# Quantitative methodology - Instrumental Methods of Analysis B. Pharma 7th Semester

Quantitative methodology

Objectives

After this session students will be able to

Discuss quantitative methodology involving single and two components by UV – Visible spectrophotometry

APPLICATIONS:

1. Qualitative Analysis:
The UV spectra of most compounds are of limited value for qualitative analysis as compared to IR and Mass spectra. Qualitative analytical use of UV spectra has largely involved λ-max and absorptivities, occasionally includes absorption minima. In pharmacopoeias, absorption ratios have found use in identity tests, and are referred to as Q-values in USP.

2. Quantitative Analysis:
UV spectroscopy is perhaps the most widely used spectroscopic techniques for the quantitative analysis of chemical substances as pure materials and as components of dosage forms.

A)    Single component Analysis:
Direct Analysis:
Essentially all compounds containing conjugated double bond or aromatic rings, and many inorganic species absorb light in the UV-visible regions. In these techniques the substance to be determined is dissolved in suitable solvent and diluted to the required concentration by appropriate dilutions and absorbance is measured.
Indirect Analysis:
(Analysis after addition of some reagent) indirect methods are based on the conversion of the analyte by a chemical reagent that has different spectral properties.

Chemical derivatization may be adopted for any of the several reasons.

1) If the analyte absorbs weakly in the UV region.

2) The interference form irrelevant absorption may be avoided by converting the analyte to a derivative, which absorbs in the visible region, where irrelevant absorption is negligible.

3) This technique can be used to improve the selectivity of the assay in presence of other UV radiation absorbing substance.

4) Cost.

Methods of calculating concentration in single component analysis
·        By using the relationship: A = a b c
·        By using the formula: Cu = (Au/As) X Cs
·        By using the equations: Y = mX + C
·        By using the Beer’s curve

A) Multi component Analysis:
a) Simultaneous Equations method:
If a sample contains two absorbing drugs (X and Y) each of which absorbs at the λ-max of the other (λ1 and λ2), it may be possible to determine both the drugs by the simultaneous equations method.

Criteria for obtaining maximum precision, below mentioned ratio should lie outside the range 0.1-2.0
(A2/A1) / (aX2/aX1) and (aY2/aY1) / (A2/A1)

The information required is
·        The absorptivities of X at λ1 and λ2, aX1 and aX2
·        The absorptivities of Y at λ1 and λ2, aY1 and aY2
·        The absorbances of the diluted sample at λ1 and λ2, A1 and A2

Let Cx and Cy be the concentration of X and Y respectively in the sample
The absorbance of the mixture is the sum of the individual absorbances of X and Y

At λ1          A1 = aX1* Cx  + aY1* Cy                                            (1)
At λ2          A2 = aX2* Cx  + aY2* Cy                                            (2)
Multiply the equation (1) with aX2 and (2) with aX1

A1 aX2 = aX1 Cx aX2  + aY1 Cy aX2                                             (3)
A2 aX1 = aX2 Cx  aX1+ aY2 Cy aX1                                              (4)

A1 aX2 - A2 aX1 =  aY1 Cy aX2 - aY2 Cy aX1
A1 aX2 - A2 aX1 =  Cy (aY1 aX2 - aY2  aX1)
Cy = (A1 aX2 - A2 aX1) / (aY1 aX2 - aY2  aX1)         (5)

Same way we can derive
Cx = (A2 aY1 – A1 aY2) / (aY1 aX2 - aY2  aX1)         (6)

Equations 5 and 6 are known as simultaneous equations and by solving these simultaneous equations we can determine the concentration of X and Y in the sample.

b) Q-Absorbance ratio method
The absorbance ratio method is a modification of the simultaneous equations procedure. It depends on the property that, for a substance, which obeys Beer’s law at all wavelength, the ratio of absorbances at any two wavelengths is a constant value independent of concentration or path length.

In the quantitative assay of two components in admixture by the absorbance ratio method, absorbances are measured at two wavelengths, one being the λ-max of one of the components (λ2) and other being a wavelength of equal absorptivity of two components (λ1), i.e. an iso-absorptive point.

