Experiment 2

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016}

Measurement of Density and Determination of Partial Volume of Ethanol-Water System Calderon, Edna1_,

Benjamin, Zidrick Ed C2_{, Lola, Ernest Nicolo}2_,

1_{Professor, School of Chemical Engineering, Chemistry and Biotechnology, Mapua Institute of Technology;}

2_{Student (s), CHM170L/A1, School of Chemical Engineering, Chemistry and Biotechnology, Mapua Institute of Technology}

ABSTRACT

This experiment is primarily focused on the measurement of the density and the determination of the partial molar volume of ethanol-water system. A partial molar volume is a thermodynamic quantity defined as a change in volume per mole of substance added to the mixture at constant temperature and pressure, indicating that molar volumes are non-additive. Solutions of ethanol and water had been prepared with varying concentrations and a pycnometer was calibrated and used by weighing it along with the liquid samples one at a time, for the accurate measurement of the density of each mixture. The latter was measured in order to calculate for the excess molar volume and partial molar volume for both components. The data were then used for calculating other physical quantities such as molar volume, molar fraction, and molecular weight. For the determination of the partial molar volume of each component, tangent lines to the curve were drawn from the graph relating the negative excess molar mass of the concentrated mixture, and the mole fraction of water. From these lines, the y-intercepts at certain points had been identified for the determination of the partial molar volume of ethanol and water which were used for correlation. Results showed that the partial molar volume of a substance increases with an increase of its molar fraction. Hence, in this experiment, the partial molar volume of ethanol water-mixtures is to be determined using density and specific gravity measurement.

Keywords: density, partial molar volume, pycnometer, mole fraction, tangent lines, excess molar volume

INTRODUCTION

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016}

Volume, by definition, is the amount of space occupied by a substance measured in cubic units. Molar volume, on the other hand is the volume occupied by one mole of a solid, liquid, or gas. This experiment focuses on determining the partial molar volume of ethanol-water system. Partial molar volume is the “contribution that a component of a mixture makes to the total volume of a sample” [1]. In other words, the partial molar volume of a substance in a mixture is the change in volume per mole of the substance added to the mixture. Moreover, it is the easiest extensive property to visualize.

Generally, for solutions with different components, the volumes of the components are not additive. Partly because the molecules in each component undergo different intermolecular forces than in pure substances. For instance, a water molecule, together with an ethanol molecule, observe a different interaction than that of two water molecules alone, or two ethanol molecules alone [2]. Also, the water and ethanol molecules have various shapes and sizes. Hence, the molecules of a solution of ethanol and water fit quite differently than that of pure water and pure ethanol [3].

Given a system with two components X and Y, the partial molar volume of the first component X can be determined mathematically by the equation:

´

V_x=( ∂ V

∂ nA)T , P ,n_y (1)

Where V is the total volume ,NX is the number of molecules of X , NY is the number of molecules of Y, T is the temperature, and P is the pressure. As can be seen, the partial volume of X is the change in volume per mole of X added, assuming that the temperature and pressure are constant.

This experiment will try to use the concept of partial molar volume using the materials and methods provided. The objectives of this experiment are, first, to be familiarized with the use of pycnometer and the

chain balance for measuring density and specific gravity, respectively, and second, to determine the partial molar volume of ethanol-water system at different concentration using density and specific gravity measurement.

MATERIALS AND METHODS

I. Sample Preparation

The solutions needed were initially prepared as such. One containing pure ethanol, another with pure water, and several containing a mixture of both, having different concentrations, with an increment of 10% by volume for each. By means of using a graduated cylinder and a pipette, the necessary amounts of water and ethanol had been obtained. Shown in Table 1 are the specified and distinct volume of water and ethanol respectivelyadded per sample solution to be evaluated.

Table 1. Volume of Each Component of Mixture Volume of water , Volume of Ethanol ,

cm3 cm3 0 30 3 27 6 24 9 21 12 18 15 15 18 12 21 9 24 6 27 3 30 0

II. Molar Volume Determination

Prior to the actual utilization of the flask with a close-fitting ground glass stopper with fine hole through it, the pycnometer was first calibrated by means of getting the required measurements. It was initially weighed dry and then after filling it up with water, the mass reading was taken note of. The filled-in weight reading was subtracted to that of the empty reading to determine the weight of the water alone.

Knowing that the density of water at a temperature of 26˚C as 0.9983 g/cm3_{, the corresponding volume of}

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016}

the pycnometer could be ascertained substantially. Calculations underwent through quite a few reckonings for the molar volume count. These included densities, molecular weights, and mole counts of each differently concentrated solution.

First, the mole count of water and of the ethanol was measured with the corresponding volume that both occupied in a solution and then their mole fractions were obtained varying to the quantity they occupy. The molar volume of the mixture was computed with the density and the average molecular weight which was then identified with the mole fractions and molecular weights of water and of ethanol. The density of the mixture was measured with the mass in grams of the sample and the volume it occupies. Having the pycnometer weighed with a full amount, the empty pycnometer weight was simply subtracted and yielded the mass of the mixture. Subdividing the average molecular weight with that of its corresponding density gave the molar volume.

