Detailed introduction to the internal standard method and the external standard method
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The internal standard method is an important technique in the quantitative analysis of gas chromatography. When using the internal standard method, a certain amount of a standard substance is added to the sample; this substance can be separated by the chromatographic column and is not affected by the peaks of other components in the sample. By measuring the peak areas and relative response values of the internal standard and the component of interest, it is possible to determine the percentage concentration of that component in the sample. When quantification is performed using the internal standard method, the selection of the internal standard is a very important task. Ideally, the internal standard should be a known compound for which pure samples are available, so that it can be added to the sample in an accurate and known quantity. It should have essentially the same or as similar physicochemical properties (such as chemical structure, polarity, volatility, and solubility in solvents) as well as chromatographic behavior and response characteristics as the component being analyzed; preferably, it should be a homolog of the substance being analyzed. Of course, under chromatographic analysis conditions, the internal standard must be able to be fully separated from the various components in the sample. It should be noted that in a few cases, analysts may be more concerned with the recovery rate of a compound in a complex process; in such cases, they can use a compound that can be easily completely recovered in that process as an internal standard to determine the percentage recovery of the compound of interest, without having to follow the selection principles mentioned above. When quantification is performed using an internal standard, what factors can affect the ratio of the peak heights or peak areas of the internal standard to those of the component being analyzed? The factors that influence this ratio fall into three categories: chemical, chromatographic, and instrumental. Changes in the area ratio caused by chemical reasons often occur when analyzing repeated samples. Chemical factors include: 1. Poor mixing of the internal standard in the sample ； 2. Reactions occur between the internal standard and the sample components, 3. The purity of the internal standard can vary, etc. For a relatively mature method, chromatographic problems are more likely to occur. Common chromatographic issues such as leaks have a significant impact on the absolute area, while their effect on the area ratio is smaller. However, if the change in the absolute area is large enough to cause a significant change in the area ratio, then there must be some serious chromatographic problem at hand, such as an excessive change in the injection volume, a large difference between the concentrations of the sample components and those of the internal standard, or detector non-linearity. The injection volume should be small enough and remain constant, so as to prevent saturation of the detector and the integration device. If the method is considered reliable and the chromatography appears normal, attention should be focused on checking the integration device and settings, as well as the slope and peak width determination. The strongest evidence suggesting a problem with the integration device is that the area ratio varies, while the peak height ratio remains relatively constant. What should be taken into account when creating a standard curve using an internal standard? In colorimetric quantitative analysis using the internal standard method, a mixture of the component to be analyzed and the internal standard in a certain weight ratio is first prepared for chromatographic analysis; the peak areas are measured, and a relationship curve between the weight ratio and the area ratio is created – this curve constitutes the standard curve. The chromatographic conditions used in the analysis of actual samples should be as consistent as possible with those used when preparing the standard curve. Therefore, when preparing the standard curve, it is necessary to specify not only the chromatographic conditions (such as the stationary phase, column temperature, carrier gas flow rate, etc.), but also the injection volume and the concentration of the internal standard. When preparing the internal standard calibration curve, the points do not lie entirely on a straight line; in such cases, it is necessary to determine the ratio of area ratios to weight ratios as well as the standard deviation of their average value. During use, single-point corrections should be performed regularly. If the deviation of the obtained values from the average value is less than 2, the curve can still be used; if it is greater than 2, the curve must be redrawn. If the curve shows changes over a short period of time, it is not appropriate to use the internal standard method for quantification. The external standard point method involves using a control solution of a certain concentration to compare and determine the content of component i in the sample solution. The control solution and the sample solution are injected multiple times under the same conditions, and the average value of the peak areas is determined. The amount of component i in the sample is calculated using the following formula: w = a(w) / (a), where w and a represent respectively the weight of component i in the volume of the sample solution injected, and the corresponding peak area. (w) and (a) represent respectively the weight of the pure component i in the injection volume of the control solution and the corresponding peak area. The external standard method is simple; it does not require the use of correction factors, and the component of interest can be quantified regardless of whether other components in the sample exhibit peaks. However, the accuracy of this method is affected by sample injection repeatability and the stability of experimental conditions. Furthermore, in order to reduce the experimental error of the external standard single-point method, the concentration of the prepared standard solution should be made as close as possible to the concentration of the component in the sample. The external standard method is a quantitative technique used in chromatographic analysis. Instead of adding a standard substance to the sample being analyzed, it is measured separately under the same chromatographic conditions as the sample. The area of the chromatographic peak obtained is then compared with that of the peak corresponding to the component of interest, thereby determining the concentration of that component. The external standard is the same substance as the component being analyzed, but it must have a certain level of purity. During analysis, its concentration should be similar to that of the component being measured in order to ensure the accuracy of quantitative analysis.
