Review on Simultaneous Equation Method (Vierodt’s Method)

 

Amitkumar J. Vyas, Shalini Anilkumar Jha, A.B. Patel, AI Patel, S. R. Shah, D. B. Sheth

B.K. Mody Government Pharmacy College, Rajkot, Gujarat, India.

L. M. College of Pharmacy, Ahmedabad, Gujarat, India.

 

ABSTRACT:

The article consists of brief review on Simultaneous equation method (Vierodt’s method). This method is applicable for estimation of those drugs whose spectra overlap properly I.e. If a sample contains two absorbing drug each of which absorbing at λ_max of the other, it is possible to determine both drugs by technique of simultaneous equation method. This article consists of the list of various combined dosage form and food sample analyzed by Vierodt’s method with its wavelength, linearity range and choice of solvents. This method permits simple, rapid and direct determination of combined dosage form without prior separation and therefore can be used in routine analysis. Quantitative estimation is necessary before introduction of any drug into the market because if concentration is more in formulation it can lead to toxicity problem or if concentration is found less, then formulation will not be effective in prescribed dose.

 

 

 

1. INTRODUCTION¹:

The branch of science “Analytical Chemistry” is useful in field of medicine because of its various application. It helps us to determine Qualitative (what it is?) and Quantitative (how much it is?). In present era the market is flooded with various combination of combined dosage form because fixed combination drugs may produce greater convience, lower cost, sometimes greater efficacy and safety. The motto behind this quantitative estimation is to ensure the amount of the drug present in the formulation because if it will be high it would lead to toxicity and if low then patient won’t get desired dose.

 

For estimation of multicomponent analysis instrumental techniques like spectrophotometric, HPLC, GC etc. are employed. UV spectrophotometric methods for simultaneous determination of drugs by using simultaneous equation method are highlighted in this review. UV spectrophotometric techniques are mainly used for multicomponent analysis thus minimizing the cumbersome task of separating interferents and allowing the determination of number of analytes, consequently reducing analysis time and cost.

 

Multicomponent UV spectrophotometric methods like Simultaneous Equation Method has some advantages like,

1. Avoiding prior separation techniques e.g., extraction, concentration of constituent, and clean    up steps.

2. Wide applicability to both organic and inorganic compounds.

3. Typical detection limits of 10^-4 to 10^-5 (µg/ml)

4. Moderate to high selectivity.

5. Absorption measurement are obtained with ease, the process is fast, accurate, and simple.

6. Spectral data are acquired with ease.

 

1.1 Simultaneous Equation Method (Vierordt’s Method).²

If a sample contains two absorbing drugs (X and Y) each of which absorbs at the λ_max of the other (Fig ₁ and ₂), it may be possible to determine both the drugs by the technique of simultaneous Equation (Vierordt’s method) provided that certain criteria apply.

 

Figure 1. The individual absorption spectra of substances X and Y, showing the wavelength for the assay of X and Y in admixture by the method of simultaneous equations.

 

The information required is:

a) The absorptivities of X at λ₁ and _2,a_x1 and a_x2 respectively

b) The absorptivities of Y at λ₁ and λ₂, a_y1 and a_y2 respectively

c)  The absorbances of the diluted sample at ₁ and λ₂, A₁ and A₂ respectively.

Let C_x and Cy be the concentration of X nd Y respectively in the diluted Sample.

 

Two equations are constructed based upon the fact that at λ and λ the absorbances of the mixture is the sum of the individual absorbances at X and Y.

At λ₁

A₁ = a_{x 1}bc_x +a_y1 b c_y                                                                                  (1)

At λ₂

A₂ = a_x2 bc_x +a_y1 bc_y                                                                                   (2)

For measurement in 1 cm cells, b = 1.

Rearrange eq, (2).