The change in molar volume due to mixing was calculated by differentiating the computed molar volume with the appropriate molar volume. This value tells the increment in volume with that of a pure and of

a mixture.

As for the determination of the partial molar volumes of ethanol and water accordingly, the excess molar volume of the mixture vs. the mole fraction of water was plotted. From the graph, tangent lines were drawn with respect to the curve and specified points from which the equations of these tangent lines were known. By getting the y-intercepts at x=0 for the solute and x=1 for the solvent, the partial molar volume of the ethanol-water system could be determined.

Figure 1. Pynometer with Thermometer

RESULTS and DISCUSSIONS

V1 (water) V2 (ethanol) M1 M2 X1 Mavg, g/mol ρmix, g/cm3 Ṿ, cm3/mol ∆Ṿmix, cm3/mol

0 30 0 0.511 0 46.068 0.998 46.160 -12.548 3 27 0.166 0.460 0.265 38.634 1.031 37.472 -13.451 6 24 0.332 0.409 0.448 33.501 1.065 31.456 -9.030 9 21 0.498 0.358 0.582 29.742 1.088 27.336 -7.711 12 18 0.665 0.307 0.684 26.880 1.126 23.872 -6.992 15 15 0.831 0.256 0.765 24.636 1.156 21.311 -6.288 18 12 0.997 0.205 0.830 22.812 1.180 19.332 -5.626 21 9 1.163 0.153 0.884 21.269 1.191 17.858 -4.938 24 6 1.329 0.102 0.928 20.035 1.219 16.436 -4.528 27 3 1.495 0.051 0.967 18.941 1.231 15.387 -4.018 30 0 1.661 0 1 18.015 1.243 14.493 -3.568

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016}

Ethanol-water solutions of different concentrations had been prepared and each of them had been placed in the pycnometer and then weighed afterwards. A pycnometer had been used in order for a given volume and density to be accurately obtained by reference to an appropriate working fluid, using an analytical balance.

At the start of the experiment, you would need to calibrate the pycnometer to reduce and minimize errors in computations of the different values. You could see on table 1 the result in calibration of the pycnometer.

Table 3. Calibration of Pycnometer

After the calibration of the pycnometer, we performed the measuring of masses of different concentration of ethanol-water solution. In table 2, the data such as the masses, number of moles, mole fraction, average molecular weight and molar volume of the mixture at different concentration can be seen.

As you can see on table 2 that the average molecular weight of the mixture decreases as you increase the concentration of water in the mixture, because the water has a lower molecular weight than the water(Figure 2.1).

Figure 2.1.Average molecular weight/ Molar volume of the

mixture VS mole fraction of water.

In table 2, the density of the solution increases since the density of ethanol is lower than water(Figure 2.2). The molar volume of the mixture decreases because of the presence of hydrogen bond, these makes the distance between molecules of ethanol and water smaller(Figure 2.1).

From the data gathered, it could be observed that there is a trend between concentration of solution and the density of the mixture. This relationship could further be elaborated by having the illustrated graph as follows:

Figure 2.2.Density of mixture VS mole fraction of

water graph.

In addition, the ∆Vmix column in table has a

distinct noticeable data that we can concur. Both the pure ethanol and pure water has a positive data, while the mixed solutions have negative. This leads to the conclusion that the intermolecular molecules affect the mixture of the solution. Since we know that both the ethanol and water are polar protic solvents, they are miscible with each other, thus interacting between the two.

The pure water has higher value than that of the pure ethanol; this also leads to the fact that the Weight of empty pycnometer 32.319 g Weight of empty pycnometer + water 52.019 g Temperature of water, T 26 C Density of water at T 0.9983 g/cm^2 Volume of pycnometer 19.73 ml

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016}

water has stronger intermolecular force that exhibits hydrogen bonding. Also, the data from the mixture also supports the conclusion because the more the volume of water increases, the higher the value of the ∆Vmix.

For Ethanol, the table below shows a summary of its partial molar volume for each concentrated solution:

X1, ml V1 – V1* V1* V1 0 0.5941 5 19.73 59.7795897 0.265 -1.2204 2 19.73 59.040299 0.448 -2.4621 2 19.73 58.498829 0.582 -3.3765 7 19.73 57.778079 0.684 -4.0713 1 19.73 56.711289 0.764 -4.6185 4 19.73 56.333329 0.829 -5.0613 5 19.73 53.733329 0.884 -5.4254 7 19.73 52.007419 0.928 -5.7317 7 19.73 50.2193790 0.967 -5.9912 3 19.73 48.4198690 1 0 0 0

Table 3.1.Determination of Partial Volume of Ethanol.

Where V1– V1* is obtained from the y-intercept of the tangent lines, V1 stands for the volume of ethanol, obtained by dividing the molar masses of ethanol over its density, and V1* for the partial molar volume of ethanol.

