### Lab Report: To determine the solubility behavior of naphthalene in toluene

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Aim To determine the solubility behavior of naphthalene in toluene.
Results and calculation
Amount of naphthalene added:  20.0 g
Solvent used: toluene
Melting point of naphthalene: 79.9 oC
 Vol. of toluene used / mL Temp. when crystals 1st appeared, T1 / °C Temp. when crystals disappeared, T2 / °C Temperature required for saturation, T= (T1 + T2 )/ 2 / °C 2.00 74.7 74.2 74.4 4.00 68.7 69.2 69.0 6.00 64.7 65.3 65.0 8.00 60.9 61.1 61.0 10.00 56.8 57.5 57.2 12.00 53.1 54.2 53.6 14.00 51.0 51.7 51.4 16.00 48.0 48.3 48.2 20.00 42.1 42.8 42.4 24.00 38.3 39.3 38.8
Table 1: experimental data
Molar mass of naphthalene, C10H8 = (12.01 x 10) + (1.0079 x 8) = 128.16 g/mol                                      No. of moles of naphthalene = 20.0 / 128.16 = 0.1561 mol
When 2.00 ml of toluene is added to naphthalene,                                                                                   Mass of toluene = 2.00 x 0.82 = 1.64 g                                                                                                             No. of moles of toluene = 1.64 / (12.01 x 7 + 1.0079 x 8) = 0.01780 mol                                                                 Mole fraction of naphthalene, x2 = 0.1561 / (0.1561 + 0.01780) = 0.8976

 Volume of toluene used / ml Temperature required for saturation, T / K Solubility, mole fraction of naphthalene, x2 Log x2 103 / T (K-1) 2.00 347.6 0.8976 -0.04690 2.877 4.00 342.2 0.8143 -0.08924 2.922 6.00 338.2 0.7451 -0.1278 2.957 8.00 334.2 0.6867 -0.1632 2.992 10.00 330.4 0.6368 -0.1960 3.027 12.00 326.8 0.5937 -0.2264 3.060 14.00 324.6 0.5560 -0.2549 3.081 16.00 321.4 0.5229 -0.2816 3.111 20.00 315.6 0.4672 -0.3305 3.169 24.00 312 0.4222 -0.3745 3.205
Table 2: Solubility(x2), log x2 and 1000/T with various amount of toluene added
Log x2 =
Ideal log x2 =  ( -)
To plot ideal solubility line, arbitrary values of log x2 are used to calculate the 1000/T (k-1) values. Their respective values are being tabulated in Table 3 below.
 Solubility, X2 log (X2­) 1000/T (K-1) 1.00 0 2.83 0.40 -0.398 3.23
Table 3 : 1000/T (k) values for respective log x2 values
Graph 1: graph of log x2 against 103 / T (K-1)
From the equation of experimental data, y = -0.991 x + 2.806, where y=log x2 and x=1000/T.
Therefore, gradient = -0.991 = -Lf / (2.303 x 8.314)
Lf = -0.991 x 2.303 x 8.314 18.97 kJ mol-1.
Also, y-intercept = 2.806 = Lf / (2.303 R) x 1000 / Tm
Tm =  = 353.17K 80.0 0C

 Lf ideal

 Lf real

Solid A + solvent B                                           Solution

 ΔHmix

Solute A + solvent B
By Hess’s law, Heat of mixing = 19.02 – 18.97 = 0.05 kJ mol-1
Discussion

## Solubility behaviour

Napthalene may exhibit these solubility behaviours:
1)      Approximately ideal: when dissolved in various non-polar or weakly polar solvents
2)      Less than ideal: when dissolved in hydroxylic solvents
3)      Greater than ideal: when there are also electrolytes in water
Diagram 1: How soluble a solute is in a particular solvent depends on the relative strength of intermolecular forces in the solute, solvent and solution. The stronger the forces of intermolecular attraction in the solution, the more favoured mixing will be.
The eventual solubility behaviours depend on the relative strength of intermolecular solute-solute, solute-solvent and solvent-solvent interactions.  In this experiment, non-polar naphthalene is dissolved in non-polar solvent toluene; since the intermolecular forces of these two compounds are comparable, there is little deviation from the behaviour of an ideal mixture.
If naphthalene is dissolved in polar, hydroxylic solvents, its solubility behaviour will be less ideal than expected. This is because the interaction between napthalene-hydroxylic solvent are weaker than that between napthalene-napthalene or solvent-solvent; the components have little affinity for each other, hence leading to poor mixing.
A positive deviation, meanwhile, will be observed when naphthalene is dissolved in electrolytes in water. The resultant strong attractive forces between the solute and solvent implies that mixing is favourable and solubility, greater than ideal.

