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MLAB 2401:
Clinical Chemistry
Basic Principles and Practice of Clinical
Chemistry
Part One
UNITS OF MEASURE
 Measurement requires a numerical value and a unit
 Laboratory results almost always have units of measurement associated
with them
 SI units:
 length ( meter )
 mass ( gram )
 quantity ( mole )
 Volume ( liter )
 Time ( second )
 Basic units describe unrelated physical quantities
2
Unit of Measure: Prefixes
 Common prefixes and abbreviations that are added to units of measure:
 deci (d) 10-1
 centi (c) 10-2
 milli (m) 10-3
 micro ( μ) 10-6
 nano (n) 10-9
 pico (p) 10-12
 femto (f) 10-15
 Example: A common unit of liquid measurement is a deciliter( dl ), or one –
tenth of a liter
 Combine a prefix with a basic unit results in a statement of a specific length,
weight or volume
 Reporting clinical chemistry results may be in units such as :
 mg / dL
 g / dL
 mEq / L
3
Scientific Notation
 True scientific notation format:
 1.22 X 104
 BUT in hemo, for example a hemoglobin result
would look like = 12.2 X 103
4
Water Specifications
 Tap water is unsuitable for lab use (too many impurities)
 Types of water purification techniques
 Distillation – removes most organic matter
 Reverse osmosis-removes organic, ionic, microbial, and viral
contaminants
 Ultrafiltration – removes particulate matter, bacteria, emulsified solids
 Deionization – ions removed
 Reagent Grades of water
 Type I Purest – Required for sensitive tests
 Type II Acceptable for most uses
 Type III OK for washing glassware
 CAP - QC of water : pH, electrical resistance, bacterial culture
5
6
Water filtration system for
Automated chemistry analyzer.
Solutions
 The clinical lab almost always uses solutions. A solution means that
something has been dissolved in a liquid. In the clinical laboratory the
solvent we measure most of the time is human plasma. The solute is
whatever the substance is we want to measure.
 Mixtures of substances – the substances in a solution are not in
chemical combination with one another.
 Dispersed phase - the substance is dissolved (the solute)
 The substance in which the solute is dissolved is the solvent.
 Solute + Solvent = Solution
7
Concentration
 Amount of one substance relative to the amounts of the other substances in
the solution.
 Concentration can be measured in many different units
 % Solutions: w/w, v/v , w/v (parts of solute / 100 totals parts )
Note: liquids + liquids and solids + solids alters the
total parts, but solutes + solvents does not
 Molarity: Moles / Liter
 Molality: Moles / 1000 grams solvent
 Normality: equivalent weight/ liter
8
Expressing Concentration:
Percent Solution (parts/100)
 % w/w – percentage weight per weight
 Most accurate method of expressing concentration, but can be
cumbersome (especially with liquids), not often used in clinical
labs.
 % w/w = gram of solute OR gram of solute per 100.0 g of solution
100.0 g of solution
 How many grams of NaOH are needed to make a 25.0% w/w
solution using deionized water as the solvent?
25.0% w/w = X g of solute in 100 g of solution
X= 25.0 g NaOH
9
Expressing Concentration:
Percent Solution (parts/100)
 % w/v – percentage weight per volume
 Easiest & most commonly used, very accurate if temperature controlled.
 %w/v= g of solute OR g of solute per 100.0 mL of solution
100 mL of solution
What is the %w/v of a solution that has 15.0 g of NaCl dissolved into a total
volume of 100 mL deionized water?
X% w/v = 15.0 g NaCl
100 mL of solution
X= 15.0 %
10
Expressing Concentration:
Percent Solution (parts/100)
 % v/v –percentage volume per volume
 Least accurate, but used when both substances are liquids
 Note: volumes of liquids are not necessarily additive
 %v/v= mL of solute OR milliliter of solute per 100 mL of solution
100 mL of solution
 How many milliliters of ethanol are needed to make a 75.0% v/v
solution using deionized water as the solvent?
75.0% v/v EtOH = X mL EtOH in 100 mL of solution
= 75.0 mL EtOH
11
Expressing Concentration: Molarity
 Three components of Molarity
 Gram weight of solute
 Solute’s gram molecular weight
 Solvent quantity
 Number of moles per one liter of solution
 Mole = 6.022 X 1023
number of atoms or
molecules OR
 Mole= Molecular weight in grams
12
Determinig Molarity: First step
 Molecular Weight
 Sum of the atomic weights of each element in the compound
 What is the molecular weight of Na3PO4?