C_y = A₂ – a_x2 C_x/a_y1

Substitituting for C_y in equation 1. And rearranging gives

C_x = A₂a_y1 – A₁ a _y2 /a_x2 a_y1 -a_x1 a _y2                                             (3)

C_y = A₁ a_x2 – A₂ a_x1 /a _x2a_y1 – a_x1 a_y2                                           (4)

 

As an exercise one should derive modified equations containing a symbol (b) for the pathlength, for the application in situations where A and A are measured in cells other than 1 cm pathlength.

 

Criteria for obtaining maximum precision, based upon absorbance ratios, have been suggested (Glenn 1960) that place limits on the relative concentrations of the component of the mixture. The criteria are that ratios should lie outside the range 0.1-2 for the precise determination of Y and X respectively.

 

A ₂/ A₁/a_x2 / a_x1 and a_Y2 / a_Y1/A ₂/A₁

These criteria are satisfied only when the λ of the two components are reasonably dissimilar. An additional criterion is that two components do not interact chemically, thereby negating the initial assumption that the total absorbance is the sum of the individual absorbances. The additivity of the absorbances should always be considered in the development of new application of this technique. The British Pharmacopoeia assay of quinine related alkaloids and cinchonine related alkaloids in Cinchona Bark is based upon this technique.

 

