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?

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?

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.

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.

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-

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

• Pressure, since freezing point depends on the pressure. All experiments done under atmospheric pressure.
• Initial temperature of the substances was kept the same using a water bath, all experiments started from 110⁰C.
• Total Mass of the mixture was kept the same in all experiments, using a mass balance (addition is always 5 grams).
• Surface area, since heat loss depends on the surface area and can change the rate of heat loss. (Same test-tube used everywhere)
• Cooling process, in all experiments the mixture was cooled using the same process.

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.

(Refer to appendix A2 for material required)

(Refer to appendix A3 for apparatus required)