TITRATION CURVE OF AMINO ACIDS

TITRATION CURVE OF AMINO ACIDS

(Determination of pKa and pI values of amino acids)

Objectives:

1) To determine the titration curve for an amino acid and

2) To use this curve to estimate the pKa values (pKa1, pKa2 and pKa3) of the ionizable groups of the amino acid and the amino acid’s pI.

Introduction:

A titration curve of an amino acid is a plot of the pH of a weak acid against the degree of neutralization of the acid by standard (strong) base. Consider the ionization of a weak organic acid such as acetic acid by NaOH.

As more of the strong base (titrant) is added to the aqueous solution, more of the weak acid is converted to its conjugate base. During this process, a buffer system forms and the pH of the system will follow the Henderson-Hasselbalch relationship. The titration curve of the neutralization of acetic acid by NaOH will look like this:

When a weak monoprotic acid is titrated by a base, a buffer system is formed. The pH of this system follows the Henderson-Hasselbalch equation:

This curve empirically defines several characteristics (the precise number of each characteristic depends on the nature of the acid being titrated): 1) the number of ionizing groups, 2) the pKa of the ionizing group(s), 3) the buffer region(s).

Based on the number of plateaus on a titration curve, one can determine the number of dissociable protons in a molecule. The one plateau observed when acetic acid is titrated indicates that it is a monoprotic acid (i.e., has only one dissociable H⁺). Many organic acids are polyprotic (have > one dissociable H⁺).

The protein building blocks, amino acids, are polyprotic and have the general structure

The majority of the standard amino acids are diprotic molecules since they have two dissociable protons: one on the alpha amino group and other on the alpha carboxy group. There is no dissociable proton in the R group. This type of amino acid is called a “simple amino acid”. A simple amino acid is electrically neutral under physiological conditions. NOTE: Under this definition it is possible to have a simple amino acid which is triprotic. Which of the 20 common or standard amino acids are simple & triprotic? Ionization of a diprotic amino acid will proceed as follows:

The order of proton dissociation depends on the acidity of the proton: that which is most acidic (lower pKa) will dissociate first. Consequently, the H⁺ on the α-COOH group (pKa₁) will dissociate before that on the α-NH₃ group (pKa₂). The titration curve for this process looks similar to the following:

This curve reveals, in addition to the same information observed with a monoprotic acid, an additional characteristic of polyprotic acids and that is the pH at which the net charge on the molecule is zero. This pH defines the isoelectric point (pI) of the molecule, a useful constant in characterizing and purifying molecules. Using a titration curve, the pI can be empirically determined as the inflection point between the pKa of the anionic and cationic forms. Mathematically, the pI can be determined by taking the average of the pKa for the anionic and cationic forms. The ionic form of the molecule having a net charge of zero is called the zwitterion.

A few amino acids are classified as triprotic. This is because, in addition to the ionizable protons of the α-COOH and α-NH₃ groups, they also have a dissociable proton in their R group. Although triprotic amino acids can exist as zwitterions, under physiological conditions these amino acids will be charged. If the net charge under physiological conditions is negative, the amino acid is classified as an acidic amino acid because the R group has a proton that dissociates at a pH significantly below pH 7. The remaining triprotic amino acids are classified as basic amino acids due to a) their having a net positive charge under physiological conditions and b) an R group dissociable proton with a pKa near or greater than pH 7. Titration curves for triprotic amino acids generate the same information as those for the diprotic amino acids. The pI for a triprotic amino acid can be determined graphically, although this is somewhat more challenging. Graphical determination, as was the case with the diprotic acids, requires one to know the ionic forms of the amino acid and finding the inflection point between the cationic and anionic forms. Mathematically, the pI for an acidic amino acid is the average of pKa₁ and pKa_R (the pKa of the dissociable proton in the R group); for a basic amino acid, it is the average of pKa₂ and pKa_R.

