THE EFFECT OF
TEMPERATURE AND
SURFACTANTS ON THE
SURFACE TENSION OF WATER
“To what extent does the surface tension of water depend on
changing liquid temperature and surfactant concentration?’
Physics Extended Essay
Word Count: 3998
TABLE OF CONTENTS
INTRODUCTION ------------------------------------------------------------------------------------------2
1. Research question ----------------------------------------------------------------------------------------3
PHYSICS BEHIND SURFACE TENSION
1. Definition and Qualitative Explanation of Surface Tension ----------------------------------------3
2. Mathematical considerations to surface tension ------------------------------------------------------4
3. Surface tension of water ---------------------------------------------------------------------------------6
a. Factors affecting surface tension of water --------------------------------------------------------6
i. Temperature of liquid ---------------------------------------------------------------------------6
ii. Surfactants ---------------------------------------------------------------------------------------8
THE EXPERIMENT
1. Measuring the surface tension of water ----------------------------------------------------------------9
2. Construction of apparatus ------------------------------------------------------------------------------10
3. Procedure ------------------------------------------------------------------------------------------------11
4. Data recorded --------------------------------------------------------------------------------------------12
5. Data processing -----------------------------------------------------------------------------------------13
a. Temperature calculation results -----------------------------------------------------------------14
b. Surfactant calculation results --------------------------------------------------------------------17
ANALYSIS OF RESULTS
1. Surface tension vs temperature ------------------------------------------------------------------------20
a. Impact of error --------------------------------------------------------------------------------------20
b. Theoretical Data vs Experimental Data ----------------------------------------------------------20
2. Surface tension vs surfactant ---------------------------------------------------------------------------22
a. My Experimental Data vs Previous Experimental Data ---------------------------------------22
CONCLUSION ---------------------------------------------------------------------------------------------24
BIBLIOGRAPHY -----------------------------------------------------------------------------------------27
APPENDIX 1 -----------------------------------------------------------------------------------------------29
1
INTRODUCTION
There is no disputing that water is a valuable compound. Its utility results from unique physical
properties and chemical structure. Water’s chemical bonding, a property that is usually
underestimated, gives an explanation to a phenomenon known as surface tension.
Surface tension is witnessed in our everyday lives . It allows for small creatures to walk on
water , explains why raindrops acquire a spherical shape and also plays a crucial role in several
industrial processes such as determining the
efficiency of detergent formulation, stability of
food and pharmaceutical products, enhancing oil
recovery.{1}
My fascination about this phenomenon arose
Figure 1 – Spider walking on water
after my father showed me evidence of surface tension by being able to float a needle on top of a
water surface, even though a needle is heavy enough to sink. Therefore, I have chosen surface
tension of water as my area of investigation for this essay because of my fascination to understand
factors such as temperature of water and surfactant (present in soap) added to water which would
affect the surface tension created.
2
1. Research Question
“To what extent does the surface tension of water depend on changing liquid temperature
and surfactant concentration?’
Through external research {6}{9}{10}, it is expected that as the temperature of water increases, its
surface temperature decreases. Next, as the mass of soap and consequent concentration of
surfactants added to water increases, the surface tension decreases until a certain concentration
after which the surface tension is expected to remain constant.
PHYSICS BEHIND SURFACE TENSION
1. Definition and Qualitative Explanation of Surface Tension
Surface tension is a phenomenon in which the surface
of any liquid acquires the least surface area possible, thus
behaving like a thin membrane. Within the bulk of a liquid,
all molecules have surrounding molecules to which they
are attracted thereby making the net force zero. Such
attraction is due to the cohesive forces which hold the
liquid’s
molecules
tightly
together.
At
liquid-gas
Figure 2 - Forces acting on molecules of
a liquid
interfaces, these exterior molecules do not have neighboring molecules above, and hence only
display intermolecular forces to neighbors on and below the surface, which results in a
perpendicular net inward force acting upon these molecules. Due to this resulting net force,
molecules at the surface of a liquid will contract, acquiring minimal surface area.