## Deviation from ideal solution

An ideal solution has an enthalpy of mixing of zero and obeys Raoult’s law[1]. The intermolecular forces between solute-solute, solute-solvent and solvent-solvent of an ideal solution are the same with that of the intermolecular interactions in the respective pure compounds. When two liquids with ideal solubility are mixed, the temperature of the mixture should remain constant.
The closer to zero the heat of mixing, the more ideal the solution is. In this experiment, the experimental enthalpy of mixing is 0.05 kJ mol-1. Napthalene and toluene have comparable intermolecular interactions and hence, mixes almost ideally.
 toluene

 naphthalene

Naphthalene, consisting of two fused benzene rings, is a non-polar compound with intermolecular van der Waals attraction. Likewise, toluene is a non-polar compound with similar induced dipole-induced dipole interactions. When naphthalene is mixed with toluene, the enthalpy of mixing is almost zero; this may be attributed to the similar intermolecular forces between naphthalene-napthalene, naphthalene-toluene and toluene-toluene. The solubility behaviour, as shown by the almost overlap of experimental and ideal trend lines in graph one, resembles that of an ideal solution.
In this experiment, the enthalpy of mixing, while close to zero, is experimentally determined to be 0.05 kJ mol-1. While naphthalene and toluene have comparable intermolecular interactions, these forces of attraction are not exactly the same; the interactions between solute-solute, solute-solvent and solvent-solvent do not have the same strength. Therefore, the solution is mainly ideal, but not completely so.
Derivation of equation
At equilibrium, the Gibbs free energy of solid naphthalene = Gibbs free energy of naphthalene in solution[2]:
Gsolid* = Gsolute = Gsolute* + RT ln x2 where x2 is the mole fraction of solute.
Rearranging  RT ln x2 = Gsolid* - Gsolute*,
ln x2 = ΔGfus / RT
ln x2 = ΔHfus / RT – ΔSfus /R ---------------- (1)
For pure liquid, x2 = 1, T = Tm,
ln 1 =0 = ΔHfus / RTm – ΔSfus / R ------------------(2)
(1)    – (2)  ln x2 = ΔHfus /R (1/T – 1/Tm)
ln x2 /( 2.303) = ΔHfus / ( 2.303 R) (1/T – 1/Tm)
lg x2 = Lf / ( 2.303 R) (1/Tm – 1/T)
where ΔHfus is the standard heat of fusion, amount of thermal energy absorbed for 1 mole of a substance to change from solid to liquid state, and is also known as the latent heat of fusion, Lf.

The graph of lg x2 is plotted against 1/T to determine the latent heat of fusion and melting point of naphthalene.

Precautions
Constant stirring of the mixture in the boiling tube ensures even distribution of heat. This prevents crystals from forming faster than expected – if cold water accumulates at the top of the boiling tube – or crystals from disappearing sooner than expected – perhaps at the bottom of the boiling tube, closer to the heat source. Constant stirring, hence, ensures that the temperature at which the crystal forms or dissolves may be more accurately determined.

Also, a magnetic stirrer was placed in the water bath. This reduces the build-up of heat at the bottom of the beaker, which may cause vigorous, therefore unsafe, bubbling.

The temperature of the water bath was maintained slightly above T1 for each subsequent addition of toluene. This prevents crystals from appearing directly when the boiling tube of mixture is replaced into the water bath for recording T2.

Determination of melting point and heat of fusion
The melting point of the naphthalene calculated is 80.0 0C. This not only compares favourably with the empirically observed melting point of 79.9 0C but is also close to the literature value of 80.2 0C[5].
For further confirmation, the Büchi melting point B-545 instrument could be used. The magnifying lense in the instrument allows a more acute observation of solid naphthalene and its melting phase, thereby leading to a more accurate determination of its melting point.
The experimental heat of fusion worked out to be 18.97 kJ mol-1, which is close to the reported value of 19.00 kJ mol-1[4].
Conclusion
The solubility behavior of naphthalene in toluene is approximately ideal, albeit with slight deviation from an ideal solution. The experimentally determined latent heat of fusion of napthalene, Lf, is 18.97 kJ mol-1, while its melting point is 80.0 0C.

References
[1] Chemguide. Raoult’s law and non-volatile solutes. Article retrieved on 20 Feb 2012:                                                                                                 <http://www.chemguide.co.uk/physical/phaseeqia/raoultnonvol.html>
[2]University of Waterloo. Gibbs free energy and equilibrium. Article retrieved on 20 Feb 2012:    <http://www.science.uwaterloo.ca/~cchieh/cact/applychem/gibbsenergy.html>
[3] National Toxicology Program, Department of Health and Human Services. Properties of naphthalene. Article retrieved on 18 Feb 2012:                                                                                                 < http://ntp.niehs.nih.gov/index.cfm?objectid=E8841CC3-BDB5-82F8-F8FF6B2922FA31BA>
[4] National Institute of Standards and Technology, Material Measurement Laboratory. Heat of fusion of naphthalene. Article retrieved on 18 Feb 2012:                                                                                < http://webbook.nist.gov/cgi/cbook.cgi?ID=C91203&Units=SI&Mask=1EFF

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2. I am some what confused on the way you determined the mass of toluene ,
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3. The graph is not shown

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