At the end of this chapter, the reader should be able to do the following: 1. Convert between absorbance and transmittance values. 2. Calculate the concentration of unknown samples using Beer’s law. 3. Calculate the concentrations of unknown samples by single-standard, multiple standards, and millimolar absorptivity methods. 4. Calculate the concentration of enzyme unknown samples using the principles of kinetic analysis. 5. Calculate the pH of solutions using the Henderson-Hasselbalch equation. 6. Calculate bicarbonate, pH, and pCO2 of unknown samples using the derivation of the Henderson-Hasselbalch equation. 7. Interpret a patient’s acid-base status. 8. Calculate the anion gap of unknown samples. 9. Calculate serum and urine osmolality concentrations. 10. Calculate the osmol gap in patient samples. 11. Calculate the concentration of LDL and VLDL cholesterol. Beer’s law is possible because of the concept of transmittance. As depicted in Figure 7–1, a cuvette containing the solution to be analyzed is placed within a basic spectrophotometer so that light can be shown through it. The solution will absorb some of the light (absorbance) and the remainder will be transmitted through the cuvette to the photodetector. Notice that the arrow to the right of the cuvette, which represents the transmitted light, is smaller than the arrow to the left of the cuvette, which represents the incident light. The ratio of the amount of transmitted light divided by the amount of incident light is known as transmittance. This is demonstrated mathematically as follows: This can be manipulated to the following formula: The formula can be converted from T to % T: In contrast to transmittance ratios, absorbance values range from 0.000 to infinity on a logarithmic scale. Figure 7–2 is a picture of an absorbance and percent transmittance meter. Notice how much easier it is to interpret the linear percent transmittance scale versus the logarithmic absorbance scale. Given a transmittance ratio of 0.400, what is the absorbance value? To solve this problem, first convert the transmittance ratio to a percent transmittance value. Next, substitute 40.0% T into the conversion formula: Using a calculator or the logarithm table in Appendix 2–A, determine the log of 40: Therefore, the transmittance ratio of 0.400 is equal to an absorbance value of 0.398. Given an absorbance value of 0.875, what is the % T value? Using the formula and substituting into it the given values, the following equation is derived: Solving this equation leads to the following: To verify this result, use 13.34 as % T and determine the absorbance. To solve this problem, use ratio and proportion: Using algebra and crossmultiplying: A manual serum creatinine is performed in a MLT student laboratory experiment. A 5.0 mg/dL standard is used and the following results were obtained: Absorbance of the standard = 1.142, absorbance of the unknown = 0.778. What is the concentration of the unknown? Using ratio and proportion, the following formula is derived: Given a standard concentration of 300 mg/dL with an absorbance equal to 1.262 and an unknown concentration’s absorbance of 0.715, what is the concentration of the unknown? Using ratio and proportion, the concentration of the unknown is 170 mg/dL. Use the formula to determine the concentration of BUN in the patient’s serum: Given the absorbance of a 150 mg/dL standard is 0.425, and the absorbance of QC level 1 is 0.205, calculate the concentration of QC level 1. Using the formula from Example 7–5, and substituting into it the values from this problem, the following formula is derived: The concentration of QC level 1 is 72 mg/dL. Given the absorbance of a 250 mg/dL standard is 0.750, and the absorbance of QC level 2 is 0.680, what is the concentration of QC level 2? Each of these unknowns could be calculated as in Example 7–5. However, calculating six unknowns by this method is time consuming. Using a factor speeds up the calculations involved in multiple samples. To calculate the factor for this assay, divide the concentration of the standard by the obtained absorbance of the standard: Next, use the factor 444 and multiply each sample absorbance to obtain the sample concentration: Using the factor method and the information given in the table, complete the table by calculating the concentrations of three unknowns that were analyzed using the single-point standard method. Using the factor method and the information given in the table, complete the table by calculating the concentrations of three unknowns that were analyzed using the single-point standard method. Using the factor method and the information given in the table, complete the table by calculating the concentrations of three unknowns that were analyzed using the single-point standard method. Students of clinical laboratory science often learn the