A internal standard is a substance with properties similar to those of the substance being measured, which is used as a reference for comparison. The external standard method involves comparing different concentrations of the substance being measured with corresponding values on a graph in order to determine the content of the sample under test. In either of these methods, the operations must be carried out under the same conditions as those applied to the sample, and parallel samples must also be prepared
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Additional note: The external standard method (standard curve method) involves using a pure sample of the component to be analyzed to create a standard curve. For the single-point correction method (using one sample), a standard sample Ws% with a concentration very close to that of the component being analyzed (Wi%) is prepared. An aliquot is injected for quantification; since the standard curve passes through the origin, an identical volume of the unknown sample is then injected to obtain Ai. Wi% can be calculated using the ratio Ai:As = Wi%:Ws%. For the two-point correction method (using two samples), there is a slope f1 and an intercept f2. For example, when analyzing samples containing 2–3% CO2, standard CO2 gases with concentrations of 1%, 2%, 3%, and 4% can be used – 1 ml of each is injected, and the peak areas are measured to create a standard curve. After that, 1 ml of the sample to be analyzed is injected, and its concentration is determined from the standard curve. Advantages of the external standard method: it’s fast and simple, as long as the component of interest peaks and is fully separated. Disadvantages: it’s an absolute method that requires constant injection volumes and operating conditions. Multiple-point correction requires a series of standard samples. The internal standard method can be used when the target compound does not peak completely or when only certain components in a mixture need to be measured. The procedure involves accurately weighing the sample and adding a certain amount of internal standard; then, the concentration of a specific component is determined based on the weights of the target compound and the internal standard, along with their respective peak areas. Generally, the internal standard is used as a reference, so fs=1. Requirements for the internal standard: a. Its peak should be close to that of the target compound, but still fully separated from it. b. There must be a pure sample of the internal standard, and its weight must be measured accurately. c. It should be miscible with the sample, and its quantity should be similar to that of the component being analyzed. Steps for the internal standard method: a. Select an internal standard. b. Measure fw(i/s) (fi). c. Weigh the unknown sample W, add the internal standard Ws, and measure Ai and As. Advantages of the internal standard method: it’s a relative method that doesn’t require complete peak formation or identification of all peaks. Disadvantages: it requires a pure sample of the internal standard, as well as two weighings, which makes it more complicated
If you still don’t understand, let me give an example: Qualitative and quantitative analysis in gas chromatography. I. Experimental principle – The successful separation of a mixed sample is the prerequisite and foundation for carrying out qualitative and quantitative analysis using gas chromatography. The degree of separation between a pair of chromatographic peaks can be expressed by the resolution R. Here, TR2,Y2 and TR1,Y1 represent the retention times and base widths of the two components respectively; when R=1.5, the two peaks are completely separated ； When R=1.0, 98% separation. In practical applications, R=1.0 is generally sufficient to meet the requirements. The task of qualitative analysis using chromatography is to determine the substance represented by each peak on the chromatogram. Under fixed chromatographic conditions, any substance has definite retention parameters such as retention value, retention time, retention volume, retention index, and relative retention value. Therefore, under the same chromatographic operating conditions, the identity of an unknown substance can be determined by comparing its retention parameters or position on the stationary phase with those of a known pure sample. When a pure sample of the component to be tested is available, it is very simple to perform qualitative analysis by comparing it with a known substance. During the experiment, the single-column comparison method, peak height addition method, or dual-column comparison method can be used. The single-column comparison method involves performing chromatographic analysis on a known pure sample and the sample to be tested under identical chromatographic conditions. Two chromatograms are obtained, after which their retention parameters are compared. When the values of the two are equal, it can be considered that a pure component is present in the sample under test. The double-column comparison method involves using two chromatographic columns with completely opposite polarities, and under predetermined operating conditions, determining the retention parameters of a pure sample and the component to be analyzed on each column. If these parameters are identical, it can be concluded with certainty that the sample contains a substance identical to the pure sample. Since some different compounds can exhibit the same thermodynamic properties on a given stationary phase, the two-column method is more reliable for qualitative analysis than the single-column method. Under certain chromatographic conditions, the mass m of component i, or its concentration in the mobile phase, is proportional to the peak area Ai or peak height h of the detector’s response signal: 2-10 or 2-11. In these equations, fia