Is there any correlation between the freezing point of a mixture of naphthalene and 4-nitrophenol and the composition of the mixture (in terms of mole-fraction), determined using temperature versus composition diagram?
Inquirer and reflective are the two best profiles that describes me as a learner. I always believe that production or pursuit of knowledge begins from something we observe and want to explore more. This essay has also been a similar journey. I would like to begin with an anecdote; during my visit to Kashmir (the most popular hill station in India), I observed something really unusual. Local habitats were spreading common salt on the ice to melt it. The reason being unknown, I explored more and came to know that addition of salt can depress the freezing point of ice. Being an inquirer, I wanted to check it myself; I took two bottles –one with normal water and other with salt water; kept both of them in the refrigerator. As expected, after a while, I found that the pure water was converted to ice while the salt water not. This evoked me to search more. I made an effective search from reliable and credible secondary sources and came to know about the addition of impurity to change the freezing point of mixtures. The immediate question I had – What is the application or use of this phenomenon? Further exploration on the application of this topic led me to know about the existence of eutectic mixture, which is mainly a mixture of two solids in such a ratio so that the freezing point of the mixture in that ratio is lower than the freezing point of the pure component in the mixture. Learning from a text book on Physical Chemistry by Engel and Red exposed me to the fact that the mixture of poly-nuclear aromatic hydrocarbon and phenolic compounds behave as eutectics. Immediately, a consultation with my laboratory technician, I got to know that we have naphthalene (binuclear aromatic hydrocarbon) and phenol in our school laboratory, which can be the perfect choice of two materials for making an eutectic mixture. Thus, I decided to conduct my Extended Essay in Chemistry to address the research question stated below:
Is there any correlation between the freezing point of a mixture of naphthalene and 4-nitrophenol and the composition of the mixture (in terms of mole-fraction), determined using temperature versus composition diagram?
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Freezing is the process of converting a substance from liquid state to solid state. Freezing of a substance in the liquid state will occur at a constant value of temperature and that is considered as the freezing point. During freezing there exists equilibrium between the solid and the liquid phase.
During any phase change like freezing, the temperature of the system remains unchanged until the phase change is completely over. The heat lost by the system is lost in the form of latent heat and does not decrease the temperature of the system. During freezing, the heat lost by the system is manifested in decreasing the disorderness or entropy of the system as it changes from a more disordered liquid state to a less disordered solid state.
To determine the freezing point, the component is taken in the liquid state and then allowed to cool. The temperature of the system (whether one single component or a homogenous mixture of two components) is recorded at regular intervals of time unless the entire system gets converted into solid. A graph is plotted with temperature along the y axes and time along th e x axes. In the graph, a straight line parallel to the x axis is obtained. This line is extrapolated to intersect the y axes and the temperature at the intersection point is taken as the freezing point of the system.
In the above figure (Figure - 1), the line XY represents the compound in liquid state while the line WZ represents the compound in solid state. The line YW represents the coexistence of both the solid and liquid phase in equilibrium and thus denotes the phenomenon of freezing.
For a mixture of two components A and B with number of moles nA and nb,
Mole-fraction of A (XA) = \(\frac{^nA}{^nA+^nB}\) ; mole-fraction of B (XB) = \(\frac{^nB}{^nA+^nB}\)
Sum of mole-fraction = XA + XB = 1
There are certain mixture of two solid components which exhibits a freezing point of a much lower value than the freezing point of the individual pure components. For example a mixture of Sn and Pb exhibits a freezing point of 183°C at a composition of 62% of Sn and 38% of Pb by mass and this freezing point is much lower than the freezing point of the pure components (Sn = 232°C and Pb = 327°C). Such points in the temperature versus composition graphs are known as eutectic points and the composition of the mixture at those points is known as the eutectic composition while the temperature is known as the eutectic temperature. Although, the scientific reason behind existence of such points is still not clear, yet some researches claim that it is due to the variation in the crystal structure of the compounds in the pure form and the solids formed by cooling of the molten mixture at the eutectic point.
Refer to Appendix A-1
nitrophenol: Refer to Appendix A-1
To analyse or understand the variation of freezing point of a mixture of two components, we need to first understand how the freezing point of a pure compound will change if a foreign substance is added to it. Addition of non-volatile solutes to a pure solvent decreases the freezing point which is very well defined in Raoult’s law of colligative properties. For example, the freezing point of an aqueous solution of NaCl would be lower than the freezing point of pure water.