At λ1          A1 = aX1* Cx  + aY1* Cy                                            (1)

At λ2          A2 = aX2* Cx  + aY2* Cy                                            (2)

Now divide (2) with (1)

A2/A1 = (aX2* Cx  + aY2* Cy)
(aX1* Cx  + aY1* Cy)

Divide each term with (Cx + Cy)

A2/A1   =            (aX2* Cx  + aY2* Cy) /  (Cx + Cy)
(aX1* Cx  + aY1* Cy) / (Cx + Cy)

Put Fx = Cx / (Cx + Cy) and Fy = Cy / (Cx + Cy)

A2/A1 = [aX2 Fx + aY2 Fy] / [aX1 Fx + aY1Fy]

Where Fx is the fraction of X and Fy is the fraction of Y i.e. Fy = 1-Fx

There fore A2/A1 = [aX2 Fx + aY2 (1-Fx)] / [aX1 Fx + aY1(1-Fx)]
= [aX2 Fx + aY2 – aY2Fx] / [aX1 Fx + aY1 – aY1Fx]

At iso-absorptive point aX1 = aY1 and Cx = Cy

There fore A2/A1 = [aX2 Fx + aY2 – aY2Fx] / aX1
= (aX2 Fx/ aX1) + (aY2/ aX1) –( aY2Fx/ aX1)

Let Qx = aX2/aX1 ,  Qy = aY2/aY1 and absorption ratio Qm = A2/A1

Qm = Fx Qx + Qy - Fx Qy
= Fx (Qx-Qy) + Qy

Fx  = (Qm – Qy) / (Qx – Qy)                                                                                       (3)

From the equations (1)

A1 = aX1 (Cx + Cy)   there fore  Cx + Cy = A1 / aX1

There fore Cx = (A1/aX1) – Cy    (4)

From the equation  (3)

Cx / (Cx + Cy) = (Qm – Qy) / (Qx – Qy)

There fore Cx / (A1 / aX1)  = (Qm – Qy) / (Qx – Qy)

There fore Cx = [(Qm – Qy) / (Qx – Qy)] X (A1 / aX1) (5)

a) Derivative spectroscopy

Derivative spectroscopy involves the conversion of a normal spectra to its first, second or higher derivative spectra.
The normal spectrum is known as fundamental, zero order or D0 spectra. The first derivative spectrum (D1) is a plot of the rate of change of absorbance with wavelength against wavelength, i.e. plot of ΔA/Δλ vs. λ.

The second derivative spectrum is a plot of Δ2A/ Δλ2 vs. λ. For the quantitative estimation of binary mixtures by the derivative spectroscopy, first of all we have to find out the Zero Crossing Points (ZCP) for both the components (A and B). Now select ZCP for A and B so that at that particular ZCP other component shows remarkable absorbance. Now prepare calibration curve of A at the ZCP of B and of B at the ZCP of A.

Find out the unknown concentration using calibration curves.

1)      Determination of Dissociation constant of an indicators
Indicators give different color at different pH. Methyl red is red in color in acidic medium and is yellow in alkaline medium because in acidic medium it remains as HMR (Unionized form) and in alkaline medium as MR- (Ionized form).
HMR                      MR- + H+
Ka = [(MR-) (H+)] / (HMR)
Therefore Pka = pH – Log [(MR-) (H+)]

2)      Determination of composition of Complex.

M + L = Complex
There is two methods for the determination of composition of complex first is Mole ratio method. In this technique concentration of one of the components of the complex is kept constant and other is increased and the absorbance of the resulting solution is measured. Now from the plot of absorbance Vs concentration. Another method is Job’s curve method (Continuous variation method).
5) As a detector in HPLC

Summary

Quantitative methodology is important in UV spectroscopy

Single components and two components can be determined

Simultaneous equation method and absorbance ratio methods are examples of   methodology for determination of two component systems

Determination of multiple component systems involve complicated computational methodology