1) This experiment aimed to determine the statistical errors associated with diluting a 10M NaOH solution to 0.05M using seven different dilution pathways, including both direct and serial dilutions. 2) The results showed that all dilution pathways produced solutions with concentrations between 0.024M to 0.031M, indicating errors of 0.02-0.03 compared to the theoretical concentration of 0.05M. The serial dilution pathways had higher errors than the direct dilution. 3) Sources of error included inaccuracies in measuring and transferring small volumes, inefficiencies in mixing during serial dilutions, and analyte absorption to container surfaces during transfers. The highest number of dilution steps corresponded to the largest

1. DEPARTMENT OF BIOCHEMISTRY, CELL AD MOLECULAR BIOLOGY
EXPERIMENT 1
STATISTICAL ERRORS IN DILUTIONS
GROUP 9
SAMUEL MENSAH BAFFOE 10623514
ADELAIDE OHUI FIERTI
NANA AMA KONADU -YIADOM
ALEXANDER DANQUAH
KUZAGBE KAFUI ESI
ERNEST ADJEI OKERTCHIRI
06/09/17
PRACTICAL PERIOD: TUES-1:30PM -4:30PM
UNIVERSITY OF GHANA-LEGON

2. INTRODUCTION
In our various homes, a cup of tea is enough to begin the day. In preparing this, you may unintentionally
increase the amount of sugar required. In order to reduce this sugar content, a volume of water is added to
the tea. This is a basic life principle that dates back to the advent of civilization. In science this process is
known as dilution.
Dilution is the process of reducing the concentration of solutes in a solution, usually simply by adding more
solvent to achieve the desired concentration. A number called the dilution factor is used to determine the
extent of the dilution in each dilution step. In a single dilution for example, suppose you must prepare a
diluted solution of 400ml disinfectant from the concentrated stock solution with water, a volume of 350ml of
water can be added to 50ml of the stock solution. The dilution factor is therefore 50ml/400ml which is 8.
To make a highly diluted solution, scientist employ a sequential dilution process known as serial dilution. In
serial dilution, the concentration of the stock solution decreases by same quantity in successive steps. Serial
dilution is mostly applied in microbiology, biochemistry and pharmacology. A microbiologist may decide to
dilute a bacterial culture in three step 1:100 serial dilution. In each step, he may add 990ml of water to 10ml
of the bacterial culture yielding dilution of 1:100, 1: 10000 and 1: 1000000 for the first, second and third
dilution steps respectively. The formula C1V1=C2V2 is used where C1 and C2 represents initial and final
concentrations while V1 and V2 are the initial and final volumes respectively.
In daily experiments conducted in the laboratory, errors are said to be inevitable. Some sources of errors
include; human errors of the experimenter, the instrumental errors of the measuring devices and the errors
associated with the method of analysis he employs. (Skoog & West, 1996).
According to Blobel (2005), statistical errors are due to statistical uncertainties; the difference between the
measured value and the expectation value. They are special kind of error in the class of random errors
(variation in repeated measurement taken).
This experiment is aimed at determining the errors in dilution of 10M NaOH to 0.05M using seven different
pathways.
1

3. METHODOLOGY
DILUTIONS
A stock solution of 10M NaOH was diluted serially to 0.05M in seven different experimental pathways.
Experiment 1.
In a conical flask I, a 0.1ml of 10M NaOH was collected and diluted with 19.9ml of distilled water to 0.05M
making a total volume of 20ml. The 10ml pipette was used in this transfer.
Experiment 2
Distilled water of 5ml was added to 5ml of 10M NaOH to dilute it to 5M in test tube A. A volume of 0.1ml
of the 5M NaOH in test tube A was collected into conical flask II and diluted to 0.05M using 9.9ml of
distilled water. The 1ml and 10ml pipette was used in the transfer.
Experiment 3
Step 1 in experiment 2 was repeated. From the 5M NaOH obtained in test tube A was transferred 5ml into
test tube B and diluted to 2.5M using a 5ml of distilled water. A 5ml pipette was used in this transfer. A
volume of 0.2ml of 2.5M NaOH was collected into conical flask III and a 9.8ml of distilled water was added
to dilute it to 0.05M.
Experiment 4
Steps 1 and 2 in experiment 3 was repeated. In test tube C, a volume of 4ml of 2.5M NaOH from test tube B
was collected and diluted to 1.0M NaOH by adding 6ml of distilled water. In conical flask IV, 0.5ml of
1.0M NaOH was transferred and diluted to 0.05M with 9.5ml of distilled water.
Experiment 5
Steps 1, 2 and 3 in experiment 4 was repeated. A volume of 5ml of 1.0M NaOH in test tube C was delivered
into test tube D and a 5ml of distilled water was added to dilute it to 0.5M using the 5ml pipette. From this
0.5M NaOH, 1ml was transferred into conical flask V and diluted to 0.05M with 9ml of distilled water.
MATERIAL
10 NaOH, 0.05M HCL, phenolphthalein
2

