Volume of a Drop
Research question:
To what extent does the concentration of sucrose in water affect the volume of its droplet?
Aim
The aim is to find out whether the concentration of sucrose will affect the volume of one droplet,
and if so, how great this changes accordingly. In order to test this, we will be measuring the
volume of 120 droplets of water that fall from the tip of a burette, at different concentrations of
sucrose and a control without sucrose, to determine whether the volume of a single droplet will
change the volume of a single droplet.
Background research
The volume of a drop is determined by a couple of factors, namely the density and surface
tension of the liquid. The shape of a drop is largely determined by surface tension, which means
that molecules of water near the surface have greater cohesive forces in relation to each other,
due to the lack of water molecules ‘above’ the surface of the liquid.[1] Due to these cohesive
forces, it causes a droplet to be a spherical shape, which would provide the droplet with the
smallest surface area to volume ratio. Adhesion of water molecules to other surfaces also
causes the droplet to hold a certain shape (not yet spherical) before dropping. In this
experiment, the water droplet would adhere to the tip of the burette before falling into the
measuring cylinder. [2]
When sucrose is dissolved in water, its concentration changes, and hence the density changes
too. The greater the concentration of sucrose, the higher the density would be. [3][4] In addition,
the greater the density, the greater the surface tension is [5], and with greater surface tension,
the more likely a droplet of that liquid will form or hold its shape on a flat, horizontal surface.
In addition, another factor that affects the size of a droplet is the burette. The material of the
burette impacts the size of a droplet, due to the adhesive forces the droplet experiences with the
material. When comparing the adhesive forces between water and a material with cohesive
forces within water molecules, especially on a flat surface, when the adhesive forces are
greater, the liquid would be more likely to spread out, thus reducing the chances of a larger
droplet being formed.[6] However, this would be a case of multiple droplets merging together to
form one and hold its shape, rather than the volume of a single droplet being impacted. In
relation to this, the burette tip circumference also determines how large a droplet can become. A
droplet will only fall from the tip when there is a larger downward force from the weight of the
droplet than the adhesive forces between the drop and the burette tip.[7] Taking this into
consideration, it would seem that a droplet would only fall when it has a certain minimum weight.
Based on the equation 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠
,
𝑣𝑜𝑙𝑢𝑚𝑒
in which mass would be a constant (due to a specific
weight of the drop being necessary for it to fall), it would suggest that the volume of a drop will
be greater when the density is lower (ie with a lower concentration of sucrose).
Method, apparatus
Refer to instruction sheet
Analysis
Raw data
Table 1: raw data showing the raw data collected (ie volume of 120 drops across several
trials at different masses of sucrose used)
Volume 120 drops (cm³) +/- 0.1cm³
Mass sucrose
(g) +/- 0.002g
Volume
water/cm³ +/0.12cm³
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
0.000
50.00
6.6
6.0
6.0
6.6
6.4
2.000
50.00
6.2
6.2
6.2
*
4.000
50.00
6.2
6.2
6.2
6.000
50.00
6.2
6.2
6.2
8.000
50.00
6.2
6.0
6.0
6.2
6.0
Observations:
● Measuring cylinder (used to collect drops) were slightly wet before the drops were added
● Burette wasn’t always dry before the solution was poured inside, which could impact the
concentration of the solution
● The first trial at 0.00g/cm³ solution was done on a separate day as the rest, likely with a
different burette
● First few drops observed were very fast
● When a new solution of sucrose was added to the burette, there would be some air
bubbles when the solution came out
● Total volume not always entirely at the line of the measurement, but very close
● * 4th and 5th trials for 2, 4, 6g sucrose not taken
Data processing
Table 2: data processing table showing the concentration and corresponding average
volumes for 120 and 1 drop of solution
For 2.000g sucrose:
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑢𝑐𝑟𝑜𝑠𝑒
Concentration of solution: 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 =
Average volume 120 drops:
Average volume 1 drop:
𝑡𝑜𝑡𝑎𝑙 𝑡𝑟𝑖𝑎𝑙𝑠
2.000
= 0.04
50
6.2+6.2+6.2
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 120 𝑑𝑟𝑜𝑝𝑠
120
3
6.2
= 6.2
= 120 = 0.052
Concentration/g/cm³
Average volume 120 drops
(+/- 0.1) cm³
Average volume 1 drop (+/8.3 × 10−4) cm³
0.00
6.3
5.3 × 10−2
0.04
6.2
5.2 × 10−2
0.08
6.2
5.2 × 10−2
0.12
6.2
5.2 × 10−2
0.16
6.1
5.1 × 10−2
Table 3.1: data processing table showing uncertainties the concentration of sucrose
solution (independent variable)
For 0.04g/cm³ solution:
% uncertainty of concentration:
𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑢𝑐𝑟𝑜𝑠𝑒)
𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑣𝑜𝑙𝑢𝑚𝑒 𝑤𝑎𝑡𝑒𝑟)
𝑣𝑜𝑙𝑢𝑚𝑒 𝑤𝑎𝑡𝑒𝑟
× 100 =
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑢𝑐𝑟𝑜𝑠𝑒
0.002
0.12
2
× 100 +
50
× 100 +
× 100 = 0.34
* absolute uncertainty of mass is 0.002 due to uncertainty to tare the scale as well as
taking the mass of the sucrose (each 0.001g)
** due to variations in uncertainties based on different masses used for each
concentration, it couldn’t be displayed on the graph
Concentration
/g/cm³
% uncertainty
sucrose mass
% uncertainty
water volume
% total
uncertainty
Absolute
uncertainty
concentration/g/cm³
0.00
0
0.24
0.24
0
0.04
0.1
0.24
0.34
1.4 × 10−4
0.08
0.05
0.24
0.29
2.3 × 10−4
0.12
0.03
0.24
0.27
3.2 × 10−4
0.16
0.03
0.24
0.27
4.3 × 10−4
Table 3.2: data processing table showing uncertainties for the volume of a drop
(dependent variable)
% uncertainty volume:
0.1
𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑚𝑒𝑎𝑠𝑢𝑟𝑖𝑛𝑔 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟)
𝑣𝑜𝑙𝑢𝑚𝑒 120 𝑑𝑟𝑜𝑝𝑠
× 100 +
𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑟𝑜𝑝𝑠
×
2
100 = 6.2 × 100 + 120 × 100 = 3.3
* taking uncertainty of volume using
𝑚𝑎𝑥−𝑚𝑖𝑛
2
would not be relevant as it would mean 0
uncertainty for results for which all trials had the same result, therefore uncertainty is
taken as 0.1cm³ as this is the uncertainty of the measuring cylinder used
** % uncertainty for one drop is the same as that for 120 drops (as it’s a percentage), so
% uncertainty is taken from the values measured, not the calculated values (ie using
volume of 120 instead of 1 drop to find the % uncertainty)
*** although the average mass of 120 drops vary slightly, the % uncertainty all round to
the same when rounded to 2 s.f.
**** absolute uncertainty for counting the number of drops is taken as +/- 2 drops
Concentration/
g/cm³
Volume 1 drop/cm³
% uncertainty
Absolute
uncertainty/drop
0.00
5.3 × 10−2
3.3
1.7 × 10−3
0.04
5.2 × 10−2
3.3
1.7 × 10−3
0.08
5.2 × 10−2
3.3
1.7 × 10−3
0.12
5.2 × 10−2
3.3
1.7 × 10−3
0.16
5.1 × 10−2
3.3
1.7 × 10−3
Graphs
This graph shows the data (average
volume of 1 drop against sucrose
concentration). The error bars for
sucrose concentration weren’t
possible to add in, as the %
uncertainty for each value varied, and
the system only enabled a constant
uncertainty as input.
This is the same graph as above, but
with a smaller scale on the y-axis, to
show the trendline better with regards
to the results. This graph does make
the error seem much bigger and the
trend more significant, but that is
simply a result of using a much
smaller scale.
Conclusion
The results point towards the idea that as sucrose concentration increases, the mass of the
volume decreases very slightly, as followed by the trendline. However, from the average (mean,
median and modal) result of the volume of 1 drop, through combining all concentrations, it
indicates that the volume of one drop is largely unaffected by the concentration of sucrose,
based on the insubstantial changes in volume.
The graph’s correlation coefficient is -0.77, which is not very close to -1, the ideal value to
measure the correlation between the two variables with a negative correlation. From this value,
the coefficient of determination would be 0.59, thus showing that the regression line is not a
good representation of our results as there is no significant correlation between the two
variables. Thus, our results were not very relevant in determining the impact of sucrose
concentration on drop volume, as the line is essentially almost completely horizontal, pointing
towards the idea that concentration doesn’t affect droplet size.
This correlation coefficient also points towards a number of errors being made. One of the most
significant factors would be the inability to measure the exact volume of 120 drops. When we
took the measurements (eg the 6.2cm³ values), the meniscus was not always exactly at the 6.2
level. While this may not be very significant in measuring 6.2cm³ of solution, it would impact the
calculated volume of a drop, as one drop is very small. Another factor that could have
influenced this level would be the fact that the measuring cylinder may not always have been
completely dry before drops were added. More errors, and their improvements are highlighted
below.
With regards to the background knowledge, the results show a vague similarity, in the sense
that a lower concentration of sucrose (and hence lower density) had a larger volume per drop
than solutions with higher sucrose concentrations. However, once again, the difference between
the volume of each drop at different concentrations were quite insignificant, thus showing that
there was a high level of error made in the experiment. Despite this, we were able to show that
a droplet would only fall when it had a certain mass, otherwise it would simply hang from the tip
of the burette (eg when water was added very slowly). Overall, though, our results did not align
with the background context regarding density and surface tension of a liquid and how these
factors interact with a burette to determine the volume of a drop.