2. APPLICATION OF SIMULTANEOUS EQUATION METHOD:

2.1. Binary Component Analysis:

Sr. No	Compounds	Wavelength (nm)	Linearity Range (µg/ml)	Solvents	Ref.
1.	Abacavir Lamivudine	260nm 271nm	5-25 (µg/ml) 5-25 (µg/ml)	Methanol Acetonitrile Distilled water	3
2.	Ledipasvir Sofosbuvir	290nm 260nm	5-25 (µg/ml) 5-25 (µg/ml)	Methanol Phosphate Buffer	4
3	Tamoxifen Coenzyme	236nm 275nm	2-14(µg/ml) 2-14(µg/ml)	Methanol	5
4	Atorvastatin Clopidogrel	246nm 202nm	5-25 (µg/ml) 5-25(µg/ml)	Methanol	6
5	Propranolol hydrochloride Etizolam	255nm 288nm	5-10 (µg/ml) 5-10µg/ml	Methanol	7
6	Amiloride Hydrochlorothiazide	244nm 280nm	5-25 (µg/ml) 5-25  µg/ml)	0.1 N NaOH Distilled water	8
7	Aspirin Omeprazole	257nm 300nm	4-20 (µg/ml) 2-10µg/ml	Methanol	9
8	Dapagliflozin Sax gliptin	222nm 272nm	5-25(µg/ml) 5-25(µg/ml)	Methanol Acetonitrile	11
9	Furosemide Spironolactone	275nm 237nm	2-10(µg/ml) 2-10(µg/ml)	Methanol Water	12
10	Empagliflozin Linagliptin	233nm 277nm	5-15(µg/ml) 2-6(µg/ml)	Methanol	13
11	Ofloxacin Ornidazole	240.6nm 279.4nm	20-40(µg/ml) 16-32(µg/ml)	Methanol Distilled water	14
12	Paracetamol Diclofenac	247nm 276nm	5-35(µg/ml) 5-40(µg/ml)	0.1 M Urea	15
13	Paracetamol Flupirtine maleate	245nm 344.5nm	5-15(µg/ml) 1.53-4.61(µg/ml)	0.1 N HCl	16
14	Rabeprazole sodium Levosulpride	284nm 232nm	1-20(µg/ml) 1-20(µg/ml)	Methanol	17
15	Diacerein Accelofenac	258.5nm 274nm	2-14(µg/ml) 4-18(µg/ml)	Methanol	18
16	Sitagliptin phosphate Pioglitazone hydrochloride	267nm 269nm	20-120(µg/ml) 20-120(µg/ml)	0.1 N HCl	19
17	Nimesulide Diclofenac sodium	276nm 395nm	2.5-25(µg/ml) 2.5-25(µg/ml)	Methanol	20
18	Norfloxacin Tinidazole	243nm 226nm	2-6(µg/ml) 16-4(8µg/ml)	Methanol AR	22
19	Rabeprazole Cinitapride hydrogen tartarate	282.6nm 265.6nm 282.6nm	4-20(µg/ml) 4-20(µg/ml) 4-20(µg/ml)	Methanol	23
20	Aspirin Lansoprazole	276nm 284nm	26-130(µg/ml) 4-20(µg/ml)	Methanol	24
21	Buprenorphine hydrochloride Naloxane HCL	289nm 283.8nm	40-200(µg/ml) 40-260(µg/ml)	Methanol	25
22	Cefepime Hydrochloride Sulbactum Sodium	227nm 260	24-52(µg/ml) 16-26(µg/ml)	0.1 N NaOH 0.1 N HCl	26
23	Aspirin Omeprazole	257nm 300nm	4-20(µg/ml) 2-10(µg/ml)	Methanol	27
24	Azithromycin Prednisolone	298.6nm 245nm	5-45(µg/ml) 10-90(µg/ml)	0.1 N HCl Methanol Phosphate buffer	28
25	Cefpodoxime Proxetil Levofloxacin Hemihydrate	263nm 294nm	1-12(µg/ml) 1-12(µg/ml)	0.1 N HCl Methanol	29
26	Clinidipine Telmisartan	357nm 297nm	1-80(µg/ml) 1-30(µg/ml)	Methanol	30
27	Domperidone Illaprazole	285nm 320nm	25-75(µg/ml) 10-50(µg/ml)	Methanol	31
28	Timolol maleate Brimonidine tartatate	257nm 295nm	2-35(µg/ml) 2-35(µg/ml)	Methanol	32
29	Losartan Potassium Hydrochlorothiazide	227.4nm 270.4nm	4-22(µg/ml) 6-27µg/ml)	Methanol	33
30	Mesalazine Prednisolone	320nm 246nm	2-20(µg/ml) 2-20(µg/ml)	Dimethyl formamide Phosphate buffer	61
31	Salbutamol Sulphate Ambroxol Hydrochloride	242nm 272nm	1-50(µg/ml) 10-50(µg/ml)	Methanol	34
32	Nabumetone Paracetamol	229.2nm 248nm	2-8(µg/ml) 2-20(µg/ml)	Methanol	35
33	Monteleukast Sodium Ebastine	344nm 252nm	5-25(µg/ml) 5-25(µg/ml)	Methanol	36
34	Etodolac Thiocolchicoside	223nm 259.4nm	1-6(µg/ml) 4-24(µg/ml)	Methanol	60
35	Diacerin Accelofenac	258.5nm 274nm	2-14(µg/ml) 4-18(µg/ml)	Methanol	62
36	Tenegliptin hydrobromide Hydrate Metformin	237nm 246nm	1-20(µg/ml) 1-20(µg/ml)	Methanol	59
37	Ofloxacin Ornidazole	240.6nm 279.4nm	20-40(µg/ml 16-32(µg/ml)	Methanol	53
38	Norfloxacin Tinidazole	273nm 319nm	2.5-20(µg/ml) 5-40(µg/ml)	Methanol	53