 Step 1: Sodium has an atomic weight of 22.99, but there are 3 molecules so
22.99*3= 68.97
 Step 2: Phosphorus has an atomic weight of 30.97, and only 1 molecule, so
30.97 *1= 30.97
 Step 3: Oxygen has an atomic weight of 16, but there are 4 molecules ,so
16*4= 64.00
 Step 4: Add 68.97+ 30.97+ 64.00= 163.94 gram molecular weight
13
Determinig Molarity: Next Step
 How many grams are contained in one mole of Na3PO4?
 Use the formula for mole calculations
Number grams of solute
Gram molecular weight of solute
1 mole Na3PO4 = X g Na3PO4
gram molecular weight(gmw)
X= 163.94 g Na3PO4
So, 163.94 grams of trisodium phosphate are contained in 1 mole of
trisodium phosphate or 6.022 X 1023
trisodium phosphate molecules
weigh 163.94 grams
14
Determinig Molarity: Final Step
 Molarity (M) = 1 mole of solute
1L of solution
We are asked to make a 1.00 L volume of a 0.100 molar solution of trisodium phosphate. How many
grams would we need?
M= grams
gmw
1.00 L of solution
0.100 molar= X grams of Na3PO4
163.94 gmw of Na3PO4
1.00 L of solution
(0.100M)(1.ooL) = X g
163.94 gmw
0.100= X
163.94
(0.100)(163.94)= X 15
Expressing Concentration:
Molality
 Amount of solute per one kg of solvent
 Expressed in terms of weight per weight or
moles per 1000 grams of solvent
 Used to measure the physical properties of
solutions
 Molality = 1 mole of solute
1 kg of solvent
16
17
Expressing Concentration:
Normality- First Step
 Equivalents Weights / Liter
 Equivalent weight is equal to the gram molecular weight of
a substance divided by its valence
 Valence = the electrical charge of an ion, or the number
of moles that react with 1 Mole H+
 Example
 The MW of calcium = 40 grams
 Calcium ions carry a +2 electrical charge ( valence = 2 )
 Equivalent Weight of calcium = 40 / 2 = 20 gram equivalent
weight
Normality:
N= number of grams of solute
Gram equivalent weight of solute
1.00 L of solution
 Normality (N)
 N = Molarity (M) x valence
 Molarity = N / valence
 M is always < N
18
Solution Properties
 Titration – Method of measuring concentration of one solution by comparing
it with a measured volume of a solution whose concentration is known
 General formula: when you have a volume and concentration of one,
and either the volume or the concentration of the other: V1 C1 = V2 C2
 For Example:
How many mls of 1.0 N HCl is required to prepare 25 mls of 0.5 N HCl ?
( 1.0 N ) ( ? mls ) = ( 0.5 N ) ( 25 mls)
? mls = 12.5 mls
You would need to add 12.5 mls of 1.0 N HCl to 12.5 mls of deionized water
( a total volume of 25 mls) to prepare 25 mls of 0.5 N HCl
19
20
Solution Properties
 Density – An expression in terms (usually) of
a mass per unit of volume
 Many examples - including specific gravity,
osmolality
pH and Buffers
 Buffers resist change in acidity
 Buffers are usually weak acids ( or bases) and their salts
 pH is the unit used to measure acidity ( Hydrogen ion concentration )
 “p” = “negative log” of the concentration of a substance in solution.
 Example: pH = - log [H+
]
 The Hydrogen ion concentration of deionized H2O is 1 x 10-7
M
 The negative log of 10-7
= 7. The pH of H2O is 7.0
 The pH scale ranges from 0 - 14
 pH 7 = neutral
 pH > 7 = alkaline (basic)
 pH < 7 = acid
21
Temperature
 Measurement of temperature is an important component of
the clinical lab. Instruments, refrigerators and incubators are
required to operate within specific temperatures that must be
maintained and monitored daily.
 Examples
 Heat blocks, water baths, and incubators shall be
maintained at least +/- 1 degree C. of the desired
temperature
 Refrigerators shall be maintained at 2 -8 degrees C.