Evaluation
Table 4.1: evaluation table showing strengths and their significance from the experiment
Strength
Significance
Use of volumetric flask to
measure volume of water
This allows for a much more accurate measurement of the
volume of water as compared to equipment like a
measuring cylinder
Use of scale with high precision
The scale used went up to 3dp, which allows for a precise
value of the mass in order to reduce uncertainties from the
mass measured
Use of a control (test with no
sucrose)
We carried out a test to find the volume of a drop without
any sucrose dissolved in it, to determine whether sucrose
affected the volume in the first place
Repeats (3-5 times)
The use of many repeats helps to reduce the random error
in the experiment, and allows us to identify any anomalous
results (if any)
Table 4.2: evaluation table showing limitations, their significance and possible
improvements
Limitation
Significance
Improvement
Measuring cylinder
slightly wet before
drops were added.
Since the aim was to measure the
volume of a single drop, the water
in the measuring cylinder would
lead to less accurate results, as a
greater volume of solution would be
measured.
Dry the measuring cylinder each
time before counting droplets,
such as by using a paper towel to
dry the inside.
Using a different
burette for the first
trial as compared
to the rest.
Each burette is slightly different, so
the size of each droplet may vary
from one burette to the other,
causing a different total volume due
to the varying sizes of droplets.
Try to collect all the data on the
same day to ensure the burette
used is the same, or alternatively
label the burette such that the
same one will be used the next
time round.
First few drops
from the burette
were added very
quickly; counting
120 droplets.
When the droplets were added to
the measuring cylinder quickly, it
was hard to accurately take note of
how many drops had fallen. The
speed of which the droplets fell
could also have impacted the
volume of each drop.
It was also tedious to count 120
droplets properly, so there could’ve
been uncertainties regarding
For the first few droplets, it could
be better to open the burette really
slowly each time, to ensure that
the falling drops are easy to count.
When taking into account
inaccuracies of counting the
droplets, we adopted a method to
count to 20 6 times, so as to make
the counting process easier.
To count exactly 120 drops, we
whether or not it was exactly 120
droplets that fell.
could also use a counter, which
would likely be more accurate
than humans.
Air bubbles at the
start of the first
trials
When there were air bubbles, it
was sometimes difficult to
differentiate between a water
droplet and an air bubble with a tiny
bit of water surrounding it, which
could eventually make the volume
seem lower than it actually was.
When we realised the problem
with air bubbles, we would open
the burette until a normal stream
of water would be released, after
which we close the burette,
poured that solution away, and
started counting the droplets from
0.
Errors in
determining the
concentration of
sucrose
We added a specific mass of
sucrose to a beaker with some
distilled water and stirred until the
sucrose dissolved, after which we
poured that into the volumetric flask
and added more distilled water until
it reached the 50cm³ mark.
However, this provides
inaccuracies with regards to the
concentration of sucrose, because
a large mass of sucrose would
likely mean a smaller volume of
water used (since we only added
water until 50cm³), and thus, the
calculated concentration of sucrose
would’ve been lower than the
actual value.
To calculate the concentration
accurately, we would need to
ensure that the volume of water
used, that a set mass of sucrose
was dissolved, in was constant. In
this case, it could be better to
measure out 50cm³ distilled water
using the volumetric flask, and
pouring this into a beaker to
dissolve the sucrose into. Then,
the solution would be poured back
into the volumetric flask until
50cm³ of solution was used. Then,
with a constant, specific volume of
water used, you would be able to
calculate the actual concentration
of the solution more accurately.
Different people
counted for
different trials
Since people may have different
types of consistent, systematic
errors, having different people
count the droplets can lead to
inconsistencies in the results,
leading to a reduced level of
precision.
Having the same person count
each time will help to reduce this
source of error. Alternatively, an
electronic counter can be used to
provide more accuracy.
Improvements and extension
Based on the conclusion and evaluation of our methodology, it is clear that we experienced a
handful of errors that impacted our results. In terms of random error, it was quite low due to our
use of precise equipment and repeated trials, but it would be better if we did at least 5 trials for
all concentrations of sucrose, rather than just 2.
With regards to the systematic errors, the improvements possible are highlighted in the table
above, so it would be better to repeat the experiment again by taking those changes into
account the next time round. This could help to compare results to the original experiment done,
to see how similar the results turn out to be. In addition, repeating the experiment would also
allow us to test the reproducibility of the method, as it could show us if similar results or trends
can be found when the experiment is done again at a separate point in time using the same
method and taking improvements into account.
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