4. Experiment 6
Steps1, 2, 3 and 4 in experiment 5 was repeated. A 5ml pipette was used to transfer 5ml of 0.5M NaOH
from test tube D into test tube E and diluted to 0.25M with 5ml of distilled water. A 1ml pipette was used to
transfer 2ml of 0.25M NaOH into conical flask VI and this solution was diluted to 0.05M with 8ml of
distilled water.
Experiment 7
Steps 1, 2, 3, 4 and 5 in experiment 6 was repeated. From the resulting 0.25M NaOH was collected 4ml into
test tube F and diluted with 6ml of distilled water to 0.1M NaOH. A conical flask VII was used to collect
5ml of 0.1 NaOH and diluted to 0.05M using 5ml of distilled water.
All but experiment 1 was repeated to obtain a duplicate of the solutions of 10ml of 0.05M NaOH in the
conical flasks. In experiment 1, the 20ml of 0.05M NaOH diluted solution was divided into two.
TITRATION PROCEDURE
In each conical flask containing 10ml of NaOH solution, two drops of phenolphthalein was added changing
the colour of the NaOH from colorless to pink. The burette was filled with 0.05M HCl and titrated against
the 10ml of NaOH. Each titration was done two times and the titre values were recorded.
3

5. RESULTS
TABLE 1. TITRE VALUES OF HCl FOR SEVEN EXPERIMENTAL PROCEDURES
TABLE 2. CALCULATED ERRORS IN DILUTION OF NaOH FROM 10M TO 0.05M
THEORETICAL VALUE OF CONCENTRATION (CT) =0.05M NaOH
Moles of Acid and Base at equivalent
point n= CV
CAVA=CBVB
CA = Concentration of HCl,
VA= volume of HCl used
CB = Concentration of NaOH ,
VB= volume of NaOH used
EXPERIMENTS TITRE VALUE
1
(ml)
TITRE VALUE
2
(ml)
AVERAGE
TITRE
(ml)
1 6.1 5.0 6.1
2 5.0 5.0 5.0
3 5.1 5.5 5.3
4 5.1 5.0 5.1
5 4.8 5.2 5.0
6 5.0 5.1 5.1
7 5.0 4.8 4.9
EXPERIMENTS
CONCENTRATION
OF NaOH FROM
TITRATION Cm
(M)
ERROR IN
DILUTION
CT-Cm
1 0.031≡0.03 0.02
2 0.027≡0.03 0.02
3 0.026≡0.03 0.02
4 0.025≡0.03 0.02
5 0.026≡0.03 0.02
6 0.026≡0.03 0.02
7 0.024 ≡ 0.02 0.03
4

6. DISCUSSION
The titration of HCl against NaOH is a strong acid- base titration with mole ratio of 1:1.
NaOH (aq) + HCl (aq) NaCl (aq) + H2O (aq)
From the experimental results in table 2, it can be deduced that the concentration of the NaOH in experiment
3 that neutralized the acid had the least error (0.02) as calculated from the theoretical value of concentrated
of 0.05M. Experiment 7 recorded the maximum error of 0.03.
The two titre values recorded in experiment 1 differed from each other with a volume of 1.1ml. This value
exceeds in large extent the maximum expected difference of 0.2ml. The first titre value was used as the
average titre to compensate this error. Transfer inaccuracies during the dilution might have contributed to
the error in the two titre values. That is, in preparing two solutions of a 10ml NaOH, 20ml of the NaOH was
prepared from the stock solution of 0.1ml and this solution was divided into two separate conical flasks.
The final concentration of the NaOH solution in experiment 7 (0.024M) indicates the highest amount of
dilution from the stock solution of 10M.
The serial dilution process is faced with two major challenges: The first is error propagation across columns,
or rows. The second is the efficiency in mixing of samples (NaOH and distilled water) in the test tubes. Each
step in the serial dilution process leads to a less precise dispensing. (Gomes, Korbowski & Yates, 2017).
Comley (2007) argues that chemical substances adsorb the surfaces of the test tubes and the pipette tips used
to transfer the liquid. The concentration of the analyte then becomes far less than anticipated. (More
diluted).
It is observed that direct dilutions has some drawbacks in that small volumes of a stock solution of high
concentration is needed to dilute it to a very small concentration. The measurement of this small volumes are
done using micro pipettes and measuring equipment that measures very small quantities (<10-3 unit).
With the invention of the CyBio, pipetting of very small volumes is done easily. The CyBio® Diluspro is
used in serial dilutions while the CyBi®-Nanojest is applied in direct dilution of highly concentrated
solutions
5

7. CONCLUSION
The aim of this experiment was successfully achieved. Statistical errors are associated with dilution
processes either serial or direct. The error associated with the serial dilution was maximum.
The highest dilution step used in this experiment was seven. Does increasing the number of steps increase
the extent of dilution?
REFERENCE
Blobel, V. (2005). Statistical error in Analysis. University of Hamberg.
Comley, J. (2007). Serial dilution vs direct dilution: Drug discovery Work Spring. Pg 36-50.
Gomez, M, Korbowski,J. & Yates, I. ( March 15, 2017). Assay: Accuracy and precision with serial Dilution.
Sample mixing efficiency with the BravoTM Liquid Handling Platform. Retrieved from genengnews.com-
articles/assay-accuracy-and-precision-with-serial-dilution/2038
Scoog, D.A & West, M.D (1969) Fundamentals of Analytical Chemistry, 2nd Ed. United State of America:
Holt, Rinehart and Winston Inc.
Statistical Errors (1997) Retrieved from teacher.nsrl.rochester.edu/phy.labs/statistics/statistics.htm
6