 Each laboratory must have a NIST calibrated thermometer in
order to ensure the accuracy of other thermometers in the
laboratory
 Out-of-range temperatures should be addressed asap
22
Temperature
 Scientific measurement of temperature is always expressed in the
Celsius ( C) scale , not Fahrenheit ( F )
 Celsius scale: 0 degrees = freezing point of water
100 degrees = boiling point of water
23
Conversion: Temperature
 Conversion of Celsius to Fahrenheit and Fahrenheit to
Celsius
 F° = ( C ° x 1.8 ) + 32
 C° = ( F ° - 32 )
1.8
 For example:
 Your refrigerator at home is probably around 40 ° F. What is that in
Celsius?
 Celsius= 40-32 = 4.4
1.8
 Water boils at 100 ° C. What is that expressed in Fahrenheit?
 (1.8)(100) +32 = 212
24
Conversions
 Most conversions within the metric system occur in units of TEN
where changing a unit of measure to a higher or lower designation
requires moving the decimal one place either to the left or to the
right.
 When converting measures in either the high end of the scale
(example kilo to mega) or the low end of the scale (examples milli to
micro, micro to nano, etc.) the decimal must be moved three places
right or left as the prefix designations are assigned only to every
third unit in the extreme ends.
25
Example of a conversion
How many mls are there in 2.5 liters?
26
The question you have to ask yourself is, what is the relationship between
liters and mls? The answer : 1 liter = 1000 ml
But now what?
We want to get rid of the “liters’ units and end up with “mls” … Right ?
( ) mls2500
Liter1
mls1000
Liter2.5 =





27
( )1 2 5
1 0 0 0
1
1 2 5 0. L i t e r s
m l s
L i t e r
m l s





 =
1.25 liters = _____ mls ? Remember, write a fraction that does two things:
1. Equals 1
2. Gets rid of unwanted units and / or adds needed
units
100 mg = _________ ug ?
( )1 0 0
1 0 0 0
1
1 0 0 0 0 0m g
u g
m g
u g





 = ,
Dilutions
 A ratio of the concentrate to the total (final) volume.
 A 1:4 dilution has a 1 volume of sample and 3 volumes of diluent
mixed together.
 Any volume can be used to create this dilution, but it must be the
same unit of volume
 Keep in mind the sample size when making your dilution
 For example: a 2:3 dilution could contain:
 2 mL serum: 1 mL pure water
 20 µL of serum: 10 µL of pure water
 0.2 mL of serum: 0.1 mL of pure water
28
Dilutions for the Clinical Laboratory
Example:
A technician performed a laboratory analysis of
patient’s serum for a serum glucose determination.
The patient’s serum glucose was too high to read on
the glucose instrument.
The technician diluted the patient’s serum 1:2 and
reran the diluted specimen, obtaining a result of 210
g/dl. To correct for the dilution, it is necessary to
multiply the result by the dilution factor (in this case
x 2).
The final result is 210 g/dl x 2 = 420 g/dl.
30
Examples of dilutions and dilution factors
Parts Parts Total Dilution Dilution
Specimen Diluent Volume Factor
1.0 1.0 2.0 1 : 2 2
1.0 2.0 3.0 1 : 3 3
1.0 3.0 4.0 1 : 4 4
1.0 9.0 10.0 1 : 10 10
0.5 4.5 5.0 1 : 10 10
0.2 1.8 2.0 1 : 10 10
0.2 9.8 10.0 1 : 50 50
Serial Dilutions
 In these types of questions, you are given a series of tubes.
 Each tube having a measured amount of a diluent.
 You are instructed to add a specified amount of specimen into the first
tube, mix well and transfer a specified amount of the mixture to the next
tube, etc.
31
Serial Dilutions
 Example:
 6 tubes, each with 0.5 mL DI water
 Add 0.2 mL serum to first tube and serially dilute
 Find the dilution in tube # 6
 Find the dilution factor (will be the same in each of these tubes)
 1/dil factor x 1/dil factor x 1/dil factor (etc. 6 times)
 Result multiplying the numerator 1x1x1x1x1x1x1x = 1
 Multiplying the denominators
 Will give the result as 1 / 1838
32
Resources
 Serial dilution
 http://tinyurl.com/cw7e3ok
33
References
 Bishop, M., Fody, E., & Schoeff, l. (2010). Clinical Chemistry:
Techniques, principles, Correlations. Baltimore: Wolters
Kluwer Lippincott Williams & Wilkins.
 Doucette, L. (2011). Mathematics for the Clinical Laboratory
(2nd ed.). Maryland Heights, MO: Saunders.
