I.
ABSTRACT
The focus of this experiment is the determination of the partial molar volume of ethanol-water system. This experiment also emphasized the demonstration on how to use the pycnometer for measuring density and specific gravity, which was then further explained in the procedures part of this report. These density and specific gravity measurements were then used to determine the partial molar volume of the considered ethanol-water system at different concentrations. By the end of the data gathering, the results were then interpreted and the group was able to present that the 3 3 molar volume of pure ethanol is 58.801 cm /mol and that of distilled water is 18.073 cm /mol.
II.
INTRODUCTION
The volumes of the components of a solution are not additive in general. First of all, considering a mixture of water and ethanol, the molecules experience different intermolecular forces than in the pure substances in the solution. That is, the intermolecular forces between a water molecule and an ethanol molecule, is different from the intermolecular forces between two water molecules, or between two ethanol molecules. Secondly, water and ethanol molecules have different sizes and shapes, and, consequently, the molecules in pure water, or in pure ethanol, are going to fit together differently, than the molecules in a solution of ethanol and water. These two factors: differences in molecular sizes and shapes and differences in intermolecular forces, compared to the pure substances, cause the molecules to pack together differently in the mixture than in the pure liquids, and result in the non-additivity of the volumes. A quantitative treatment of this behavior requires the introduction of the partial molar volume. Consider a solution at constant pressure and temperature pre pared by mixing n1, n2…ni moles of substances 1, 2, …i. The total volume of the unmixed pure substances is: V*= n1Vm,1* + n2Vm,2* + …niVm,i*
Where Vm,i* is the molar volume of pure substance i. After the pure substances are mixed to form the solution, the total volume of the solution is: V = n1V1 + n2V2 + …niV
In equations (1) and (2), V is not necessarily equal to V*. In equation (2), the quantity Viis the molar volume of the ith substance in the solution, and is called the partial molar volume of substance i. For the reasons mentioned above, Vi is not necessarily equal to Vm,i*. That is, the volume occupied by one mole of i in solution is different from the volume occupied by one mole of pure i. The partial molar volume of a substance is an intensive property. That is, it depends on the composition of the solution, but not on the amount of solution. Another way of saying this is that Vi depends on the mole fractions and not on the number of moles. The total volume, on the other hand is an extensive property. The partial molar volume of a substance is the molar volume of the substance in a solution at a particular composition. The value of V(m) is obtained for several values of m. The slope of V(m) plotted versus m is the first derivative. The slope at any point on the curve is obtained by drawing a line tangent to the curve at the point of interest. The slope of t he curve at that point is the slope o f the tangent line, and is equal to the partial molar volume of the solute, V2. The graph above shows that, generally, the slope and, hence, the partial molar volume varies with concentration.
1
III.
METHODOLOGY
LIST OF CHEMICALS AND APPARATUS
Ethanol Distilled water Acetone (for drying) 25 ml pycnometer This apparatus is used for measuring the density of a solution using a reference liquid, such as water. This would identify the specific gravity of the solution which was then used to determine the partial molar volumes. The total volume of the mixture could also be computed afterwards.
Erlenmeyer flasks Since ethanol is volatile the Erlenmeyer flasks were needed to be covered with parafilm paper to prevent ethanol from evaporating in the surrounding. Each flasks were labeled according to the % volume of ethanol content.
Analytical balance Thermometer/barometer 25 ml graduated cylinder
Water bath
2
It is important that the temperature is the same throughout the measurement of densities of the samples. Thus, water bath is essential in this experiment. Flaks had to be put in water bath within 3-5 minutes to ensure that they had the right temperature.
A. PREPARATIONS OF LIQUID MIXTURES 1. 7 clean empty labeled erlenmeyer flasks covered with parafilm paper were weighed in an analytical balance. Each flask was labeled according to its % vol. ethanol content. (0, 17, 33,50, 67, 83 and 100%) 2. Each flasks contained 30ml samples of solutions of ethanol and water. The mass of each component were determined by using this procedure: i. Put approximate volume of water into flask (mass of flask + water) ii. Put the ethanol (mass of flask + water + ethanol) iii. Data were recorded in the data blanks 3. After the mass determinations, actual mole fraction of each solutions prepared were calculated. 4. These solutions were put in a thermostated bath for atleast 3 minutes before measuring their densities. 5. The temperature of the bath was recorded afterwards.