concept of a standard curve by graphing on linear graph paper the concentrations of standards on the x axis and the absorbance of the standards on the y axis. A “standard curve” is shown in Figure 7–3. The following brief discussion of manually produced standard curves is designed to assist the students of clinical laboratory science to better understand what is happening inside the “black box” of an automated instrument. A standard curve of the percent transmittance values of the standards can also be plotted. However, if plotted on linear graph paper, the % T standard curve is curvilinear, as shown in Figure 7–4. To form a straight line, % T values must be plotted on semilogarithm graph paper as shown in Figure 7–5. Using the absorbance values and the concentration of each standard, the following standard curve (Figure 7–6, A) can be produced. Notice that the line does not extend beyond the 300 mg/dL standard concentration and intersects 0,0. To solve this problem, use the graph of the standard curve (see Figure 7–6, A). Find on the y axis scale 0.400 absorbance (Figure 7–6, B). Next, using a ruler or straightedge, a line is drawn across the graph until it intersects the standard curve line. Now a line is drawn straight down to the x axis (Figure 7–6, C). The point where the vertical line intersects the x axis is the concentration of the patient sample with an absorbance of 0.400. This glucose value from Figure 7–6, C is 135 mg/dL. Figure 7–7 is a graph of the standards. From the standard curve line obtained, what are the concentrations of the quality control materials and each of the patient specimens? The standards used for standard curves are obtained usually either by buying them directly from a vendor or obtaining one concentration of standard and, by performing dilutions, preparing a series of working standards. When performing dilutions of the standard, it is important to remember that there is a limited supply of the standard. Therefore, the limiting factor for the dilutional series is the total quantity of standard available to dilute. When the standard that must be used or that is available contains only 3 mL, it serves no useful purpose to devise a dilutional scheme that requires 5 mL of standard. To prepare a series of working standards, the calculation of C1V1 = C2V2 is used. (Refer to Chapter 6 for additional information.) The formula C1V1 = C2V2 is used to solve this problem. Where: C1 = original concentration (stock concentration of 10 g/dL) How is the 6.0-g/dL working standard prepared? Use the same formula and substitute into it the 6.0-g/dL instead of the 8.0-g/dL: How is the 4.0-g/dL standard prepared? Use the same formula as above: How is the 2.0-g/dL working standard prepared? An MLT student had to make four working standards with a total volume of 3.0 mL from a 300 mg/dL standard. The concentrations of the working standards were 200, 150, 75, and 50 mg/dL. How would this student prepare these standards? A series of four working standards with a 2.0 mL volume had to be prepared from a 40.0 mg/dL standard. The concentrations of the working standards are 30, 20, 10, and 5 mg/dL. How are these working standards prepared? A series of four working standards with a 3.0 mL volume had to be prepared from a 15.0 mg/dL standard. The concentrations of the working standards are 12, 9, 7, and 5 mg/dL. How are these working standards prepared? The molar absorptivity of NADH is Using Beer’s law that A = abc, substitute the data that is known into it: Therefore, the concentration of the compound is 2.65 × 10−4 M. End-point assays can use a single standard, a standard curve, or the molar absorptivity method to calculate the concentration of patient samples. End-point assays may use enzymes within the reaction as part of the reagent, but analyses of enzymes are not performed as end-point reactions. In many laboratories, analytes are measured by large multichannel random access analyzers. In the quest for increased speed, kinetic reactions were developed. A kinetic reaction differs from an end-point assay in that the reaction does not go to completion; rather, absorbances are taken at certain intervals for short periods. Some analyzers continuously monitor the absorbance readings instead of monitoring at fixed intervals to improve accuracy. In any reaction, kinetic or end-point, there may be three phases: the lag phase in which the reactant and reagents are first reacting together, the reacting phase during which the product is formed, and the reagent depletion phase as shown in Figure 7–8.
Clinical Chemistry Laboratory
SPECTROPHOTOMETRY
Beer’s law:
A = abc
where:
A = absorbance
a = absorptivity coefficient
b = pathlength
c = concentration
Example 7–2
Example 7–3
Single-Standard Method for Determining the Concentration of Unknowns
Example 7–4
Example 7–5
Example 7–6
Sample No.