39	Perindopril Erbumine Amlodipine Besylate	298.3nm 231.9nm	10-150(µg/ml) 0.5-10(µg/ml)	Methanol	39
40	Tamsulosin Dutasteride	226nm 206nm	1-30(µg/ml) 1-30(µg/ml)	0.1 N HCl Methanol	30
41	Losartan potassium Hydrochlorothiazide	227nm 270nm	2-22(µg/ml) 3-27(µg/ml)	Distilled water	41
42	Rosiglitazone maleate Glimperide	247nm 4228nm	2-20 (µg/ml) 2-20(µg/ml)	Methanol	42
43	Thiamine Pyridoxine	452nm 482nm	1.5-11(µg/ml) 0.4-5(µg/ml)	Methanol	43
44	Palbociclib Letrozole	220nm 240nm	2-10(µg/ml) 2-10(µg/ml)	Distilled water	44
45	Eperisone Hrydrochloride Diclofenac Sodium	277nm 255nm	2-12(µg/ml) 2-12 (µg/ml)	Methanol Distilled water	45
46	Moxifloxacin Cefixime	289nm 295nm	3-9(µg/ml) 3-9(µg/ml)	0.1 N HCl Water	46
47	Domperidone Naproxen	286nm 270nm	10-50(µg/ml) 2-5(µg/ml)	Methanol	47
48	Kanmcycin Ketoconazole	240nm 230nm	10-50(µg/ml) 5-30(µg/ml)	Methanol	48
49	Lornoxicam Paracetmol	289.4nm 257nm	2-12(µg/ml) 2-30(µg/ml)	Methanol	49
50	Olmesartan Medoximil hydrochlorthiazide	266.5nm 270nm	1-20(µg/ml) 1-20(µg/ml)	Methanol	50
51	Drotaverine Hydrochloride Paracetamol	230.4nm 257nm	2-80(µg/ml) 2-30(µg/ml)	Methanol	51
52	Nabumetone Paracetamol	332.6nm 237.4nm	2-20(µg/ml) 4-20(µg/ml)	Methanol	52
53	Rabeprazole sodium Accelofenac	283nm 276nm	10-60(µg/ml) 10-60(µg/ml)	Methanol	53
54	Glimepride Rosiglitazone maleate	228nm 247nm	2-20(µg/ml) 2-20(µg/ml)	Methanol Distilled water	54
55	Mesalamine Prednisolone	320nm 246nm	2-20(µg/ml) 2-20(µg/ml)	Dimethyl formamide Phosphate buffer	55
56	Ofloxacin Nitazoxanide	347nm 295nm	2-30(µg/ml)	Methanol	56
57	Tezacafor Ivacaftor	239nm 351nm	5-30(µg/ml)	Ethanol	57
58	Esomeprazole Ondansetron	248nm 310nm	2-10(µg/ml)	Dilute Hydrochloric acid	58
59	Ciprofloxacin Tinidazole	272nm 365nm	2-7(µg/ml) 4-24(µg/ml)	0.1 N NaOH	59
60	Propranolol Hydrochloride Rosuvastatin calcium	289nm 243nm	2-40(µg/ml) 2-42(µg/ml)	Methanol	60
61	Drotaverine HCL Mefenamic acid	228nm 288nm	2-12(µg/ml) 4-24(µg/ml)	Methanol 0.1 N NaOH	61
62	Sitagliptin Phosphate Simvastatin	267nm 238nm	10-50(µg/ml) 5-25(µg/ml)	Methanol water	62
63	Quinfamide Mebendazole	260nm 232.4nm	1-6(µg/ml) 2-12(µg/ml)	Methanol	63
64	Atenolol Amlodipine besylate	224.6nm 239.6nm	4-28(µg/ml) 4-32(µg/ml)	0.1 N HCl	64
65	Famotidine Rabeprazole Sodium	263nm 284nm	5-30(µg/ml)	Distilled water	65
66	Levocetirizine Pseudoephedrine	231nm 251nm	5-30(µg/ml) 12-96(µg/ml)	Distilled water	66
67	Amoxicillin trihydrate Ranitidine Bismuth citrate	272nm 313nm	2-20(µg/ml)	Acetate Buffer	67
68	Valdecoxib Tizanidine	237nm 319nm	5-30(µg/ml) 0.5-3(µg/ml)	Methanol	68
69	Prednisolone Aspirin	243nm 226nm	2-6(µg/ml) 16-48(µg/ml)	Methanol	69
70	Ezetimibe Glimpride	226nm 233nm	10-30(µg/ml) 1-3(µg/ml)	Methanol	70
71	Azithromycin Cefixime Trihydrate	222nm 289nm	10-50(µg/ml) 10-50(µg/ml)	Methanol	83
72	Dapoxetine Phosphodiesterase	250nm 270nm	10-20(µg/ml) 10-20(µg/ml)	Methanol	84
73	Atenolol Losartan	240nm 260nm	10-50(µg/ml) 10-50(µg/ml)	Methanol	85
74	Olmesartan Medoxomil Hydrochlorothiazide	249nm 273.5nm	0-25(µg/ml) 0-25(µg/ml)	Methanol	86
75.	Cefixime Erdosteine	289nm 235nm	10-50(µg/ml) 10-50(µg/ml)	Methanol	87
76.	Metformin HCl Glibendamide	237nm 229nm	10-50(µg/ml) 10-50(µg/ml)	Methanol	88
77.	Mifepristone Misoprostol	304nm 257nm	8-24(µg/ml) 8-24(µg/ml)	Methanol	89
78	Ofloxacin Nitazoxanide	295nm 347nm	2-30(µg/ml) 2-30(µg/ml)	Methanol	90
79	Metoprolol tartrate Chlorthalidone	257nm 284nm	25-200(µg/ml) 25-200(µg/ml)	Methanol	91