Table: 1 Amino Acid Classification Based on Number of Dissociable Protons

1-Letter code	3-Letter code	Name	Mnemonic help for 1-letter code*	Classification
A	Ala	Alanine	Alanine	Simple
C	Cys	Cysteine	Cysteine	Simple
D	Asp	Aspartate	AsparDic acid	Acidic
E	Glu	Glutamate	GluEtamic acid	Acidic
F	Phe	Phenylalanine	Fenylalanine	Simple
G	Gly	Glycine	Glycine	Simple
H	His	Histidine	Histidine	Basic
I	Ile	Isoleucine	Isoleucine	Simple
K	Lys	Lysine	before L	Basic
L	Leu	Leucine	Leucine	Simple
M	Met	Methionine	Methionine	Simple
N	Asn	Asparagine	asparagiNe	Simple
P	Pro	Proline	Proline	Simple
Q	Gln	Glutamine	Q-tamine	Simple
R	Arg	Arginine	aRginine	Basic
S	Ser	Serine	Serine	Simple
T	Thr	Threonine	Threonine	Simple
V	Val	Valine	Valine	Simple
W	Trp	Tryptophan	tWo rings	Simple
Y	Tyr	Tyrosine	tYrosine	Simple

*EG Schulz and RH Schirmer, Principles of Protein Structure (1979), p. 2.

Use of the pH meters.

1. Plug in the meter

2. By GENTLY twisting and pulling remove the cap from the electrode. Be careful not to spill the electrode storage solution.

3. Open the hole at the top of the electrode, there is a plastic door that slides open to expose hole

4. Rinse the electrode with deionized water

5. Standardize the meter (steps 6 – 11)

6. If the display reads a small number 4 and/or 7 press “Set up”

7. When screen reads “clear” press “enter” (this removes old standards)

8. Place electrode in pH 4.0 buffer (pink)

9. Press “Standardize”

You should see numbers 2, 4, 7, 10, 12 and an icon of an electrode blinking

When meter is standardized an upper case S will appear in a box on the display, followed by (pH 100) also a small number 4 should appear and stay.

Rinse electrode again in deionized water

10. Place electrode in buffer pH 7.0

11. Repeat step 9, once again when the meter is standardized an upper case S will appear in a box on the display. Now it will be followed by a number from 90 to 105 and the number 4 and 7 should appear and remain on the display. (you are now ready to measure pH)

12. Immerse the electrode in the solution, when the upper case S appears the reading is steady and record this pH

Procedures:

A) Determine the titration curve for an amino acid

1. Using a 25-mL graduated cylinder or serological pipet, transfer 25 mL of a 0.2 M amino acid solution to a 150 - 250 mL beaker. Set up the apparatus as shown below:

2. Titrate the amino acid with 1.0 M HCl (titrant)

a. Determine the pH of the amino acid solution before the addition of titrant.

b. Initially add approximately 0.5 mL of the titrant to the amino acid at a time. Record the data IN YOUR NOTEBOOK as indicated below.

mL 1.0 M HCl pH

0.0

0.5

1.0

etc.

Note: In the beginning, the pH will change very dramatically with each addition of titrant. As you get closer to the pKa of the ionizable group, the pH will change much more slowly. When this phenomenon occurs, add 1 mL of titrant at a time.

c. After the addition of each volume of HCl, stir the solution briefly.

d. Turn the stirrer off and measure the pH using the pH meter.

e. Continue with the titration until the pH ~1.5.

3. Repeat steps 1 and 2 above, this time using 1.0 N NaOH as the titrant for a fresh 25-mL sample of the same amino acid. Record the data IN YOUR NOTEBOOK until you get to pH ~13.

mL 1.0 M NaOH pH

0.0

0.5

1.0

etc.

B) Estimate the amino acid's pKa values of the ionizable groups and its pI.

4. Using Microsoft Excel (or some similar program), construct your titration curve plotting pH versus mL of acid and base added to the amino acid solution as indicated below.

5. On your curve, designate the buffer region(s), pKa(s), and the amino acid’s pI.

6. From your graph, estimate the pKa values of the ionizing groups and the pI of the amino acid. Compare your experimental values with those found in the literature. You can, for example, use either the Handbook of Biochemistry or your textbook. Cite some reasons why your values might differ from those found in the literature.

In your report, you must categorize your amino acid as diprotic or triprotic. Based on the pKa values in the lecture Textbook state which amino acids are possibilities.

Record data in your notebook:

Titration Curve of an Amino Acid STUDY GUIDE

1. Draw the titration curve of an amino acid having only two ionizable groups (e.g., glycine). Indicate on the curve the pKa values of the α-COOH (pKa₁) and α-NH₃ (pKa₂) groups, and the pI of the amino acid.

2. The prevailing structure of the molecules in the 0.2 M amino acid solution used in today’s experiment before titrating with 1 M HCl or 1 M NaOH is

What is the structure produced after the amino acid is titrated with 1 M HCl? With 1 M NaOH?

