**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.

**UV spectroscopy is perhaps the most widely used spectroscopic techniques**

2. Quantitative Analysis:

2. Quantitative Analysis:

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.

**(Analysis after addition of some reagent) indirect**

Indirect Analysis:

Indirect Analysis:

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**

**If a sample contains two absorbing drugs (X and Y) each of which absorbs at**

A) Multi component Analysis:

a) Simultaneous Equations method:

A) Multi component Analysis:

a) Simultaneous Equations method:

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 D^{0}

spectra. The first derivative spectrum (D^{1}) 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 Δ^{2}A/ Δλ^{2 }*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

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

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