B. MEASURING THE MASS OF THE REFERENCE LIQUID USING A PYCNOMETER 1. A clean and dry pycnometer was weighed. 2. It had been filled with water and mass was also measured. This set to be the Mass reference. 3. Upon using the pycnometer, it had to be clean using technical acetone. C. DENSITY MEASUREMENTS 1. The procedure outlined in part B was also performed for other samples prepared in part A as well as for the pure alcohol sample. 2. Data were recorded 3. Densities of each mixture was then calculated. 4. Ideal molar volume of each prepared solution(Vm*) was then determined using the density of pure ethanol and water. 5. Actual volume and actual molar volume (Vm) of each prepared solution could also be calculated by using the density values of each solution. D. PARTIAL MOLAR VOLUME CALCULATION
3
1. The graph of molar volume (Vm) vs. Mole Fraction of ethanol using the data could now be plotted. 2. Using the tangent method, the partial molar volume of water and ethanol for each concentration was then determined. These values had to be compared with the molar volumes of the pure compounds and conclusions could now be drawn from these comparisons.
IV.
RESULTS AND DISCUSSIONS:
Table 2.1: Preparation of Liquid Solutions Approx Volume % of Ethanol
Appr ox Vwater , mL
Approx Vethanol , mL
mass of empy flask (mo), g
flask + A (mA*)
flask + A +B (mB*) ,g
mA* – m0 mA, g
mB*-mA* mB, g
nA
nB
100 83 67 50 33 17
0 5 10 15 20 25
30 25 20 15 10 5
93.4693 92.7797 95.0010 95.1046 93.8422 88.6713
93.4693 97.0732 104.3756 109.6534 113.2388 113.1670
117.133 116.2086 119.5494 120.8670 120.6230 116.5632
0 4.2935 9.3746 14.5488 19.3966 24.4957
23.6637 19.1354 15.1738 11.2136 7.3842 3.3962
0 0.23853 0.52081 0.80827 1.07759 1.36087
0.5144 0.4160 0.3299 0.2438 0.1605 0.0738
Temperature of water bath:
300K
Density of distilled water:
0.996513 g/cm
molar volume of distilled water:
18.0730 cm /mol
3
3
Table 2.2: Density Determinations Approx Volume % of Ethanol
XB
100
XA(1-XB)
Mavg (g/mol)
Mass of pycnometer, g
mass pycnometer + liquid
Mass of liquid, g
Density 3 ρmix g/cm
1
0
46.0000
13.6428
33.7450
20.1022
0.7823
83
0.6356
0.3644
35.7958
13.6500
35.5330
21.8830
0.8516
67
0.3878
0.6122
28.8575
13.6505
36.2593
22.6088
0.8798
50
0.2317
0.7683
24.4880
13.6467
37.9011
24.2544
0.9439
33
0.1297
0.8703
21.6303
13.6561
38.1307
24.4746
0.9524
17
0.0515
0.9485
19.4409
13.6385
38.7350
25.0965
0.9766
0
0
1
18.0000
13.627
39.2343
25.6073
0.9965
Molar volume, like the term implies, is the volume occupied by 1 mole of a substance or mixture of substances at a particular temperatur and pressure. Distilled water, for instance has a molar volume of 18.0630 cm3/mol at 300K. Just like density, which is the ratio of mass to volume, and specific gravity which is the ratio of a subtance’s density to that of a reference substance, molar volume is an intensive property. Its value is constant for a specific substance or mixture at certain temperature and pressure. This means that the molar volume of 20 mL of distilled water is the same even if the volume is increased to 30 or 40, and so on. 4
Partial molar volume, in contrast to molar volume, is an intensive property. The partial molar volume of a substance in a mixture, say substance A, is the change in volume per mole of A added to a large volume of the mixture. As an illustration, imagine a huge volume of pure water at 25°C. When a 3 3 further 1 mol H2O is added, the volume increases by 18 cm so it can be reported that 18 cm / mol is the molar volume of pure water. However, when 1 mol H2O is added to a huge volume of pure 3 ethanol, the volume increases by only 14 cm . The reason for the differen (Atkins & de Paula, 2010)t increase in volume is that the volume occupied by a given number of water molecules depends on the identity of the molecules that surround them. In the latter case there is so much ethanol present that each H2O molecule is surrounded by ethanol molecules. The network of hydrogen bonds that normally hold H2O molecules at certain distances from each other in pure water does not form. The packing of the molecules in the mixture results in the H2O molecules increasing the volume by only 3 3 14 cm . The quantity 14 cm /mol is the partial molar volume of water in pure ethanol. In this experiment, the effect of increasing the molar concentration of ethanol in a 30 mL waterethanol mixture to the its partial molar volume and eventually to the molar volume of the entire mixture was illustrated. The molar volume of the seven solutions with varying molar concentration of ethanol was obtained in three different methods:
; this was considered as the experimental value of molar volume.