 Sunheimer, R., & Graves, L. (2010). Clinical Laboratory
Chemistry. Upper Saddle River: Pearson .
34

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Basic Principles and Practice of Clinical Chemistry quality management lec 2 power point

  • 1. 1 MLAB 2401: Clinical Chemistry Basic Principles and Practice of Clinical Chemistry Part One
  • 2. UNITS OF MEASURE  Measurement requires a numerical value and a unit  Laboratory results almost always have units of measurement associated with them  SI units:  length ( meter )  mass ( gram )  quantity ( mole )  Volume ( liter )  Time ( second )  Basic units describe unrelated physical quantities 2
  • 3. Unit of Measure: Prefixes  Common prefixes and abbreviations that are added to units of measure:  deci (d) 10-1  centi (c) 10-2  milli (m) 10-3  micro ( μ) 10-6  nano (n) 10-9  pico (p) 10-12  femto (f) 10-15  Example: A common unit of liquid measurement is a deciliter( dl ), or one – tenth of a liter  Combine a prefix with a basic unit results in a statement of a specific length, weight or volume  Reporting clinical chemistry results may be in units such as :  mg / dL  g / dL  mEq / L 3
  • 4. Scientific Notation  True scientific notation format:  1.22 X 104  BUT in hemo, for example a hemoglobin result would look like = 12.2 X 103 4
  • 5. Water Specifications  Tap water is unsuitable for lab use (too many impurities)  Types of water purification techniques  Distillation – removes most organic matter  Reverse osmosis-removes organic, ionic, microbial, and viral contaminants  Ultrafiltration – removes particulate matter, bacteria, emulsified solids  Deionization – ions removed  Reagent Grades of water  Type I Purest – Required for sensitive tests  Type II Acceptable for most uses  Type III OK for washing glassware  CAP - QC of water : pH, electrical resistance, bacterial culture 5
  • 6. 6 Water filtration system for Automated chemistry analyzer.
  • 7. Solutions  The clinical lab almost always uses solutions. A solution means that something has been dissolved in a liquid. In the clinical laboratory the solvent we measure most of the time is human plasma. The solute is whatever the substance is we want to measure.  Mixtures of substances – the substances in a solution are not in chemical combination with one another.  Dispersed phase - the substance is dissolved (the solute)  The substance in which the solute is dissolved is the solvent.  Solute + Solvent = Solution 7
  • 8. Concentration  Amount of one substance relative to the amounts of the other substances in the solution.  Concentration can be measured in many different units  % Solutions: w/w, v/v , w/v (parts of solute / 100 totals parts ) Note: liquids + liquids and solids + solids alters the total parts, but solutes + solvents does not  Molarity: Moles / Liter  Molality: Moles / 1000 grams solvent  Normality: equivalent weight/ liter 8
  • 9. Expressing Concentration: Percent Solution (parts/100)  % w/w – percentage weight per weight  Most accurate method of expressing concentration, but can be cumbersome (especially with liquids), not often used in clinical labs.  % w/w = gram of solute OR gram of solute per 100.0 g of solution 100.0 g of solution  How many grams of NaOH are needed to make a 25.0% w/w solution using deionized water as the solvent? 25.0% w/w = X g of solute in 100 g of solution X= 25.0 g NaOH 9
  • 10. Expressing Concentration: Percent Solution (parts/100)  % w/v – percentage weight per volume  Easiest & most commonly used, very accurate if temperature controlled.  %w/v= g of solute OR g of solute per 100.0 mL of solution 100 mL of solution What is the %w/v of a solution that has 15.0 g of NaCl dissolved into a total volume of 100 mL deionized water? X% w/v = 15.0 g NaCl 100 mL of solution X= 15.0 % 10
  • 11. Expressing Concentration: Percent Solution (parts/100)  % v/v –percentage volume per volume  Least accurate, but used when both substances are liquids  Note: volumes of liquids are not necessarily additive  %v/v= mL of solute OR milliliter of solute per 100 mL of solution 100 mL of solution  How many milliliters of ethanol are needed to make a 75.0% v/v solution using deionized water as the solvent? 75.0% v/v EtOH = X mL EtOH in 100 mL of solution = 75.0 mL EtOH 11