 

2.2. Tertiary Component Analysis:

Sr. No	Compounds	Wavelength	Linear Range (µg/ml)	Solvents	Ref.
1	Paracetamol Prophenazone Caffeine	243nm 266nm 272.8nm	2-16(µg/ml) 4-40(µg/ml) 6-60(µg/ml)	Distilled water	71
2	Tenofovir Efavirene Lamivudine	260nm 347nm 272nm	10-60(µg/ml) 5-30(µg/ml) 5-30(µg/ml)	Methanol	74
3	Amlodipine Besylate Losartan Potassium Hydrochlorothiazide	236.5nm 254nm 271nm	5-25(µg/ml) 10-50(µg/ml) 5-25(µg/ml)	Methanol	73
4	Amlodipine Besylate Valsartan Hydrochloride	359nm 250nm 317nm	5-25(µg/ml) 5-25(µg/ml) 10-50(µg/ml)	Methanol	73
5	Quercetin Curcumin Piperine	371.31nm 424.68nm 343.76nm	5-30(µg/ml) 1-5(µg/ml) 1-10(µg/ml)	Methanol	73
6	Emtricitabine Tenofovir dispril fumarate Rilpivirine HCl	240.8nm 257.6nm 305.6nm	4-12(µg/ml) 6-18(µg/ml) 0.5-1.5(µg/ml)	Methanol Water	76

 

2.3 Food Sample Analysis:

Sr. No	Compounds	Wavelength Range	Linear Range (µg/ml)	Solvents	Ref.
1.	Tartrazine Ponceau	300-700nm 300-700nm	1-52(µg/ml) 1-60(µg/ml)	Methanol water	77
2.	Indigotin Ponceau	300-700nm 300-700nm	1-50(µg/ml) 1-52(µg/ml)	Methanol Water	78

 

 

3. CONCLUSION:

The UV-Spectrophotometric “Simultaneous Equation Method (Vierordt’sMethod)” was developed and validated for simultaneous estimation of various multicomponent analysis of drugs either for Binary component analysis or for Tertiary component analysis and even for component present in food samples containing sucrose and citric acid. The simultaneous equation method is simple, accurate, precise, rapid and economical for routine analysis of two drugs or more without any prior separation. Vierordt’s Method is an analytical technique for extracting both qualitative and quantitative information from mixtures. On the other hand, it does not require separation steps and the instruments used in the determination of analytes are relatively not expensive and sophisticated. It does not elaborate system and can be easily set up in manufacturing environment. Also, it is not labour-intensive, does not require higher skilled personnel, is cheap, is less time consuming, and, therefore, is very productive. Simultaneous equation method was applied for spectrophotometric data as a powerful and simple tool to enhance the accuracy of both qualitative and quantitative analyses of mixtures.

 

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Received on 16.02.2022       Modified on 19.03.2022

Accepted on 24.04.2022   ©Asian Pharma Press All Right Reserved

Asian J. Pharm. Ana. 2022; 12(2):149-156.