Due to the contrasting intermolecular cohesive forces between the molecules at the surface and
molecules in the bulk of the liquid, exterior molecules have a higher energy state than those in the
3
interior. According to the second Law of Thermodynamics, which states that the total entropy of
an isolated system can never decrease over time, the surface of the liquid will minimize its surface
area to minimize the amount of high energy molecules at the surface. {2}{3}
2. Mathematical considerations to surface tension
Surface tension, denoted with the Greek letter , can be embodied in the form of surface energy
or force. These concepts will be explained by the illustration below, a thin film of liquid ABCD of
length L, contained on a rectangle composed of three unmovable sides and a fourth movable side
BC that can slide to the right, where surface tension is the force, F, preventing it from sliding .
B 𝛥𝑥
A
𝛥𝐴
L
D
F
C
Surface energy can be defined as the amount of energy required to grow the surface area of a liquid
per unit area (Jm-2):
=
𝑊
(𝟏)
𝛥𝐴
Where 𝑊 is the change in energy stored in the surface and 𝛥𝐴 is the change in area of the film
due to the sliding right side of the frame
The energy stored in the system is proportional to surface area growth, therefore as surface
area decreases, so does the energy stored in the surface of the liquid. That is why liquids minimize
its surface area when no external forces are exerted on the surface as it wants to arrive at a state of
4
least energy. Therefore, if the energy stored in the molecules of the surface increases, work must
be done to also increase the surface area.
According to Newton’s Second Law of Motion and considering that F is the force that prevents
the movable side to move to the right (Figure 1), F would also be the force that moves the side at
constant speed to the right. As the side moves to the right, the surface area of the liquid is increasing
while the force is doing work on the liquid. The more the applied force, more work being done on
the liquid, hence the energy of the film increases. The work done, 𝑊, by applied force, 𝐹 in moving
the side by Δx is:
𝑊 = 𝐹Δx (𝟐)
Simultaneously, the area of the film, ΔA increases as Δx also increases.
ΔA = LΔx (𝟑)
Substituting equations (2) and (3) into equation (1),
=
𝐹Δx 𝐹
=
LΔx L
Since the liquid has two surfaces, surface energy needs to be multiplied by a factor of ½ so that
an equal force is applied one each side.
=
𝐹
(𝟒)
2L
Equation (4) is the mathematical representation of how surface tension manifests itself as a
force. Thus, surface tension can also be defined as the force per unit length (N/m) required to grow
the surface of a liquid. {4}
5
3. Surface tension of water
Within the bulk of water, cohesive forces are strong. Water molecules are made of two
hydrogen atoms and one oxygen atom, which have contrasting electronegativities – the oxygen
atom has a larger tendency to attract the shared pair of electrons compared to hydrogen . Giving
opposite charges to each of these atoms, water becomes polar. As a result, hydrogen bonds are
formed, providing water molecules with strong cohesive forces between them.{5}
a. Factors influencing the surface tension of water
i. Temperature of liquid
Cohesive
forces
between
water
molecules are experienced due to hydrogen
bonds
between
neighboring
molecules.
Increasing temperature agitates the molecules
and increases their kinetic energy . Such
movements disturb these hydrogen bonds,
Figure 3 - Surface Tension and Temperature
causing molecules to move away from each other. Thus, their hydrogen bond length increases and
consequently becomes less strong. Since the hydrogen bond strength is a direct measurement of
how strong cohesive forces between molecules are, as temperature increases, cohesive forces
decrease, causing the surface tension of water will also decrease. {6}{9}
6
The concept developed from this has been named after
the Hungarian physicist Loránd Eötvös (1848–1919) and William
Ramsay Shield, and first formally published in 1886, the Eötvös
Ramsay Shields rule enables the determination of the surface
tension value of a liquid at any temperature, given the density,
molar mass and critical temperature of this liquid. This
empirically derived rule assumes that surface tension has a linear
correlation relationship with temperature, which is satisfied for
Figure 4 - Loránd Eötvös
all liquids as a straight-line result from a plot of temperature vs surface tension. At the critical
temperature point, surface tension is zero. The line from the plot intercepts the temperature axis
6K before critical temperature.
