This document discusses Vierordt's method, a technique for simultaneous multicomponent analysis using UV-VIS spectrometry. It involves measuring absorbances at multiple wavelengths to generate equations that can be solved to determine the concentrations of each component in a mixture. The key steps include measuring calibration curves for each component at different wavelengths, measuring the sample mixture absorbances, and simultaneously solving the equations derived from Beer's law. Advantages include avoiding separation techniques and allowing simultaneous analysis, while requirements include components having distinct absorption profiles and obeying Beer's law. Applications described include pharmaceutical drug analysis using this spectroscopic method.

1. Vierordt’s Method
Azad H Alshatteri
azadalshatteri@garmian.edu.krd
Ph.D. candidate in Bioanalysis and bionanosensors

2. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
Vierordt’s method
• Simultaneous equation analysis is a multicomponent analysis. It is also known as
Vierordt’s method.
• Multicomponent analysis has become one of the most appealing topics for analytical
chemists recently, in fields of clinical chemistry, pharmaceutical drug analysis, pollution
control, and extra.
• Different analytical techniques can be applied for multicomponent analysis. Including:
spectrophotometry, chromatography, and electrophoresis.
• In my webinar, I will focus on using UV-VIS spectrometry for multicomponent analysis
frequently. Since it is more applicable and most of the scientific works have been done by
this technique.

3. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
In this webinar, I am trying to highlight of simultaneous equation analysis (Vierordt’s method).

4. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
It has been seen that UV/VIS absorption peaks are generally broad, so if there are two
compounds, X and Y, in solution, it is likely that they will not be completely resolved from
each other. That is, both X and Y contribute to the absorbance at most wavelengths.
It is possible to calculate the concentrations of X and Y from a series of measurements.

5. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
Measurements must be made at a number of wavelengths equal to the number of
components in the mixture. if there are two components, two wavelengths are needed.
Four calibration curves need to be prepared: X at λ1, X at λ2, Y at λ1, and Y at λ2. All
calibration curves should be blank corrected to pass through the origin. The absorbance
of the sample mixture is measured at λ1 and at λ2.

6. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
Procedure
1. The λmax value of each component is determined using its solution of suitable
concentration
2. The solutions of various concentrations of each component is prepared separately,
and the Beer’s law is tested at respective λmax by plotting absorbance values vs. the
concentration. This is a calibration curve of the given component at its λmax. The
slope (ɛb) of the calibration curve is determined.
3. Solutions of each component is measured at wavelengths chosen for other
components and respective slopes are calculated.
4. The absorbance values of mixture at each of the wavelengths are determined by the
same pathlength cuvette.
5. The measurements thus obtained are inserted in the following equations:

7. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
UV Spectra

8. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
Two equations can be written:
Aλ1 = 𝐴𝑥
λ1 + 𝐴𝑦
λ1 = ɛx
λ1Cx + ɛy
λ1Cy 1
Aλ2 = 𝐴𝑥
λ2 + 𝐴𝑦
λ2 = ɛx
λ2Cx + ɛy
λ2Cy 2
Aλ1, Aλ2 are the absorbances of the unknown at λ1and λ2
CX, the concentration of X in the unknown, CY, the concentration of Y in the unknown.
ɛx
λ1, the slope of the calibration curve for X at λ1., ɛx
λ2, the slope of the calibration curve
for X at λ2
ɛy
λ1 the slope of the calibration curve for Y at λ1 , ɛy
λ2, the slope of the calibration curve for
Y at λ2
λ1, λ2 are the λ max of X and Y respectively.

9. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
If we simultaneously solves the equations 1 and 2
𝐶𝑥 =
𝜀𝑦
λ1𝐴λ1 − 𝜀𝑦
λ1𝐴λ2
𝜀𝑥
λ1
𝜀𝑦
λ2
− 𝜀𝑦
λ1
𝜀𝑥
λ2
𝐶𝑦 =
𝜀𝑥
λ1𝐴λ2 − 𝜀𝑥
λ2𝐴λ1
𝜀𝑥
λ1
𝜀𝑦
λ2
− 𝜀𝑦
λ1
𝜀𝑥
λ2
Equations 3 and 4 give concentration of x and y in their mixture.
3
4

10. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
The advantage of Vierordt’s Method
1. Avoiding prior separation techniques e.g. extraction, preconcentration of constituents,
which cause to get more accurate result.
2. Spectral data are readily acquired with ease.
3. Wide applicability for organic and inorganic multicomponent.
4. Typical limit of detection is 10−4 to 10−5 M with high selectivity.
5. Multicomponent can be analyzed simultaneously. So, it is the time and cost effective
method.
6. It is green chemistry method because we do not use much solvents and we do not
have byproducts as we have in traditional methods

11. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
shortcoming (requirements) to apply simultaneous equation method:
1. The λmax of two drugs should be reasonable different.
2. There is no chemical interaction between the absorbing components.
3. Each component act independently that is each one absorbs as if others are not
present.
4. They should obey Beers law at their wavelength maximum (λmax) if used in UV-VIS
spectrophotometry.
5. Two absorbing species (for example drug x and drug y), each of which should have
some absorbance at λmax of others.
6. Interpretation of data is more complicate than traditional calibration curve.

12. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
1. New Simple Spectrophotometric Method for the Simultaneous Estimation of Paracetamol and
Flupirtine Maleate in Pure and Pharmaceutical Dosage Form
2. Applications of simultaneous equation method and derivative method for the determination of
rabeprazole sodium and levosulpiride in pharmaceutical dosage form and dissolution samples
3. Two different spectrofluorimetric methods for simultaneous determination of gemfibrozil and
rosiglitazone in human plasma
4. Application of different spectrophotometric methods for simultaneous determination of elbasvir and
grazoprevir in pharmaceutical preparation
5. Validation and application of Vierordt’s spectrophotometric method for simultaneous estimation of
tamoxifen/coenzyme Q10 in their binary mixture and pharmaceutical dosage forms
6. Simultaneous estimation of dutasteride and tamsulosin hydrochloride in tablet dosage form by
Vierordt’s method

13. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
7. Simultaneous determination of Indigotin and Ponceau-4R in food samples by using Vierordt’s
method, ratio spectra first order derivative and derivative UV spectrophotometry
8. A comparative study of the ratio spectra derivative spectrophotometry, Vierordt’s method and high-
performance liquid chromatography applied to the simultaneous analysis of caffeine and
paracetamol in tablets
9. Simultaneous Spectrophotometric Method for Determination of Emtricitabine and
Tenofovir Disoproxil Fumarate in Three-Component Tablet Formulation Containing
Rilpivirine Hydrochloride

14. INTRODUCTION CALCULATION ADVANTAGE SHORTCOMING APPLICATION REFERENCE
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