Freezing is basically converting a substance from liquid state to solid state. In this process, the molecules in the liquid state are brought closer to each other to decrease the intermolecular distance between them. This is achieved by decreasing the temperature and thus reducing the average kinetic energy of the molecules which in turn slows down the motion of the molecules and brings them closer.
If we are cooling pure water, as we decrease the temperature, the water molecules will come closer and finally gets converted into solid state at it’s freezing point. But, if some other substance like NaCl is present along with water in the system, these particles will come in between the water molecules when they are trying to come closer and hence inhibit them from coming closer and go into the solid state. To counteract this interference of NaCl, we need to reduce the motion of all the particles in the system to a greater extent and thus decrease the temperature to a greater extent. Thus, the freezing point of the system decreases. Thus, in short as the amount of impurity added to a pure component increases, the freezing point decreases more.
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Freezing is an exothermic process. Hence the value of enthalpy change (∆H) is negative. During freezing, liquids are converted to solid, disorderness of the system decreases; value of entropy change (∆S) is negative.
∆G = ∆H - T∆S
Since ∆S is negative, the term (-T∆S) becomes positive. So, the value of Gibb’s free energy change(∆G) would be negative only if the magnitude of ∆H exceeds the magnitude of T∆S. Thus, as the temperature decreases, the value of ∆G becomes less positive or more negative and the process becomes more spontaneous.
To simplify, we may say that as the freezing point decreases, the process of freezing becomes more thermodynamically favoured.
Gibb’s phase rule states that: F = C-P+1 (assuming pressure to be constant).
F = Degrees of freedom
C = number of components
P = number of phases (solids, liquids or gases).
The degrees of freedom of a particular point in a temperature versus composition graph represent the number of intensive (mass independent) variables which we can alter for that particular point. For example, if the degrees of freedom calculated for a particular point is 1; it means that even if we change a particular variable like temperature or mass, the system will still be in the same phase (solid/liquid/gas).
In order to study the variation of the freezing point of a mixture of two solids against the composition of the mixture, we may use the resistivity method. We have to take the mixture, allow it to cool and measure the resistance at regular intervals of time. At the freezing point, the mixture will get converted from the liquid to solid state, the ions in the system will stop moving and the value of resistance will increase sharply. Thus, if we plot the values of resistance of the system against temperature, a sharp jump will be observed in the graph indicating the freezing point of the liquid.
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The method is appropriate if both the components in the mixture are ionic in nature. In the current investigation, naphthalene and 4-nitrophenol have been used and both of them are organic and covalent compounds. So, this method was not used.^{15}
Independent Variable – Composition of the mixture
Different ratios of masses were taken for naphthalene and 4-nitrphenol measured using a mass balance and the moles were calculated. Then the formula for mole fraction was used to calculate the mole fraction of 4-nitrophenol. The mass ratio between naphthalene and 4-nitrphenol was varied. The substances were mixed in the following ratios-
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Dependent – Freezing temperature of the mixture of naphthalene and 4-nitrophenol.
Stainless steel temperature probe and Lab Quest was used to measure the temperature of the mixture at intervals of 30 seconds. The temperature was recorded against time for 10 minutes and the graph was plotted, the plateau region or the region where the temperature did not change for a few minutes was considered as the freezing temperature.
List of controlled variables
Null hypothesis
I hypothesize that there is no correlation between the independent variable- Composition of the mixture, and the dependent variable- freezing temperature of the mixture of naphthalene and 4-nitrophenol.
Alternative hypothesis
I hypothesize that there is a strong correlation between the independent variable-Composition of the mixture, and the dependent variable- freezing temperature of a solid solid binary mixture of naphthalene and 4-nitrophenol.
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(Refer to appendix A2 for material required)
(Refer to appendix A3 for apparatus required)
(For further information refer to appendix A5)
Ethical considerations
Environmental concerns
Calibration of temperature probe -Refer to appendix A5
Calibration of the mass balance -Refer to appendix A5
Primary procedure
In the graph above, line AB the represents pure naphthalene in the liquid state, CD represents naphthalene in the solid state and line BC represents equilibrium between naphthalene in solid state and naphthalene in liquid state. Hence, the temperature corresponding to the line BC (80C) is considered as the freezing point because during freezing the temperature of the mixture is supposed to remain constant over a period of time until the entire liquid has not been converted completely into solid state.
Refer to Appendix A-6 for other raw data tables and Appendix A-7 for other graphs.