The Eötvös Ramsay Shields rule states that for any liquid, surface tension is given by the equation:
𝛾=
𝑘(𝑇𝑐 − 𝑇 − 6)
2/3
𝑉𝑚
(𝟓)
Where 𝛾 is the surface tension of the liquid, k is the Eötvös constant, valid for any liquid
(2.12 x 10-7 JK-1mol-2/3), Tc is the critical temperature of the liquid , measured in Kelvin (K), temperature at and above which vapor of the substance cannot be liquefied, regardless of the
quantity of pressure applied - T is the measured temperature of the liquid, measured in Kelvin (K),
and Vm is the molar volume of the liquid, measured in m3/mol - it is assumed that the molar volume
of the liquid is constant regardless of temperature as thermal expansion is negligible. {7}
Considering a liquid like water, an expression can be derived in terms of temperature to
get the surface tension value. Considering the critical temperature of water is 647K, the molar
volume is 1.8x10-5m3/mol{8} and Eötvös constant is 2.12 x 10-7 JK-1mol-2/3; substituting these
values to equation (6) gives:
7
(2.12 x 10−7 )(647 − 𝑇 − 6)
𝛾=
(1.8x10−5 )2/3
Solving this equation and rounding some values up gives the equation:
𝛾 = −0.0003087𝑇 + 0.1979 (𝟔)
ii. Surfactants
Surfactants
are
one
of
many
compounds that make soap and reduce
surface tension when added to liquids.
Composed of a hydrophilic head that
strongly interacts with water and a
hydrophobic tail, surfactants preferably
adsorb at a water-air interface, orienting
themselves so that the hydrophilic head
Figure 5 – Surface Tension and Surfactants
remains inside the water while the
hydrophobic tail points towards the gaseous phase, forming strong interaction with both phases.
There is a disruption in the intermolecular cohesive forces that hold the water molecules at the
surface together - decreasing surface tension. The more surfactants adsorbed at the interface, the
lower the surface tension. Once the surface is saturated with molecules, the surface tension does
not decrease further. Instead, surfactant molecules start grouping in the bulk of the liquid forming
several clustered surfactant molecules denominated micelles. The concentration of surfactant at
and above which micelles start being formed is called the CMC, the critical micelle concentration.
Above the CMC, surface tension values do not receive further changes and remain almost constant.
{9}{10}
8
The relationship between the concentration of surfactant added to water and the surface tension
value is not described theoretically like temperature. However, experiments have been done and
successfully achieved accurate results that describe this relationship. Students at the Embry Riddle
Aeronautical University, in Florida, have been able to determine the surface tension of surfactant
aqueous solutions using a surface force tensiometer, an automated device that directly measures
surface tension. Through their experiment, it was found that as the surface tension decreases, the
higher the concentration of SLS in solution until reaching a certain concentration after which
surface tension remained constant as it reaches CMC. {11}
THE EXPERIMENT
1. Measuring the surface tension of water
Methods of force tensiometry are universally
accepted as the most efficient and reliable ways of
measuring surface tension. Consisting of a very
sensitive balance, it measures the forces acting on a
probe placed at the surface of a liquid, which can be used
to calculate the surface tension. Commonly, the probe
configuration used comes in a distinct form: the du Noüy
Figure 6 – Force tensiomeyer
ring.
The du Noüy ring utilizes a platinum ring as the probe, which is submerged below the interface
at an irrelevant depth of immersion, to then be raised, pulling through the interface and bringing
with it a meniscus of the liquid. The calculation of surface tension depends on the measurement of
maximum force needed to raise the ring.
9
Historically, this method has been widely used to measure surface tension, with the ring
designed for keeping the surface in a non-equilibrium state. When the ring is pulled through the
surface, it expands the surface searching for the maximum force in the liquid meniscus. If the
surface tension of a pure liquid is being measured, it does not affect the results. However, for
surfactant solutions, the expansion of the surface affects the orientation of the surfactant molecules
at the surface, and therefore may be inaccurate. {9}{12}
2. Construction of apparatus
For this investigation’s purpose, using an automated force tensiometer would be ideal as it
would provide accurate results and also render the data collection efficiently. Due to the
unavailability of this equipment at the time of the data collection, a self-built apparatus was used.