3. Why must the magnetic stirrer be stopped each time before reading the pH?

4. Consider the following amino acid for questions 4a – 4d.

a. Is this a diprotic or triprotic amino acid?

b. Draw the titration curve if this molecule were titrated with 1M NaOH.

c. Where would the pKa values appear on this curve?

d. What group is ionizing at each pKa?

5. Consider the amino acid D having pKa’s of 1.99 (pKa₁), 3.90 (pKa_R), and 9.90 (pKa₂). What is its pI?

6. At what pH are the anion and zwitterion species of equal concentration for an amino acid having no ionizable group in the side chain?

7. Why is the amino acid Y, which has three ionizable groups 2.20 (pKa₁), 9.21 (pKa₂), and 10.5 (pKa_R), considered a simple amino acid?

8. At what pH will the amino acid containing a negative group in the side chain not migrate in an electric field?

9. Consider the amino acid H (pKa_R = 6.00) for a – c below.

a. What is its predominant ionic form at pH 7.40?

b. Draw the structure of the conjugate base/weak acid pair that exists in solution at pH 7.00.

c. What is the ratio of conjugate base to weak acid in an H buffer if the pH drops to one unit below pKa_R?

10. If one is given an amino acid such as lysine to titrate and construct a titration curve, one might observe two, not three, buffer regions. Why?

11. The initial pH of a 0.2M arginine solution is 14.

a. What is the predominant structure of arginine in solution at this pH?

b. Draw the titration curve that would result if this solution were titrated with 1M HCl to pH 7.

Table 2: pKa and pI values of Standard amino acids

S. no. Amino Acid a-carboxylic acid a-amino Side chain 1. Alanine 2.35 9.87 2. Arginine 2.01 9.04 12.48 3. Asparagine 2.02 8.80 4. Aspartic Acid 2.10 9.82 3.86 5. Cysteine 2.05 10.25 8.00 6. Glutamic Acid 2.10 9.47 4.07 7. Glutamine 2.17 9.13 8. Glycine 2.35 9.78 9. Histidine 1.77 9.18 6.10 10. Isoleucine 2.32 9.76 11. Leucine 2.33 9.74 12. Lysine 2.18 8.95 10.53 13. Methionine 2.28 9.21 14. Phenylalanine 2.58 9.24 15. Proline 2.00 10.60 16. Serine 2.21 9.15 17. Threonine 2.09 9.10 18. Tryptophan 2.38 9.39 19. Tyrosine 2.20 9.11 10.07 20. Valine 2.29 9.72

Calibration of Micropipettes

Calibration of Micropipettes

Objective:

1. To know different parts of Micropipettes.

2. To learn how to use Micropipettes.

3. To calibrate micropipettes used in Molecular Biology laboratory.

4. To learn how to take care of Micropipettes.

Introduction:

Micropipettes used to accurately measure small volumes of liquids (volumes typically vary from 1 to 1000 µL). The parts of typical micropipettes are shown below.

Accuracy and Precision

Pipettes and micropipettes can deliver accurate and precise volumes of solution. Our goal is to determine how accurate and how precise our pipette and micropipette are.

Accuracy is a measure of how close a measured value is to the accepted or “true” value. It is related to the percent error between the average volume of solution measured experimentally and the volume that was expected (the accepted value). Smaller percent error reflects higher accuracy. Percent error can be negative, indicating that the measured volume was smaller than the expected volume or positive, indicating that the measured volume was larger than the expected volume. For example, we are attempting to measure two different volumes of water with our micropipette and two with our graduated pipette. Perfect accuracy would have us measure the exact volume we desire each time. However, the volume of water that we actually measure will be close but probably different from these volumes. The farther away from the correct volume, the lower the accuracy of our pipettes and/or our technique will be. The formula for percent error is in the Statistical Functions portion of the Lab Manual Introduction.

Precision measures the closeness of a set of values obtained from identical measurements of the same quantity. It is the ability to repetitively measure the same volume of solution (whether it’s accurate or not). Precision is related to the standard deviation of a series of measurements of the same thing. For example, if the micropipette is set to the same volume (300 µL) and four measurements are taken at this volume, a standard deviation can be taken of these five measurements. The smaller the standard deviation, the more precise the micropipette is. We will use the standard deviation as a measure of the spread of potential errors in a given measurement. The formula for standard deviation is in the Statistical Functions portion of the Lab Manual Introduction. Standard deviation is usually reported with the average value like this:

In order to minimize the waste generated from experiments in this class, a number of the experiments involve a micropipette that can deliver between 100 and 1000 microliters (µL). The micropipettes are only to be used for this volume range. For larger volumes, a graduated pipette is in your locker (bulbs available from the stockroom or one of the side drawers).