Mole fraction of 4-nitrophenol (X_{A})
Mole fraction of naphthalene (X_{B})
Freezing point/ ±0.1°C
Percentage Error (%)/ ± 10^{-2}
Mole fraction calculation for 1 gram of 4-nitrophnol and 4 grams of naphthalene
Moles of 4-nitrophenol(n_{A})
\(=\frac{mass}{molar \ mass}=\frac{1.00}{139.11}\) = 0.0072
Moles of 4-nitrophenol (n_{B})
\(=\frac{mass}{molar \ mass}=\frac{4.00}{128.17}\)= 0.031
Mole-fraction of 4-nitrophenol (X_{A})\(=\frac{^nA}{^nA+^nB}=\frac{0.0072}{0.0072+0.031}\) = 0.19
Mole-fraction of naphthalene (X_{B}) =1- X_{A}=1 - 0.19 = 0.81[since,X_{A}+X_{B }= 1]
Sample Calculation for determination of random error and percentage error in freezing point
Freezing point (x) = 58.00 °C; average uncertainty in temperature(∆x) = ± 0.1
Random error \(\frac{Δx}{x}=\frac{0.1}{58.00}\)= 0.001724
Percentage error = Random error × 100 = 0.001724 X 100 = 0.17 (approx.)
Sample calculation of uncertainty in mole-fraction of 4-nitrophenol
For 1.00 g of 4-nitrophenol and 4.00 g of naphthalene,
nA =0.0072 ± 0.01 ; nB = 0.031 ± 0.01 [uncertainties in mass and moles are considered to be identical]
n = total number of moles = nA + nB = 0.0072 + 0.031 = 0.0382 ± (0.01 + 0.01) = 0.0382 ± 0.02
\(\)X_{A}=\(\frac{^nA}{^nA+^nB};\)
\(\frac{ΔX_A}{X_A}=\frac{Δn_A}{n_A}+\frac{Δn}{n}=\frac{0.01}{0.0072}+\frac{0.02}{0.0382}\) = 0.19
ΔX_{A }= 0.19 X X_{A}= 0.19 X 0.81 = ±0.35
X_{A} = mole-fraction of 4-nitrophenol
X_{B} = mole-fraction of naphthalene
A= point indicating freezing temperature of pure naphthalene
E =eutectic point
C = point indicating freezing temperature of pure 4-nitrophenol
AEB = Liquidus and HEI = solidus
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The mole fraction of 4-nitrophenol is plotted along the x axes; as we move from left to right along x axes, mole fraction of 4-nitrophenol increases (X_{A}=0 at point D to X_{A}=1 at point E) and mole-fraction of naphthalene decreases (X_{B} = 1 at point D and X_{B} =0 at point E). The uncertainty in x axes are not considered as it differs for each data points.
The freezing temperature (± 0.1 C) is plotted along the y axes as it is the dependent variable.
As clearly understood from the nature of the experimental points, two opposite trends are observed in the graph - freezing point of the mixture decreases from 80.00C (freezing point of pure naphthalene) to 35.0°C as the mole fraction of 4-nitrophenol increases from 0.00 to 0.37, and the mole fraction of naphthalene decreases from 1.00 to 0.63.
Then the freezing point increases from 55.0°C to 105.0°C (freezing point of pure 4-nitrophenol) as the mole fraction of 4-nitrophenol increases from 0.58 to 1.00 and the mole fraction of naphthalene decreases from 0.42 to 0.00.
Thus two different best fit straight lines are plotted – AG taking the points at mole fraction of 4-nitrophenol (0.00, 0.19 and 0.37) depicting the decrease in freezing point with the increase in mole fraction of 4-nitrophenol and BF taking the points at mole fraction of 4-nitrophenol - 0.58, 0.79 and 1.00 showing the decrease in freezing point with the decrease in the value of mole fraction of 4-nitrophenol.
The two straight lines intersect each other at the point E. This point E is thus considered as the eutectic point of the mixture. A perpendicular is drawn from the point E which meets x axes at 26.0 and a perpendicular drawn from the point E meets y axes at 0.45.
At eutectic point(E),
Freezing temperature (Te) = 26.0°C
Mole-fraction of 4-nitrophenol (X_{A}) = 0.45
Mole-fraction of naphthalene (X_{B}) = 1-0.45 = 0.55
It clearly means that the mixture of naphthalene and 4-nitrophenol will exhibit the lowest possible freezing point if they are mixed in the ratio 0.55:0.45 (naphthalene:4-nitrophenol) in terms of moles and the value of the lowest possible freezing point is 26.0C
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Applying Gibb’s phase rule to the eutectic point:
F= C-P+1
At the eutectic point, there is a equilibrium as shown below:
Mixture of naphthalene and 4-nitrophenol (liquid) ↔ Napthalene(s) + 4-nitrophenol(s)
It means that at the eutectic point, the three phases- mixture of naphthalene and 4-nitrophenol in the liquid state, solid naphthalene and solid 4-nitrophenol co-exists.