Although not as accurate as automated equipment, it allowed
for the collection of data that was used to calculate the surface
tension of water.
The apparatus constructed consisted of a small equal arm
balance made from cylindrical wooden sticks and a styrofoam
base. On one side of the equal arm balance, there was a small
plastic basket and on the other, a thin ring. Like the du Nouy
ring method, the ring was placed extremely close and parallel
Figure 7 - Apparatus
to the surface of the water. Grains of rice were carefully added to the basket until ring completely
lifts from the surface. Afterwards, the mass of the basket was measured. By taking into
consideration the balance of forces between the basket with a specific mass of rice and the mass
10
of the ring, the force exerted upon the ring was able to be calculated and used to calculate surface
tension.
3. Procedure
The first experiment consisted of varying the temperature of 700ml of water. The first
increment of temperature used was 25C, while the other increments were obtained from heating
up the water using a kettle. The increments chosen are frequent with inconsistent intervals.
The second experiment consisted of adding various masses of ‘Dettol Cleanse Handwash’
soap, which contains sodium laureth sulfate (a surfactant), to 700ml of water. The mass of soap
added was measured quantitively using a weighing scale and weighing boats. Increments used
were chosen for analysis reasons. Instead of rinsing the beaker every time the increment of soap
mass is changed, more soap was simply added to the previous solution.
Clamp
Thermometer
Wooden stick
Retort
stand
Basket
Wooden stick
Styrofoam base
1000ml
beaker
Ring
700ml of
tap water
Figure 8 – Diagram of apparatus
11
4. Data recorded
Table 1 – Raw Data Table of Temperature Experiment
Table 2 – Raw Data Table of Soap Experiment
12
5. Data processing
WB
F
WR
To determine the surface tension of water, the force of surface tension was first determined.
Using the diagram above, it can be concluded that:
𝐹𝛾 + 𝑊𝑅 = 𝑊𝐵 (7)
Where 𝐹𝛾 is the force of surface tension, 𝑊𝑅 is the weight of the ring and 𝑊𝐵 is the weight of
the basket. Isolating 𝐹𝛾 and simplifying weight as a product of mass and acceleration due to gravity
(g):
𝐹𝛾 = 𝑚𝐵 𝑔 − 𝑚𝑅 𝑔 = 𝑔(𝑚𝐵 − 𝑚𝑅 ) (8)
The ring has a perfectly spherical shape and is immensely thin. Therefore, the length of ring
influenced under the force of surface tension is the diameter of the ring:
𝐿 = 2𝑅𝑅 (9)
Where 𝑅𝑅 is the radius of the ring.
13
Substituting equations (9) and (10) into the equation (4), the surface tension will be given by:
=
𝐹
𝑔(𝑚𝐵 − 𝑚𝑅 ) 𝑔(𝑚𝐵 − 𝑚𝑅 )
=
=
(10)
2L
2(2𝑅𝑅 )
4𝑅𝑅
Surface tension was calculated for each trial using equation (10), where 𝑔 is the acceleration
due to gravity (9.81ms-2), 𝑚𝐵 is the mass of the basket and whose value varies from trial to trial,
therefore giving different surface tension values, 𝑚𝑅 is the mass of the ring, constant in each trial
and which has a value of 3.708g0.001g and 𝑅𝑅 is the radius of the ring, constant in each trial and
which has a value of 1.15cm0.05cm.
a. Temperature calculation results
Table 3 – Processed Data Table
14
Table 4 – Procedure to arrive at values in table 3
1. Temperature of Water (K) = Temperature of Water (°C) + 273
2. Average mass of basket (g) = AVG (Trial 1:Trial 5)
3. Abs. Unc. Of Avg. mass of basket (g) = Abs. Unc of Each trial (lowest increment of
weighing scale) = 0.001g
4. Average mass of basket (kg) = Average mass of basket (g) / 1000
5. Abs. Unc of Avg. mass of basket (kg) = Abs. Unc. Of Avg. mass of basket (g) /1000 =
0.000001kg
6. Mass of ring (g) = 3.708g (measured value, constant for all increments)
7. Abs. Unc. Of mass of ring (g) = lowest increment of weighing scale = 0.001g
8. Mass of ring (kg) = Mass of ring (g) /1000
9. Abs. Unc. Of mass of ring (kg) = Abs. Unc of mass of ring (g) / 1000 = 0.000001kg
10. %
unc.