Use of the micropipettes

When you push down gently on the plunger of the micropipette, you will feel a “stop” where the resistance increases. If you push a little harder, the plunger will move even further to a second stop. The first stop is used to suck up the correct volume. The second stop is used to completely expel the liquid you are measuring.

Liquid is never drawn into the barrel of the micropipette itself. An appropriate tip should always be placed firmly on the end. Since the principle by which the micropipette works is the creation of a vacuum in the tip, causing liquid to be drawn up, it is critical that the tip be on tight enough to make an air-tight seal. Having said this, do NOT jam the tips on so hard that they are hard to get off. The tips used for the 1000µL pipettes are usually blue.

The volume to be taken up is set by turning the plunger on the top of the micropipette and reading the numerical settings displayed. A setting of 100 µL is equal to 0.100 mL. A setting of 1000 µL is equal to 1.000 mL. Do not set the micropipette below 100 µL or above 1000 µL under any circumstances! Doing this is essentially the only way that the micropipettes can be broken.

When drawing liquid up into the micropipette, set the dial, and then pushes the plunger down to the first stop. While holding it there, put the end of the tip under the surface of the liquid to be measured and slowly, gently allow the plunger to return to its top position. If you go too fast, you will cause some liquid to spurt up into the micropipette barrel itself, which is bad for the micropipette, bad for your results and bad for your chemistry karma, whatever that is. This also lets air in, so the volume of fluid sucked up into the tip will be lower than the amount that you want. Never let the plunger snap up by it. Next, place the end of the tip where you want the liquid to go and push the down the plunger to the second stop to deliver the exact amount of fluid desired.

Although micropipettes are usually quite accurate when first purchased, they can eventually develop problems with use. We will spend some time checking the calibration of the micropipettes that we will be using throughout the semester to ensure that they are delivering a known volume of fluid. We will measure out different exact volumes of water with the micropipette, and using the density of water at the temperature of the water, we will determine the volume of fluid delivered based on the fluids mass.

There are many techniques and tips available that will optimize your pipetting performance and increase the reproducibility of your results. A brief description of each follows:

The Equipment

1) Tips - It is advocated that only high quality tips which optimize the pipette’s performance be used. A high quality tip is one that has a smooth uniform interior with straight even sides that prevents the retention of liquids and minimizes surface wetting. Also, the tip should have a clean, hydrophobic surface and a perfectly centered opening in order to ensure the complete dispensing of the sample. These tips should always securely interface with the nosecone, because if they do not fit correctly, the amount of liquid dispensed can be dramatically influenced.

2) Liquid Viscosity - Since the pipette was originally factory calibrated using water, any liquid that has a viscosity higher or lower than water will impact the volume dispensed. Viscosity differentials should be accounted for and taken into consideration in order to enhance the accuracy of the instrument.

3) Container - The material of construction for the extraction vessel is also important, since some materials tend to force water into a convex configuration while other materials force water into a concave configuration. Obviously, this can impact the amount of liquid drawn into the tip. A glass container is recommended since it tends to force water into a concave configuration which helps to reduce or eliminate variations due to this effect.

The Operator

1) Technique - Most end users have a tendency to believe that the volume delivery is completely dependent on the setting of the micrometer dial. Obviously, this is not the case, since many factors associated with pipettes come into play.

• Position - Pipettes should be held vertical during the aspiration of liquids, however, some end users often hold pipettes at many different angles during a pipetting interval. Holding a pipette 30o off vertical can cause as much as 0.7% more liquid to be aspirated due to the impact of hydrostatic pressure. Always store pipettes in an upright position when not in use.

• Pre-Wetting/Pre-Rinsing Tips -Failing to pre-wet tips can cause inconsistency between samples

since liquid in the initial samples adhere to the inside surfaces of the pipette tip, but liquid from later samples does not. Also, if a new volume is dialed in on the pipette’s micrometer, you will receive better results at the new volume by taking the old tip off and placing a new one on the shaft before you commence pipetting.

• Release of Plunger - Releasing the plunger abruptly can cause liquid to be “bumped" inside the pipette during a liquid transfer application. This can cause liquid to accumulate inside the instrument which in turn can be transferred to other samples causing variability in sample volume and the potential for cross contamination. It is recommended that a smooth, consistent pipetting rhythm be employed since it helps to increase both accuracy and precision. After the liquid has been aspirated into the tip, the pipette should be placed against the wall of the receiving vessel and the plunger slowly depressed. This will help all of the liquid in the tip to be dispensed. After a pause of about 1 second, depress the plunger to the bottom or blowout position (if equipped) and remove the pipette from the sidewall by utilizing either a sliding action up the wall or a brief movement away from the wall (called “touching off”).