V m*=(X B*V mB ) + (X A*V mA ) ; this was considered the theoretical value of the molar volume Vm was obained by tangent method.
In the first method, Mave is the molar mass of the mixture which was obtained by using the mole fraction of the components. Component B is the ethanol and component A is water. Mave was then divided to the density, ρ, of the corresponding mixture. The derivation was as follow:
For the second method, the partial molar volume of each component was obtained by multiplying the mole fraction to the literature value of substance’s molar value at a particular temperature. For each method it can be predicted, base from the formula, that as the molar concentration of ethanol increases, the molar volume of the mixture increases also. This is true provided that all other conditions such as the components total volume of the mixture, temperature, and volume are held constant. Table 2. 3: Determination of Molar Volume of Solutions Approx Volume % of Ethanol
VM* 3 (cm /mol)
VM 3 (cm /mol)
ΔVmix 3 cm /mol
%difference
100
58.8010
58.8024
0.0014
0.0024
83
43.9547
42.0346
1.9201
4.4659
67
33.8599
32.7991
1.0608
3.1827 5
50
27.5026
25.9444
1.5582
5.8308
33
23.3448
22.7106
0.6343
2.7544
17
20.1594
19.9060
0.2534
1.2649
0
18.0630
18.0630
0.0000
0.0001
o
Temperature of water bath, C: Density of pure ethanol, 3 g/cm :
27 0.783336
3
Density of distilled water, g/cm
0.996513 3
Molar Volume of pure ethanol, cm /mol: 3
Molar Volume of distilled water, cm /mol:
58.801 18.073
In the tangent method shown below, a value of X B was chosen. In this case 0.2317. A tangent line was then drawn from it. From the tangent line, partial molar volume of B and partial molar volume of A was determined. Those values were used to calculate for the molar volume of the mixture containing XB mole fraction ethanol, using the following computation: % difference = 3.44% It was observed that the theoretical value of Vm is greater than the experimental and by tangent method, but with only a small % difference. This is can be accounted to the fact that while the theoretical value is just an estimate based on the amount of component’s molecules, the partial molar volumes of the components of a mixture vary with composition because the environment of each type of molecule changes as the composition changes from pure water to pure ethanol. It is this changing molecular environment, and the consequential modification of the forces acting between molecules, that results in the variation of the thermodynamic properties of a mixture as its composition is changed.
6
Molar Volume vs Molar Fraction of B 70.00
60.00
Partial molar volume of B at XB: 55 g/cm3
50.00
40.00 Vm 30.00
Power (Vm)
20.00
Partial molar volume of A at
10.00
XB 0.00 0.00000.10000.20000.30000.40000.50000.60000.70000.80000.90001.00001.1000
Figure 2.1. Tangent Method in Determining Molar Volumes
TANGENT-INTERCEPT METHOD X Y Approx Volume % of Ethanol
VM* (cm3/mol)
100 83 67 50 33 17 0
58.801 43.95466561 33.85990039 27.50261845 23.34482912 20.15939554 18.063
XB
ΔVmix cm3/mol
Partial Volume of Water
Partial Volume of Ethanol
1 0.635565 0.387768 0.231715 0.129654 0.05146 0
0.00140 1.92011 1.06078 1.55819 0.63427 0.25340 0.00001
0.00000 15.37605 17.87447 17.38092 18.01378 18.06324 18.06300
58.80100 57.32060 56.36307 54.33851 54.23938 53.87242 58.80100
Molar Volume Using TangentIntercept Method 58.80100 42.03456 31.26951 25.94456 22.71056 19.90599 18.06300
Values Y, given the following X of Tangent Line X
Y
Approx Volume % of Ethanol
VM* (cm3/mol)
XB
ΔVmix cm3/mol
100
58.8010
1.0000
0.0014
X=1
X=0.6356
X=0.3878
X=0.2317
X=0.1297
X=0.0515
0.0014
1.4804
2.4379
4.4625
4.5616
4.9286 7
83 67 50 33 17 0
43.9547
0.6356
1.9201
33.8599
0.3878
1.0608
27.5026
0.2317
1.5582
23.3448
0.1297
0.6343
20.1594
0.0515
0.2534
18.0630
0.0000
0.0000
3.1326 3.0176 3.7867 4.2898 4.6752 4.9288
1.9201
1.6182
3.0848
2.9171
3.1323
2.2191
1.0608
2.1480
1.7990
1.9110
2.4074
0.7098
1.5581
1.0948
1.1418
2.5305
0.4802
1.1722
0.6343
0.6388
2.6249
0.3043