Of
numerator
in
equation
𝐴𝑏𝑠.𝑈𝑛𝑐.𝑜𝑓 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑟𝑖𝑛𝑔 (𝑘𝑔)+𝐴𝑏𝑠.𝑈𝑛𝑐.𝑜𝑓 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑏𝑎𝑠𝑘𝑒𝑡 (𝑘𝑔)
9.81(Avg mass of basket (kg)−Mass of ring (kg))
(11)
=
∗ 100
11. Radius of ring (cm) = 1.15cm (measured value, constant for all increments)
12. Abs. Unc. Of radius of ring (cm) = lowest increment of ruler = 0.05cm
13. Radius of ring (m) = Radius of ring (cm) /100
14. Abs. Unc. Of radius of ring (m) = Abs. Unc of radius of ring (cm) / 1000 = 0.0005m
15. % unc. Of denominator in equation (11) =
16. Surface tension value =
𝐴𝑏𝑠.𝑈𝑛𝑐.𝑜𝑓 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑟𝑖𝑛𝑔(𝑚)
4(𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑟𝑖𝑛𝑔(𝑚))
∗ 100
𝟗.𝟖𝟏(𝑨𝒗𝒈.𝑴𝒂𝒔𝒔 𝒐𝒇 𝒃𝒂𝒔𝒌𝒆𝒕 (𝒌𝒈)−𝑴𝒂𝒔𝒔 𝒐𝒇 𝒓𝒊𝒏𝒈(𝒌𝒈))
𝟒𝝅(𝒓𝒂𝒅𝒊𝒖𝒔 𝒐𝒇 𝒓𝒊𝒏𝒈(𝒎))
17. % unc. Of surface tension value = % unc. Of numerator in equation (11) + % unc.
Of denominator in equation (11)
15
18. Abs. Unc. Of surface tension value = (% unc. Of surface tension value*Surface
tension value) /100
Table 5 – Final processed data table with values used for graph
Temperature (K)  1K
298
303
318
323
333
343
358
Surface tension calculated value (N/m)
0.072800000
0.070700000
0.068700000
0.066500000
0.065700000
0.063800000
0.059100000
Graph 1 – Temperature dependency of surface tension
Above, the best fit trendline of the relationship between temperature of water and surface
tension is shown. This experiment has found this relationship can be modelled by the following
equation of the best fit trendline:
𝛾 = −0.0002𝑇 + 0.1352
16
Where  is the surface tension value, measured in N/m and T is temperature value, measured
in Kelvin (K).
b. Surfactant calculation results
Table 6 – Processed Data Table
17
Table 7 – Procedure to arrive at values in table 6
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑎𝑝 𝑎𝑑𝑑𝑒𝑑 (𝑔)
1. Concentration of soap (PPM) = 700 (𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛 𝑔𝑟𝑎𝑚𝑠) ∗ 1000000
2. Average mass of basket (g) = AVG (Trial 1:Trial 5)
3. Abs. Unc. Of Avg. mass of basket (g) = Abs. Unc of Each trial (lowest increment of
weighing scale) = 0.001g
4. Average mass of basket (kg) = Average mass of basket (g) / 1000
5. Abs. Unc of Avg. mass of basket (kg) = Abs. Unc. Of Avg. mass of basket (g) /1000 =
0.000001kg
6. Mass of ring (g) = 3.708g (measured value, constant for all increments)
7. Abs. Unc. Of mass of ring (g) = lowest increment of weighing scale = 0.001g
8. Mass of ring (kg) = Mass of ring (g) /1000
9. Abs. Unc. Of mass of ring (kg) = Abs. Unc of mass of ring (g) / 1000 = 0.000001kg
10. %
unc.