• Immersion Depth - The pipette tip should only be inserted into the vessel containing the liquid of be transferred about 1-3mm. If the tip is immersed beyond this, the results could be erroneously high. This is due to the fact that liquid could adhere to the tip and be transferred along with the aliquot in the tip. If the tip is not immersed far enough then air could be drawn into the tip which could yield results that are incorrect on the low end.

• Equilibration Time – Troemner recommends that the tip, the pipette, the liquid being transferred, and the transfer container itself all be allowed to equilibrate to the same temperature. This is done to lessen the effects of thermal expansion which can dramatically impact the delivered volume.

• Thermal conductance – Thermal energy can be transferred from the operator’s hand to the air within the pipette (dead air) or even to the internal components themselves. This can have a dramatic impact on the amount of liquid dispensed due to the effects of expansion and/or contraction. To lessen this effect, it is recommended that some type of thermally insulated gloves like latex or cloth be worn.

2) Pipette Micrometer Setting – It is important to avoid significantly overdialing or underdialing the recommended range of the pipette. Volume delivery performance may change radically and may become completely undefined.

The Environment

1) Temperature – The volume delivery performance specifications of pipettes have been referenced by most manufacturers at room temperature which is defined as 20-25ºC. Any deviation from this specification can affect the amount of liquid dispensed due to the expansion or contraction of the internal components. Temperature is probably the most important factor that influences pipette performance. In fact, the density of water in a gravimetric analysis is calculated as a function of temperature.

2) Barometric Pressure – Pressure is reduced by 1.06" Hg for every 1000' of elevation, however, barometric pressure has only a small effect on the density formula, so the error encountered in not correcting for elevation is often ignored.

3) Relative Humidity – This is the percentage of moisture in the air at a measured dry bulb temperature compared to the amount of moisture that the air can hold at that temperature if the air is 100% saturated. Relative humidity exerts a major influence on taking accurate measurements of volume delivery. Under dry conditions, which are defined as less than 30% RH, it is extremely difficult to ensure an accurate measurement due to the rapid evaporation rate. Conversely, excessive humidity which is defined as greater than 75% can cause a measurement to be erroneously high due to condensation. Therefore, generally accepted guidelines for pipette volume delivery specify that relative humidity be maintained within the range of 45%-75%. Relative humidity also has an effect on the delivery of air displacement pipettes specifically. This is due to the evaporation of liquid from the upper several factors to consider when calibrating a pipette or choosing a calibration service:

1) If you require the “as found” data, it is advisable to obtain this before any parts or components are replaced since this can drastically change your results.

2) Clean and inspect the instrument for any visible signs of wear and tear. Make sure that the instrument can be autoclaved before autoclaving, since this can seriously damage the pipette.

3) Replace the pipette’s seals and o-rings and any other part that shows signs of wear. Remember

to pay special attention to the piston and replace if it seems especially worn or bent.

4) Ensure that the o-rings and seals have seated properly by performing a leak test and a vacuum test.

5) Allow the pipette to stabilize in an environmentally controlled, vibration-free room for a 24 – hour period to eliminate the effects of thermal expansion.

6) Decide which calibration technique that you wish to employ (i.e. Addition, Addition-Tare, Subtraction, or Subtraction-Tare).

7) Prepare the balance by “exercising” it and modifying it to accept a liquid containing vessel. It is our recommendation to use a glass container, so that the liquid has a concave meniscus.

8) Since most manufacturers originally calibrate their pipettes between 20-25°C while using bidistilled, degassed water, it is our recommendation that these conditions are duplicated.

9) Wear some type of thermally insulated gloves to lessen the transfer of heat from your hand to pipette. Latex or cloth seems to work the best.

10) Begin the liquid transfer stage of the calibration procedure utilizing the appropriate technique that you have chosen to employ.

11) Record the weightings, so that they can be converted into volumetric readings at the end of the calibration procedure.

12) Make the conversion taking into account all pertinent environmental conditions. Usually these conditions are used to calculate a Z-factor which is in turn used to convert from a mass reading to a volumetric reading.