and fih are referred to as absolute correction factors. Equations (2-10) and (2-11) are the basis for chromatographic quantification. It is easy to see that the accurate measurement of the response signals A and h, as well as the correction factors, directly affects the accuracy of the determination analysis. Since the peak area is less susceptible to influences from operational conditions such as temperature calibration, flow rate of the mobile phase, and injection speed, it is more suitable as a parameter for quantitative analysis. The methods for measuring peak area are divided into manual measurement and automatic measurement. Modern chromatographs are generally equipped with an electrical integrator that can accurately measure the area of chromatographic peaks. For manual measurement, the peak height h and the half-peak width Y1/2 are first measured, after which the calculation is carried out using the following formula: 2-12. When the peak shape is asymmetric, the calculation is performed using the following formula: 2-13. In these formulas, Y0.15 and Y0.85 represent the peak widths at peak heights of 0.15 and 0.85, respectively. From equation (2-10), the absolute correction factor can be expressed by the following formula: In equation 2-14, mi can be represented by physical quantities such as mass, amount of substance, and volume; the corresponding correction factors are referred to as the mass correction factor, the molar correction factor, and the volume correction factor, respectively. Since the absolute correction factor is greatly affected by the instrument and operating conditions, its use is limited; relative correction factors are generally employed instead. The relative correction factor refers to the ratio of the absolute correction factor of component i to that of the reference component s; that is: 2-15. Since absolute correction factors are rarely used, the correction factors mentioned in general literature are actually relative correction factors. Depending on the circumstances, different quantitative methods can be chosen. The normalization method calculates the total amount of all components in a sample as 100%, using their corresponding response signals as quantitative parameters. The mass fraction of each component is calculated using the following formula: This method is simple and accurate. When the operating conditions change, the impact on the analysis results is minimal; it is commonly used for quantitative analysis, especially suitable for liquid samples with small sample volumes for which accurate volume measurement is difficult. However, when using this method for quantitative analysis, it is required that each component in the sample produce measurable chromatographic peaks. II. Instruments, Reagents, and Experimental Conditions 1. Instruments (1) GC-4000A gas chromatograph (2) GCD-300B fully automatic hydrogen generator (3) Stopwatch (4) Syringes: 10 mL, 100 mL (5) Several Erlenmeyer flasks with ground glass joints 2. Reagents (1) n-Hexane, cyclohexane, benzene, toluene (all A.R. grade) (2) Unknown mixed sample 3. Experimental Conditions (1) Column length: 2 m, inner diameter: 2 mm (3) Mobile phase: hydrogen (4) Column temperature: 85–95°C (5) Vaporization temperature: 120°C (6) Detector temperature: 120°C (7) Bridge current: 110 mA (8) Carrier gas flow rate: slightly above 0.1 L/min III. Experimental Procedures 1. Carefully read the operating instructions for the gas chromatograph. 2. Under the guidance of a teacher, turn on the chromatograph; see Attachments 1 and 2 for details. According to the experimental conditions, the chromatograph should be adjusted to a state suitable for sample injection following the instrument’s operating procedures. Sample injection can be carried out once the electrical and gas systems within the instrument have reached equilibrium and the baseline on the recorder is stable. 3. Prepare accurately a standard solution of n-hexane, cyclohexane:benzene:toluene in a mass ratio of 1:1:1.5:2.5 for measuring the correction factor. 4. Add approximately 1.4–2 mL of the unknown mixed sample and 20–40 mL of air, 2–3 times each, and adjust the parameters of the workstation to obtain an appropriate chromatographic column. Record the retention time tR and dead time tM of each peak on the chromatogram. 5. Inject 0.2 mL of pure reagents such as n-hexane, benzene, cyclohexane, and toluene, 2–3 times each, and record the retention time tM of each peak on the chromatogram. 6. Add 1.4–2.0 mL of the prepared standard solution 2–3 times, and record the chromatogram along with the retention times of each peak. 7. Under exactly the same conditions as in Step 6, 1.4–1.6 mL of the unknown mixed sample is added each time, 2–3 times in total. The parameters of the workstation are adjusted to obtain an appropriate chromatogram, after which the chromatogram and the retention times tR of each peak are printed out. IV. Result Processing 1. Using the data obtained in Step 6, calculate the resolution between every pair of the first 3 peaks. 2. Compare the chromatographic ranges and retention times obtained in step 4 and step 5 to identify the substances corresponding to each chromatographic peak in the unknown mixed sample. 3. Using the data obtained in Step 6, and with benzene as the reference substance, calculate the mass correction factors for each component using Equation (2-15). 4. Using the chromatogram obtained in Step 7, calculate the mass fractions of each component in the unknown mixed sample according to Equation (2-16). V. Precautions 1. The operating pressure of the gas cylinder must be kept within the specified range; it must not operate under excessive pressure. It must be kept in mind to ensure safety. 2. After the experiment is completed, check whether the instrument is functioning properly and whether it has been turned off correctly.