  • 12. Expressing Concentration: Molarity  Three components of Molarity  Gram weight of solute  Solute’s gram molecular weight  Solvent quantity  Number of moles per one liter of solution  Mole = 6.022 X 1023 number of atoms or molecules OR  Mole= Molecular weight in grams 12
  • 13. Determinig Molarity: First step  Molecular Weight  Sum of the atomic weights of each element in the compound  What is the molecular weight of Na3PO4?  Step 1: Sodium has an atomic weight of 22.99, but there are 3 molecules so 22.99*3= 68.97  Step 2: Phosphorus has an atomic weight of 30.97, and only 1 molecule, so 30.97 *1= 30.97  Step 3: Oxygen has an atomic weight of 16, but there are 4 molecules ,so 16*4= 64.00  Step 4: Add 68.97+ 30.97+ 64.00= 163.94 gram molecular weight 13
  • 14. Determinig Molarity: Next Step  How many grams are contained in one mole of Na3PO4?  Use the formula for mole calculations Number grams of solute Gram molecular weight of solute 1 mole Na3PO4 = X g Na3PO4 gram molecular weight(gmw) X= 163.94 g Na3PO4 So, 163.94 grams of trisodium phosphate are contained in 1 mole of trisodium phosphate or 6.022 X 1023 trisodium phosphate molecules weigh 163.94 grams 14
  • 15. Determinig Molarity: Final Step  Molarity (M) = 1 mole of solute 1L of solution We are asked to make a 1.00 L volume of a 0.100 molar solution of trisodium phosphate. How many grams would we need? M= grams gmw 1.00 L of solution 0.100 molar= X grams of Na3PO4 163.94 gmw of Na3PO4 1.00 L of solution (0.100M)(1.ooL) = X g 163.94 gmw 0.100= X 163.94 (0.100)(163.94)= X 15
  • 16. Expressing Concentration: Molality  Amount of solute per one kg of solvent  Expressed in terms of weight per weight or moles per 1000 grams of solvent  Used to measure the physical properties of solutions  Molality = 1 mole of solute 1 kg of solvent 16
  • 17. 17 Expressing Concentration: Normality- First Step  Equivalents Weights / Liter  Equivalent weight is equal to the gram molecular weight of a substance divided by its valence  Valence = the electrical charge of an ion, or the number of moles that react with 1 Mole H+  Example  The MW of calcium = 40 grams  Calcium ions carry a +2 electrical charge ( valence = 2 )  Equivalent Weight of calcium = 40 / 2 = 20 gram equivalent weight
  • 18. Normality: N= number of grams of solute Gram equivalent weight of solute 1.00 L of solution  Normality (N)  N = Molarity (M) x valence  Molarity = N / valence  M is always < N 18
  • 19. Solution Properties  Titration – Method of measuring concentration of one solution by comparing it with a measured volume of a solution whose concentration is known  General formula: when you have a volume and concentration of one, and either the volume or the concentration of the other: V1 C1 = V2 C2  For Example: How many mls of 1.0 N HCl is required to prepare 25 mls of 0.5 N HCl ? ( 1.0 N ) ( ? mls ) = ( 0.5 N ) ( 25 mls) ? mls = 12.5 mls You would need to add 12.5 mls of 1.0 N HCl to 12.5 mls of deionized water ( a total volume of 25 mls) to prepare 25 mls of 0.5 N HCl 19
  • 20. 20 Solution Properties  Density – An expression in terms (usually) of a mass per unit of volume  Many examples - including specific gravity, osmolality
  • 21. pH and Buffers  Buffers resist change in acidity  Buffers are usually weak acids ( or bases) and their salts  pH is the unit used to measure acidity ( Hydrogen ion concentration )  “p” = “negative log” of the concentration of a substance in solution.  Example: pH = - log [H+ ]  The Hydrogen ion concentration of deionized H2O is 1 x 10-7 M  The negative log of 10-7 = 7. The pH of H2O is 7.0  The pH scale ranges from 0 - 14  pH 7 = neutral  pH > 7 = alkaline (basic)  pH < 7 = acid 21
  • 22. Temperature  Measurement of temperature is an important component of the clinical lab. Instruments, refrigerators and incubators are required to operate within specific temperatures that must be maintained and monitored daily.  Examples  Heat blocks, water baths, and incubators shall be maintained at least +/- 1 degree C. of the desired temperature  Refrigerators shall be maintained at 2 -8 degrees C.  Each laboratory must have a NIST calibrated thermometer in order to ensure the accuracy of other thermometers in the laboratory  Out-of-range temperatures should be addressed asap 22