So, number of phases (P) = 3
Number of components = 2; naphthalene and 4-nitrophenol
Hence, F = 2-3 + 1 =0
It means that at the eutectic point, there is no degree of freedom. It cannot be shifted either along the x axes or along the y axes; there is only one single and fixed composition of the mixture at which the freezing point will attain the lowest value; in case we change the composition or mole fraction of 4-nitrophenol the point will shift either to the left or right of the x axes and the equilibrium between the three phases – mixture of napthalene and 4-nitrophenol in the molten state, solid naphthalene and solid 4-nitrophenol will be lost.
The region above the line AEB represents the mixture of naphthalene and 4-nitrophenol in the molten state; it means that for each and every values of mole fraction in the x axes if the temperature is above the value on the line AEB, the mixture will be in the molten state. Similarly, the region below the line HEI represents the mixture of solid naphthalene and solid 4-nitrophenol. It means that for all values of mole fractions of 4-nitrophenol along the x axes, the mixture will contain both the components in solid state, if the temperature of the mixture is below the eutectic point (26.0C). The line AEB represents the liquidus as it represents the mixture in molten state above it while the line CD is known as solidus as it represents the mixture in solid state below it.
Point D
Mole fraction of 4-nitrophenol (X_{A}) = 0
Mole –fraction of naphthalene (X_{B})
= 1 – X_{A} = 1-0 =1
It means that at point X, the compound is pure naphthalene.
Thus, point A on the y axes will represent the freezing point of pure naphthalene.
According to the graph,
Freezing point of pure naphthalene
( T^{0}_{Bobserved}) = value of y axes at point A = 80.0°C
Literature value of freezing point of pure naphthalene
( T^{0}_{Bcaculated}) = 80.2°C
Percentage error
\(=\frac{mod(observedvalue -calulatedvalue)}{calculatedvalue}\) X 100
\(=\frac{mod(80.2-80.0)}{80.2}\)X100 = 0.25
Point E
Mole fraction of 4-nitrophenol (X_{A}) = 1
Mole –fraction of naphthalene (X_{B})
= 1 – X_{A} = 1-0 = 1
It means that at point X, the compound is pure 4-nitrophenol.
Thus, point C on the y axes will represent the freezing point of pure 4-nitrophenol.
According to the graph,
Freezing point of pure 4-nitrophenol
( T^{0}_{Aobserved})= value of y axes at point C = 105.0°C
Literature valueof freezing point of
pure 4 –nitrophenol ( T^{0}_{Bcaculated}) = 113.0°C
Percentage error
\(=\frac{mod(observedvalue-calculatedvalue)}{calculatedvalue}\)X100
\(=\frac{mod(105.0-113.0)}{113}\)X 100 = 7.7
Thus, the values of freezing point of pure naphthalene and 4- nitrophenol as calculated from the graph are 80.0°C ± 0.25% and 105.0°C ± 7.07% respectively
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Explanation behind the line AG
At point A, the system is pure naphthalene and thus it shows the freezing point of the pure component naphthalene. As we are adding more 4-nitrophenol into it, the process of freezing becomes difficult and thermodynamically unfavourable. The presence of molecules of 4-nitrophenol in between two molecules of naphthalene inhibits them from coming closer and go into the solid state. Since, for freezing both ∆H and ∆S are negative, the process becomes more spontaneous with decrease of temperature. (Refer to Page- 9, 2.7). Thus, as the mass of 4-nitrophenol added increases from 0.00 g to 2.00g, freezing point decreases from 80.00C to 35.0°C to make the values of ∆G more negative and hence the process more thermodynamically favourable.
Explanation behind the line BF
Similarly, at point B (mole fraction of 4-nitrophenol=1), the system is pure 4-nitrophenol and thus the value in y axes represents the freezing temperature of pure 4-nitrophenol. As we are decreasing the mole fraction of 4-nitrophenol, we are basically increasing the mole fraction (or amount) of naphthalene. Here, since the amount of 4-nitrophenol is more and that of naphthalene is less, we may consider the former to be a pure component and the latter to be an impurity. Thus we may explain in the same way(as we did for AG), that amount of impurity (naphthalene ) increases, freezing point decreases to make the value of ∆G more negative and the process more feasible.