Of
numerator
in
equation
𝐴𝑏𝑠.𝑈𝑛𝑐.𝑜𝑓 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑟𝑖𝑛𝑔 (𝑘𝑔)+𝐴𝑏𝑠.𝑈𝑛𝑐.𝑜𝑓 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑏𝑎𝑠𝑘𝑒𝑡 (𝑘𝑔)
9.81(Avg mass of basket (kg)−Mass of ring (kg))
(11)
=
∗ 100
11. Radius of ring (cm) = 1.15cm (measured value, constant for all increments)
12. Abs. Unc. Of radius of ring (cm) = lowest increment of ruler = 0.05cm
13. Radius of ring (m) = Radius of ring (cm) /100
14. Abs. Unc. Of radius of ring (m) = Abs. Unc of radius of ring (cm) / 1000 = 0.0005m
15. % unc. Of denominator in equation (11) =
16. Surface tension value =
𝐴𝑏𝑠.𝑈𝑛𝑐.𝑜𝑓 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑟𝑖𝑛𝑔(𝑚)
4(𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑟𝑖𝑛𝑔(𝑚))
∗ 100
𝟗.𝟖𝟏(𝑨𝒗𝒈.𝑴𝒂𝒔𝒔 𝒐𝒇 𝒃𝒂𝒔𝒌𝒆𝒕 (𝒌𝒈)−𝑴𝒂𝒔𝒔 𝒐𝒇 𝒓𝒊𝒏𝒈(𝒌𝒈))
𝟒𝝅(𝒓𝒂𝒅𝒊𝒖𝒔 𝒐𝒇 𝒓𝒊𝒏𝒈(𝒎))
18
17. % unc. Of surface tension value = % unc. Of numerator in equation (11) + % unc.
Of denominator in equation (11)
18. Abs. Unc. Of surface tension value = (% unc. Of surface tension value*Surface
tension value) /100
Table 8 – Final processed data table with values used for graph
Concentration of soap (PPM)
500
1000
1500
2000
2500
3000
3500
Surface tension calculated value (N/m)
0.0764
0.0552
0.0442
0.0409
0.0367
0.0367
0.0368
Graph 2 – Soap concentration dependency of surface tension
It was opted not to present a linear trendline as the CMC is trying to be derived from this
graph. Line becomes horizontal at values of concentration equal or superior to 2500PPM.
19
ANALYSIS OF RESULTS
1. Surface tension vs temperature
a. Impact of error
Since calculated uncertainties are so small for surface tension values in different temperatures,
error must be assessed in another way. A good way to assess the degree to which the experiment
was impacted by experimental error is by looking at the R2, a statistical measure capable of
measuring how close the data points are to the best fit line, which gives the percentage of the
variance in y values that influences the linear model.
The R2 value of the best fit line in graph is of 77.7%, meaning that 77.7% of the variance in
surface tension is given by changes in temperature, while the remaining 23.3% was caused by
experimental error. By taking to account the strength of the correlation and how much it deviates
from the data collected, R2 gives us a precise measurement of how accurate the data collection
was. By having a value of 77.7% for R2, it can be concluded that the temperature experiment was
accurate as most of the surface tension values was mainly influenced by changes in temperature.
b. Theoretical Data vs Experimental Data
Although the R2 value is a decent measure to evaluate the accurateness of the data collected, it
does not consider any theoretical theories, like the Eötvös model, which gives literature values on
what to expect the surface tension values to be at a certain temperature. Even though the line of
best fit has a high R2 value, it does not mean that the results are accurate as they can be different
from the values
Instead, our experimental data will be compared to the theoretical model of the EötvösRamsay-Shields Equation, more particularly, equation (6) derived previously.
20
𝛾 = −0.0003087𝑇 + 0.1979 (6)
By substituting the increments of temperature for the experiment, the values that would be
expected theoretically can be derived. These values were put into table 5.
Table 9 – Expected values of surface tension according to the Eotvos Ramsay Shields Equation
Temperature (K)
298
303
318
323
333
343
358
Expected value according to EötvösRamsay-Shields equation (N/m)
0.10609514
0.10455479
0.09993374
0.09839339
0.09531269
0.09223199
0.08761094
To compare these expected results to the ones that were derived experimentally, the
experimental data points were put in a plot against the theoretical data points and the % error in
their slopes and y intercepts were, as in graph 2.