  • 23. Temperature  Scientific measurement of temperature is always expressed in the Celsius ( C) scale , not Fahrenheit ( F )  Celsius scale: 0 degrees = freezing point of water 100 degrees = boiling point of water 23
  • 24. Conversion: Temperature  Conversion of Celsius to Fahrenheit and Fahrenheit to Celsius  F° = ( C ° x 1.8 ) + 32  C° = ( F ° - 32 ) 1.8  For example:  Your refrigerator at home is probably around 40 ° F. What is that in Celsius?  Celsius= 40-32 = 4.4 1.8  Water boils at 100 ° C. What is that expressed in Fahrenheit?  (1.8)(100) +32 = 212 24
  • 25. Conversions  Most conversions within the metric system occur in units of TEN where changing a unit of measure to a higher or lower designation requires moving the decimal one place either to the left or to the right.  When converting measures in either the high end of the scale (example kilo to mega) or the low end of the scale (examples milli to micro, micro to nano, etc.) the decimal must be moved three places right or left as the prefix designations are assigned only to every third unit in the extreme ends. 25
  • 26. Example of a conversion How many mls are there in 2.5 liters? 26 The question you have to ask yourself is, what is the relationship between liters and mls? The answer : 1 liter = 1000 ml But now what? We want to get rid of the “liters’ units and end up with “mls” … Right ? ( ) mls2500 Liter1 mls1000 Liter2.5 =     
  • 27. 27 ( )1 2 5 1 0 0 0 1 1 2 5 0. L i t e r s m l s L i t e r m l s       = 1.25 liters = _____ mls ? Remember, write a fraction that does two things: 1. Equals 1 2. Gets rid of unwanted units and / or adds needed units 100 mg = _________ ug ? ( )1 0 0 1 0 0 0 1 1 0 0 0 0 0m g u g m g u g       = ,
  • 28. Dilutions  A ratio of the concentrate to the total (final) volume.  A 1:4 dilution has a 1 volume of sample and 3 volumes of diluent mixed together.  Any volume can be used to create this dilution, but it must be the same unit of volume  Keep in mind the sample size when making your dilution  For example: a 2:3 dilution could contain:  2 mL serum: 1 mL pure water  20 µL of serum: 10 µL of pure water  0.2 mL of serum: 0.1 mL of pure water 28
  • 29. Dilutions for the Clinical Laboratory Example: A technician performed a laboratory analysis of patient’s serum for a serum glucose determination. The patient’s serum glucose was too high to read on the glucose instrument. The technician diluted the patient’s serum 1:2 and reran the diluted specimen, obtaining a result of 210 g/dl. To correct for the dilution, it is necessary to multiply the result by the dilution factor (in this case x 2). The final result is 210 g/dl x 2 = 420 g/dl.
  • 30. 30 Examples of dilutions and dilution factors Parts Parts Total Dilution Dilution Specimen Diluent Volume Factor 1.0 1.0 2.0 1 : 2 2 1.0 2.0 3.0 1 : 3 3 1.0 3.0 4.0 1 : 4 4 1.0 9.0 10.0 1 : 10 10 0.5 4.5 5.0 1 : 10 10 0.2 1.8 2.0 1 : 10 10 0.2 9.8 10.0 1 : 50 50
  • 31. Serial Dilutions  In these types of questions, you are given a series of tubes.  Each tube having a measured amount of a diluent.  You are instructed to add a specified amount of specimen into the first tube, mix well and transfer a specified amount of the mixture to the next tube, etc. 31
  • 32. Serial Dilutions  Example:  6 tubes, each with 0.5 mL DI water  Add 0.2 mL serum to first tube and serially dilute  Find the dilution in tube # 6  Find the dilution factor (will be the same in each of these tubes)  1/dil factor x 1/dil factor x 1/dil factor (etc. 6 times)  Result multiplying the numerator 1x1x1x1x1x1x1x = 1  Multiplying the denominators  Will give the result as 1 / 1838 32
  • 33. Resources  Serial dilution  http://tinyurl.com/cw7e3ok 33
  • 34. References  Bishop, M., Fody, E., & Schoeff, l. (2010). Clinical Chemistry: Techniques, principles, Correlations. Baltimore: Wolters Kluwer Lippincott Williams & Wilkins.  Doucette, L. (2011). Mathematics for the Clinical Laboratory (2nd ed.). Maryland Heights, MO: Saunders.  Sunheimer, R., & Graves, L. (2010). Clinical Laboratory Chemistry. Upper Saddle River: Pearson . 34