Reference to a secondary source
Pure Ibuprofen has a freezing temperature of 76.0°C and pure Thymol has a freezing temperature of 52.00C, whereas together the composition in the ratio of 2:3 has a freezing temperature of 32°C which is the eutectic point.
The basic aim of the investigation was to address the research question-
Is there any correlation between the freezing point of a mixture of naphthalene and 4-nitrophenol and the composition of the mixture (in terms of mole-fraction), determined using temperature versus composition diagram.
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Random error
Systematic error
k_{eutectic = }\(\frac{^Te}{T^0_{napthalene}+T^o_{4-nitrophenol}}=\frac{26.6}{(80.0+105.0)}\) = 0.14
The accepted value of co-efficient of eutectic temperature is 0.25 to 0.49. Hence, the experimentally calculated value of coefficient of eutectic temperature is much lower than the lowest acceptable value and does not fall within the accepted range. This finding invariably questions our claim to consider the mixture of naphthalene and 4-nitrophenol as a eutectic system.
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While doing the research, I came to know that the type of crystalline structure the components show in the pure form and in the solids formed at the eutectic point are different; it means at eutectic point the crystalline structure of the components differ from the original ones. I would like to conduct an investigation to study how the crystal structure of the solids changes when they form an eutectic mixture. It can be done if we study the crystal parameters (shape of crystals, distance between atoms) of the pure components and the solids obtained at the eutectic point using X ray diffraction study.
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Naphthalene is a white, volatile, solid polycyclic hydrocarbon with a strong mothball odour. It is obtained from either coal tar or petroleum distillation and is primarily used to manufacture phthalic anhydride, but is also used in moth repellents. Its molecular formula is C_{10}H_{8 }with a molecular weight of 128.174 g/mol.
4-Nitrophenol is a phenolic metabolite of environmental chemicals present in samples from the general population. Its measurement in urine is used in biological monitoring for establishing the presence and magnitude of exposures to pesticides. It has a molecular formula of C_{6}H_{5}NO_{3} and a molecular weight of 139.11 g/mol.
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10 cm^{3}
250cm^{3}
A laboratory thermometer is calibrated using a beaker with water and ice, the thermometer is added in the beaker with water and ice and checked if the temperature shown on the thermometer is 0 ±0.5 0C, to ensure there is no zero error in it.
Known mass of 1 gram is put on the mass balance and checked if it shows the right reading for the mass (1.00 gram) to ensure mass balance is calibrated properly.
Here,
The freezing temperature of the composition is = 58°C
Since at 38C the temperature is constant for a few minutes, which means that the composition is changing its physical state.
Here,
The freezing temperature of the composition is = 35°C
Since at 35°C the temperature is constant for a few minutes, which means that the composition is changing its physical state.
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Here,
The freezing temperature of the composition is = 55°C
Since at 35°C the temperature is constant for a few minutes, which means that the composition is changing its physical state.
Here,
The freezing temperature of the composition is = 68°C
Since at 41°C the temperature is constant for a few minutes, which means that the composition is changing its physical state.
Here,
The freezing temperature of the composition is = 105°C
Since at 51C the temperature is constant for a few minutes, which means that the composition is changing its physical state.
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In the graph it can be observed that the temperature stays constant at 58C for a few minutes showing that it is the freezing point.
In the graph it can be observed that the temperature stays constant at 35C for a few minutes showing that it is the freezing point.
In the graph it can be observed that the temperature stays constant at 55C for a few minutes showing that it is the freezing point.
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In the graph it can be observed that the temperature stays constant at 68C for a few minutes showing that it is the freezing point.
In the graph it can be observed that the temperature stays constant at 105C for a few minutes showing that it is the freezing point.
Mass of naphthalene = 4 g = 0.004 kg
Mass of 4-nitrophenol = 1 g
Number of moles of 4-nitrophenol = \(\frac{1}{139.11}\) = 0.007
Molality of the solution (m) = \(\frac{moles\ of\ solute (4-nitrophenol)}{mass\ of solvent (napthalene\ ) in \ kg}=\frac{0.007}{0.004}\) = 1.75
Cyroscopic constant (Kf) for naphthalene =7.01
Depression of freezing point (∆Tf) = Kf.m = 7.01X 1.75 = 12.26
Freezing point of the mixture (Tf) = Freezing point of pure naphthalene - ∆Tf = 80.2 – 12.26 = 67.9C
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