0.8766
0.2814
0.2534
2.6870
0.1885
0.6821
0.0492
-0.0002
8
6.00000
5.00000
4.00000
ΔVmix cm3/mol
tangent at X=0.635565
3.00000
tangent at X=0.38777 tangent at X=0.23175 tangent at X= 0.129654 2.00000
tangent at X=0.05146 Poly. (ΔVmix cm3/mol)
1.00000
y = -3.4127x3 - 1.7351x2 + 5.1345x + 0.0402
0.00000 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
-1.00000
Figure 2.2 Difference in Molar Volume vs Mole Fraction of Ethanol: Tangent-Intercept Method of Finding the Partial Molar Volume
9
70.00000
60.00000
50.00000
40.00000 Ethanol Water
30.00000
20.00000
10.00000
0.00000 0
0.2
0.4
0.6
0.8
1
1.2
Figure 2.3. Partial Molar Volume of Ethanol and Water
As mentioned earlier, that while the value of molar volume is constant no matter what the volume of a given substance or mixture is, all other conditions must remain constant as well such as temperature. Molar volume will already be different once these conditions changed. When the temperature is increased, molecules occupy a bigger volume but the number of moles remain the same. This would make the value of molar volume increase as well, but for liquids which have strong intermolecular forces of attraction such as water, this change would not be as big as compared to ethanol which evaporates easily. For ideal solutions,those that are formed from components that have very similar structures and hence similar forces of attraction operating among molecules, very similar forces of attraction lead to minimal expansion or contraction in the volume of the mixture formed from the components. Thus we can expect the partial molar volume to be equal to the molar volume of each component. However, there are no two compounds which are exactly alike, at some point there will always be a deviation so in reality, the only time that partial molar volume is equal to the molar volume is then the solution is made up of pure substance.
V.
SAMPLE CALCULATIONS
A. PREPARATION OF LIQUID SOLUTIONS: ρdH2O = 0.996573
Molar Volume of distilled water: mH2O = 28.4724 g 10
VH2O =
=
VH2O = 28.5720 g/cm Vm1H2O =
=
3
3
Vm1H2O = 18.0630 cm /mol 3
Comparing it with literature value of V mH2O = 18.0730 cm /mol B. DENSITY DETERMINATIONS (USING 83% ETOH): XB = XA=
= 0.6356
= 0.3644
ρmixture =
Mavg= XbMb + XaMa
x ρH2O @ 27°C =
= (0.6356) (46) + (0.6344) (18)
x 0.996573
ρmixture = 0.8156 g/cm
3
Mavg = 35.7968 g/mol C. MOLAR VOLUME OF SOLUTIONS (USING 83% ETOH) Vm(exp) =
=
= 42.0348
*
*
Vm*(theo) = X BVmB + XAVmA
= (0.6356) (58.8010) + (0.6344) (18.0630) 3
Vm*(theo) = 45.9561 cm /mol
VI.
SUMMARY AND CONCLUSION
The preparation of liquid solutions provided insight on the process to determine the molar volume of distilled water, with a very slight difference to the literature value of the molar density of distilled water. The calculations used in the lectures were used, and it enabled us to understand more the concept of the topic because we were able to apply it to actual experiments. The experiment could have been easier to perform if more apparatus were available for each group. The experiment also showed the direct proportionality of the amount of a substance to its mole fraction in a solution. We were able to determine the molar volume of solution, wherein ethanol was used in different volume percentages. Overall the experiment helped us to gain more knowledge in molar volumes, and varying densities, however more accurate results could have been achieved had there been more apparatus available, so more time could have been saved.
VII.
REFERENCES:
(n.d.). Retrieved on October 2014, from http://www.chemistry.mtu.edu/~kmsmith/PChem/Experiments/3511/MolVol/MolVol.pdf 11
(n.d.). Retrieved on October 2014, from http://www2.stetson.edu/~wgrubbs/datadriven/fchen/bartender/partialmolarvolumechen. html Atkins, P., & de Paula, J. (2010). Physical Chemistry. New York, NY: W.H. Freeman and Company. Epstein, L. (1986). Laboratory Manual for Chemistry. Nicol, M. F., Russell, A. A., & Siebert, E. D. (1973). Experimental Studies for General Chemistry.
12