Graph 2 – Experimental Data (dashed) vs Eotvos Ramsay Shields equation (solid)
21
The % error of the gradient of the slope is of 33.33% while the % error of the y intercept of the
slope is of 31.68%, as shown in appendix 1. The percentage errors for both the gradient and the y
intercept are significantly high because the Eötvös Ramsay Shields Equation only applies to pure
liquids, not containing any impurities. Tap water contains salts and other substances that change
the structure of the hydrogen bonding between water molecules, making them weaker. That is why
experimental data points were significantly lower than the ones expected as per the theoretical
model.
2. Surface tension vs surfactants
a. My Experimental Data vs Previous Experimental Data
Since there is no theoretical model that describes the relationship between the surfactant added
to water and its surface tension, a comparison between our experimental data and the experimental
data at Embry Riddle Aeronautical University
{11}
will be conducted to quantitively evaluate the
experimental error of the data produced. Similarly to the experiment conducted at the university,
the soap added to the water contained a surfactant called sodium laureth sulfate (a surfactant).
Their results are shown in table 10.
Table 10 – Surface tension values reported at Embry Riddle University
Concentration of SLS (PPM)
500
1000
1500
2000
2500
3000
3500
Surface tension (N/m)
0.072
0.045
0.037
0.035
0.035
0.035
0.035
22
To evaluate the error and see how experimental values deviate from those reported at this
university, percentage error will be used.
Table 11 – Experimental vs Reported Surface Tension Values for various concentrations of SLS
Concentration of SLS
(PPM)
500
1000
1500
2000
2500
3000
3500
Reported surface
tension at university
(N/m)
0.072
0.045
0.037
0.035
0.035
0.035
0.035
Experimental
Surface Tension
(N/m)
0.0764
0.0552
0.0442
0.0409
0.0367
0.0367
0.0368
Percentage
Error (%)
6.11%
22.67%
19.73%
16.86%
4.86%
4.86%
5.14%
It seems that experimental error is larger at lower concentrations of soap, with an exception to
the first increment of 500PPM. As increments of concentration approach CMC, experimental
percentage error decrease until reaching an almost constant experimental error, as concentration
does not change. It can also be seen that the reported surface tension at the university reaches CMC
before of what it was experimentally recorded. This is because pure SLS solution was used instead
of soap, obviously having a higher concentration of SLS molecules in it. Therefore, the surface of
water gets saturated with these molecules and micelles start being created a lot sooner.
23
CONCLUSION
The aim of this investigation was to identify how the temperature of the liquid and the
surfactant added to the liquid affected the surface tension of water. Taking seven different water
temperatures and adding seven different masses of soap to water, the surface tension was measured
with the help of a self-built equal arm balance. Attached to one side was a small basket, and on the
other one an immensely thin. The ring was placed extremely close and parallel to the surface of
the water, which was in the interior of a beaker. Grains of rice were gradually and carefully added
to the basket until ring completely lifts from the liquid interface. Afterwards, the mass of the basket
was measured and eventually used to calculate the surface tension of water. In total, exactly 70
trials took place, 5 times for each of the 7 different increments of temperature and soap mass added.
In doing so, the research question: “To what extent does the surface tension of water depend
on changing temperature and soap concentration?”, was successfully answered.
To reach a value for surface tension, a mathematical relationship had to be established between
surface tension and the recorded values of the mass of the basket and mass and radius of the ring,
which was done through the derived equation:
=
𝑔(𝑚𝐵 − 𝑚𝑅 )
(𝟏𝟎)
4𝑅𝑅
The above equation was used for each increment of water temperature and soap mass added to
the water, which produced graphs which established the relationship between the independent
variables and the surface tension of water. From calculations, it was found that surface tension is
indeed inversely proportional to the temperature of water, as seen in graph 1. It seems that as the
temperature of the water increases, its calculated surface tension value decreases linearly, as given
by the equation of the best fit line γ=-0.0002T+0.1352. Moreover, it was also found that surface
tension decreases linearly as the mass of soap added increases until reaching a certain
24
concentration of surfactant, as seen in graph 2. From then on, values of surface tension remained
unchanged. Such findings support the hypothesis that surface tension decreases until micelles
started being formed as the liquid is saturated of surfactant molecules.