Calibrating Micropipettes:

The two most common techniques of calibrating pipettes are the gravimetric and colorimetric (a.k.a. photometric) methods. Of these, the gravimetric method is the most common and the most widespread in use today. This method requires a stringently controlled environment, a high precision balance, a highly skilled pipetting technician, and a rudimentary understanding of statistics. The principle of this method is simple in that, given a certain mass of water with a known specific gravity; its volume can then be predicted. The accuracy and precision of the pipette can then be assessed by using an appropriate statistical approach. This method can be performed one of four ways: Addition, Addition-Tare, Subtraction, or Subtraction-Tare.

1) Addition is perhaps the most common mode of pipette calibration and it is performed by using the cumulative weight of a liquid to determine the volume dispensed.

2) The Addition-Tare method is performed by taring the balance each time before dispensing.

3) The Subtraction method uses the total subtracted weight of a liquid to determine the volume aspirated by the pipetting device. In this technique, you tare the balance only once, at the beginning, then you aspirate volumes of liquid from the vessel, take cumulative (negative) weights, and then calculate the volume aspirated based on the difference between the current and previous total weights.

4) The Subtraction-Tare method entails taring the balance each time before removing liquid from the vessel.

Since this method is not fool-proof, all variables must be stringently controlled and accounted for in order to produce results that are statistically accurate. The second most common type of pipette calibration process is the colorimetric or photometric method. This method involves the analysis of volumes of diluted dye in a cell of known path length. According to the Beer–Lambert Relationship, if a beam of monochromatic light passes through homogeneous solutions of equal pathlength, the absorbance measured is proportional to the dye concentration. So, with this in mind, an unknown volume of dye can be pipetted into a known volume of diluent, the resulting dye concentration can be measured photometrically, and the volume can be calculated. This method is less prone to environmental influences, but it requires the use of standardized consumables. Obviously, this means that each lot of standardized dye must be very carefully manufactured and calibrated in order to produce results of high accuracy. However, once solutions are prepared, calibrated and shown to be stable, accurate results can be obtained even at volumes less than one microliter11.

Principle:

The volume delivered by the pipettes is determined by weighing the amount delivered and dividing this by the density of water (at RT and 4°C).

Materials:

1. Balance (digital, upto 0.0001gm),

2. Micropipettes (1-10, 10-100, 100-1000µL),

3. Distilled water,

4. Aluminium foil

Procedure:

1. Turn on the balance

2. Place aluminium foil (prepared to cup shaped) on the pan of balance carefully

3. Zero the balance by tareing from its keyboard

4. Pipette out DW onto the foil and observe the weight of water on the data display

5. Zero the balance by tareing from its keyboard, again

6. Pipette out DW with the same pipette onto the foil and observe again the weight of water

7. Repeat steps 5 and 6 for more than 30 attempts

Observation:

Example: Pipetting of 10µL

Table 1: Weight (d=M/V) and corresponding volume (l) of water (d=1) delivered by micropipette

S. no.	1	2	3	4	5	6	7	…………………………………..	30
Experimental volume (µL)	11	12	09	10	13	09	08		11

Calculation/ Statistics:

Table 2: Determination of standard deviation (Sd) of volume of DW delivered by the micropipette

Experimental volume of DW (µL)-X	True Volume (µL) (expected volume)- X bar	(X-X bar)	(X-X bar)2
11
12
09
10
13
09
08
Calculate for all readings
11
S(X-X bar)2

Sd= Ö S(X-X bar)²/Ö n-1

Interpretation:

………………………………………………………………………………………………

Note: Ensure confidently for no handling error.

Annex:

Table 3: Relationship between temperature and water density

Temperature °C	Density of water gm/mL
15	0.9991026
16	0.9989460
17	0.9987779
18	0.9985986
19	0.9984082
20	0.9982071
21	0.9979955
22	0.9977735
23	0.9975415
24	0.9972995
25	0.9970479
26	0.9967867
27	0.9965162

Reference:

1. Experiment 1: Volumetric Measurement; Using Micropipettes and Graduated Pipettes Adapted from the CSUS Biochemistry (Chem 162) Lab Manual, Fall 2002.

2. The Science Learning Center at the University of Michigan-Dearborn TROEMNER Pipette Sttandards handbook Raising the standard

3. Tiwari K.B and Ghimire P. (2010) A Practical Handbook for Microbial Genetics and Molecular Biology. First Edition, Kantipur College of Medical Sciences, Sitapaila, Kathmandu.

Pipette Standards Handbook

Pipette Standards Handbook