Standard Concentration
Absorbance of Standard
Factor
Absorbance of Unknown
Concentration of Unknowns
Standard
12.0 mg/dL
1.455
8.2
Unknown No. 1
8.2
1.215
Unknown No. 2
8.2
0.637
Unknown No. 3
8.2
0.283
Sample No.
Standard Concentration
Absorbance of Standard
Factor
Absorbance of Unknown
Concentration of Unknowns
Standard
12.0 mg/dL
1.455
8.2
Unknown No. 1
8.2
1.215
10.0 mg/dL
Unknown No. 2
8.2
0.637
5.2 mg/dL
Unknown No. 3
8.2
0.283
2.3 mg/dL
Sample No.
Standard Concentration
Absorbance of Standard
Factor
Absorbance of Unknown
Concentration of Unknowns
Standard
80 mg/dL
0.850
94
Unknown No. 1
94
0.515
Unknown No. 2
94
0.780
Unknown No. 3
94
0.625
Sample No.
Standard Concentration
Absorbance of Standard
Factor
Absorbance of Unknown
Concentration of Unknowns
Standard
80 mg/dL
0.850
94
Unknown No. 1
94
0.515
48 mg/dL
Unknown No. 2
94
0.780
73 mg/dL
Unknown No. 3
94
0.625
59 mg/dL
Sample No.
Standard Concentration
Absorbance of Standard
Factor
Absorbance of Unknown
Concentration of Unknowns
Standard
500 mg/dL
1.280
391
Unknown No. 1
391
1.145
Unknown No. 2
391
1.080
Unknown No. 3
391
0.849
Sample No.
Standard Concentration
Absorbance of Standard
Factor
Absorbance of Unknown
Concentration of Unknowns
Standard
500 mg/dL
1.280
391
Unknown No. 1
391
1.145
448 mg/dL
Unknown No. 2
391
1.080
422 mg/dL
Unknown No. 3
391
0.849
332 mg/dL
Standard Curve Method for Determining the Concentration of Unknowns
Example 7–7
Standard Concentration
Absorbance
50 mg/dL
0.150
100 mg/dL
0.300
200 mg/dL
0.600
300 mg/dL
0.900
Example 7–8
Sample
Absorbance
3.00 g/dL standard
0.195
4.50 g/dL standard
0.290
7.50 g/dL standard
0.480
15.00 g/dL standard
0.960
QC level 1
0.270
QC level 2
0.440
Patient 1
0.580
Patient 2
0.170
Patient 3
0.260
Patient 4
0.490
Patient 5
0.900
Patient No.
Concentration
1
9.00 g/dL
2
2.70 g/dL
3
4.00 g/dL
4
7.70 g/dL
5
14.00 g/dL
Preparing Working Standards for Standard Curves Used for Manual Methods
Example 7–9
Standard Concentration
Amount of Standard Needed
Amount of Diluent Needed
300 mg/dL
200 mg/dL
2 mL of 300 mg/dL standard
1 mL diluent
150 mg/dL
1.5 mL of 300 mg/dL standard
1.5 mL diluent
75 mg/dL
0.75 mL of 300 mg/dL standard
2.25 mL diluent
50 mg/dL
0.5 mL of 300 mg/dL standard
2.5 mL diluent
Standard Concentration
Amount of Standard Needed
Amount of Diluent Needed
40 mg/dL (2 mL total volume)
30 mg/dL
1.5 mL of 40 mg/dL standard
0.5 mL diluent
20 mg/dL
1.0 mL of 40 mg/dL standard
1.0 mL diluent
10 mg/dL
0.5 mL of 40 mg/dL standard
1.50 mL diluent
5 mg/dL
0.25 mL of 40 mg/dL standard
1.75 mL diluent
Standard Concentration
Amount of Standard Needed
Amount of Diluent Needed
15 mg/dL
12 mg/dL
2.4 mL of 15 mg/dL standard
0.6 mL diluent
9 mg/dL
1.8 mL of 15 mg/dL standard
1.2 mL diluent
7 mg/dL
1.4 mL of 15 mg/dL standard
1.6 mL diluent
5 mg/dL
1.0 mL of 15 mg/dL standard
2.0 mL diluent
Molar Absorptivity Method for Determining the Concentration of Unknowns
Example 7–10
END-POINT VERSUS KINETIC REACTIONS