# Describe the job's method for determination of stability constant for a complex compound

Job's method, also known as the method of continuous variation (MCV), is a spectrophotometric method used to determine the stability constants and composition of metal complexes. This method is based on the principle that when the absorbance of each solution at a given wavelength is plotted against the mole fraction of the ligand, the maximum absorbance will occur at a mole fraction that corresponds to the composition.

### Principle of Job's Method

This method is used for solutions where only one complex is formed. It involves mixing solutions of the metal ion and ligand in varying ratios while keeping the total concentration constant. The absorbance of each mixture is measured at a specific wavelength, and the results are plotted against the mole fraction of the ligand or metal ion.

### Procedure of the Job's Method

Make 10 solutions of complex containing metal ions and ligands in such proportions that the total volume of each solution is 10 ml. as shown below-

No. of Solutions | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Volume of Metal Ion in ml. | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Volume of Ligand in ml. | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |

We see that the sum of concentrations of ligand (C_{L}) and that of metal ion (C_{M}) is constant. Only their ratios are changed.

C_{L}) + C_{M} = C (Constant) -----Equation:1

Determine the optical densities of the solutions as prepared before with the help of spectrophotometer at such a wavelength of light that the complex absorbs strongly and the metal ion and the ligand do not.

Draw a graph between the mole fraction of the ligand (m.f = C_{L}/C) and optical density (absorbance). The graph obtained is shown below-

.

When the legs of the curve are extrapolated, they cross each other at a point at which the absorbance is maximum.

If the complex is ML_{n}

then, n = C_{L}/C_{M}

Euation:1 can also be written as-

C_{L}/C + C_{M}/C = C/C = 1 -----Equation:2

As above mentioned, m.f = C_{L}/C -----Equation:3

The equation:2 becomes-

m.f. + C_{M}/C = 1 -----Equation:4

or, C_{M}/C = 1 − m.f. -----Equation:5

Dividing equation:3 by equation:4, we get-

C_{L}/C_{M} = m.f./1 − m.f. -----Equation:6

n = C_{L}/C_{M} mentioned above

so, n = m.f./1 − m.f. -----Equation:7

From the value of 'n', composition of the complex can be determined.

## Limitations of Job's Method

1. This method can be used when only one complex is formed under the experimental condition.

2. This method can be used when the total volume of the solution containing metal ions and ligands is fixed.

3. The method depends on spectrophotometric measurements, so colorless complexes cannot be analyzed by this method.

## Applications of Job's Method

Some important applications of Job's method are given below-

1. Determining the stoichiometry of metal-ligand complexes.

2. Measuring stability constants of complexes.

3. Understanding the interactions in various chemical and biological systems.