Even though the calculated findings followed the predictions, it does not mean they were
accurate. When comparing the findings of temperature dependence of surface tension to the Eötvös
Ramsay Shields Equation, and although they do follow the same general trend as proposed by the
equation (surface tension decreases linearly with an increase in temperature of the liquid), one
concludes that experimental values are generally lower than they should be, as evidenced by a
lower value of y intercept. On the other side, evaluating surface tension dependence on surfactants;
although the general trend was met, when comparing the experimentally derived data with reported
data at Embry Riddle Aeronautical University, errors start to arise, as seen in table 11.
After comparing the experiment to theoretical models and other’s accurately measured values,
a wide range of experimental error was calculated as percentage errors as seen in table 11.
One of the biggest sources of error that was assumed to have minimum to no effect was the
apparatus itself. The equal arm balance was self-built with materials that be found in a normal
household, thus there was no way to assure that friction is negligible in the axis of rotation. The
evident friction that is created in the axis of rotation might result in an inaccurate amount of rice
added to the basket, which results in a higher than supposed value of surface tension. Furthermore,
there also seems to exist a problem with the base. As it was self-built, there was no way to assure
the stability of the base – a less stable base with a shifting center of mass could mean that
measurements of mass of the basket are skewed, leading to inaccurate measurements of surface
tension.
25
Furthermore, temperature regulation can be considered as a source of error. Especially when
considering increments of higher temperatures, heat loss is significant in a shorter period, as more
particles at the surface have sufficient kinetic energy to overcome atmospheric pressure. Therefore,
at the time that the ring lifts from the surface, it is likely that the temperature at the surface is not
what was initially measured.
The position of the ring compared to the surface is something to be considered as it was
assumed that the ring was always placed parallel to the surface of the water. As there was no way
that such placement is assured, some trials might have had a wrong placement of the ring, which
means that a meniscus is not equally formed around the surface of the ring, leading to an inaccurate
calculation of surface tension.
Lastly, another factor which was not accounted for and that could have massively affected
calculated results is the nature of the water used itself. As tap water was used, the presence of
impurities and other substances is evident. As such, and considering that certain impurities might
act as surfactants, calculated results of surface tension might be lower than expected.
26
BIBLIOGRAPHY
•
Brown, C., & Ford, M. (2009). Higher Level Chemishy: Developed Spec£lically for the IB
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“Critical Micelle Concentration.” Biolin Scientific.
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s%2FAT_TN_3_cmc.pdf {10}
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of
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{8}
•
“Eötvös Rule”. Revolvy, www.revolvy.com/page/Eötvös-rule. {7}
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with a Surface Tensiometer. Embry Riddle University, Jan. 2016.
https://commons.erau.edu/cgi/viewcontent.cgi?article=1022&context=beyond {11}
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Ghosh , Pallab. “Surface Tension.”
nptel.ac.in/courses/103103033/module2/lecture1.pdf. {12}
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Laurén, Susanna. “Surface and Interfacial Tension - What Is It and How to Measure It?”
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USGS Water Science School, water.usgs.gov/edu/surface-tension.html. {2}
27
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Tension of a Liquid?” Sciencing, 30 Apr. 2018, sciencing.com/changing-temperatureaffect-viscosity-surface-tension-liquid-16797.html. {6}
•
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28
APPENDIX 1
Using the theoretical values as the slope and y intercept of the Eötvös Ramsay Shields
Equation, experimental error is given by
% 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟 =
|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 − 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒|
∗ 100
𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
Thus, and considering that for the y intercept, experimental value is 0.1352 and that the
theoretical value is 0.1979, % experimental error is given by:
% 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟 =
|0.1352 − 0.1979|
∗ 100 = 31.68%
0.1979
Furthermore, and considering that for the slope, experimental value is -0.002 and that the
theoretical value is -0.003, % experimental error is given by:
% 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟 =
|−0.002 − (−0.003)|
∗ 100 = 33.3%
−0.003
29