x (−22)] = 0.045M

Calculate the ionic strength of the solution that is 0.1 mol/kg in KCl(aq) and 0.2 mol/kg in CuSO4(aq).

Hints: 0.9

Calculate the ionic strength of 0.1M aqueous solution of Fe2(SO4)3. JAM 2014

Fe2(SO4)3 → 2Fe+3 + 3SO4-2
I = 1/2[0.1 x 2 x (3)2 + 0.1 x 3 x (-2)2]
or, I = 1/2[1.8 + 1.2] = 1.5

The concentration of a MgSO4 solution having the same ionic strength as that of a 0.1 M Na2SO4 solution is

A. 0.05
B. 0.067
C. 0.075
D. 0.133
Hints: 0.075

Ionic strength of a 0.2 M Na2HPO4 solution will be CSIR DEC 2015

A. 0.2M
B. 0.4M
C. 0.6M
D. 0.8M
Hints: 0.6


Uses Ionic Strength

Ionic strength used in theoretical chemistry for calculating dissociation of salts in heterogeneous systems such as colloids. It is also used in biochemistry and molecular biology for determining the strength of buffer solutions that should have concentrations similar to the found in nature.
The ionic strength plays a very important role in the Debye–Hückel theory. Furthermore, the Debye–Hückel theory describes the strong deviations from ideality that happen in ionic solutions.
Ionic strength is also important for the theory of double layer and related electroacoustic and electrokinetic phenomena in various heterogeneous systems and colloids.


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