To clearly understand the relationship between the partial molar volume of ethanol and the mole fraction of water, an illustration showing how these two are related is shown:

Figure 3.2.Partial Molar Volume of Ethanol VS mole of

Water

The graph portrays that as the mole fraction of water increases, the partial molar volume of ethanol decreases. In addition, it could be observed that the more dilute the solution is, the lower is the partial molar volume of ethanol.

In the case of water, the table below shows the summary of the data obtained for each mole fraction. X1, ml V2– V2* V2* V2 0 0.59415 18.01899 18.18182 0.265 -1.2204 2 18.01899 15.1406 0.448 -2.4621 2 18.01899 16.0936 0.582 -3.3765 18.05416 16.7333

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016} 7 0.684 -4.0713 1 18.05416 17.3195 0.764 -4.6185 4 18.05416 18.8190 0.829 -5.0613 5 18.06503 18.2078 0.884 -5.4254 7 18.05416 18.4842 0.928 -5.7317 7 18.05416 18.6617 0.967 -5.9912 3 18.05416 18.7566 1 -6.2161 5 18.05416 18.7850

Table 3.2. Determination of Partial Volumes of Water

Where V2 - V2* represents the y-intercept of the tangent line at x=1, V2 stands for the volume of water, obtained by dividing the molar mass of water over its density, and V2* for the partial molar volume of water.

Plotting there points and data in a graph would produce an outcome to:

Figure 3.2. Partial Molar Volume of Water VS Mole of

Water

The graph suggests that when the mole of water increases the partial molar volume of water increases as well.

Water and ethanol will always have a negative excess volume when mixed;indicating the partial molar volume of each component is less when mixed than its molar volume when pure.

The partial molar volume of the components of a mixture will always vary by its composition because when the two is mixed the environment of the two is changed, thus the interaction between the molecules also changed. Or we can also suggest that the composition of the mixture wherein the larger is its contribution to the mixture, the larger is the partial molar volume.

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016}

CONCLUSIONS AND RECOMMENDATIONS

In the experiment, different concentration of ethanol-water system was prepared. The calibrated pycnometer was used to obtained masses of the different concentrations of ethanol-water mixture needed for the computations of the necessary data required to determine the partial-molar volume of the system. The necessary data includes the number of moles, mole fraction, average molecular weight and molar volume of the mixture at different concentration. To show the some of the relationships of the data obtained certain graphs were made. These graphs include the relationship of the average molecular weight and molar volume of mixture vs. the mole fraction of water, density of mixture vs mole fraction of water,∆Vmix vs mole fraction of H2O and the like.

Furthermore, the tangent lines of the curve was determined to calculate the partial volume of ethanol and water at the given mole fraction of ethanol and water.

In the experiment, certain relationships in the ethanol-water mixture ware observed. It was observed that the average molecular weight of the mixture decreases as you increase the concentration of water in the mixture. Also, as the volume of water increases and the volume of ethanol decreases, the weight of the mixture increases. According to the results, the pure water has higher value than that of the pure ethanol, this leads to the fact that the water has stronger intermolecular force that exhibits hydrogen bonding. Moreover, water and ethanol will always have a negative excess volume when mixed which indicates the partial molar volume of each component is greater when both components are pure.

REFERENCES

[1] Caparanga A., Baluyut J.Y.G, and Soriano A. (2006) Physical Chemistry Laboratory Manual Part 1 [2] Levine I (2009) Physical Chemistry, Fifth Edition [3] Atkins, P. W., & de Paula, J. (2006). Atkins’ physical chemistry (8th ed). Oxford: Oxford UniversityPress. [4] Imai, T. (2007). Molecular Theory of Partial Molar Volume and Its Application to Bimolcular Systems. Department of Bioscience and Bioinformatics, Ritsumeikan University. P.525

[5] Engel, T. (2006). “Physical Chemistry”, p.210

Sample Computations: Part B

 m1 – moles of distilled water

m1= V₁ρ_w MMw = (3 cm3)(0.9983 g cm3) (18 g mol) =0.166 moles  m2 – moles of ethanol m₂=V2ρe MMe =

(

₎

(

)

(

)

 x1 – mole fraction of water x₁= m1

m1+m2

= 0.166

0.166 +0.460=0.265

CHM170L Physical Chemistry 1 Laboratory 2nd _{Quarter SY 2015-2016} MM_w M_avg=x₁¿ )+(1-x1)(MMe) M_avg=0.265

(

)

(

)

 ρmix – density of the mixture

ρ_mix= m V_pycnometer= 46.068 g 19.73 cm3=0.998 g /cm 3  V – molar volume V =Mavg ρ_mix = 46.07 g mol 0.998 g cm3 =46.160cm 3 mol

 ΔVmix – molar change in volume ∆ V_mix=V −30 cm 3 ntotal =46.160cm 3 mol− 30 cm2 (0+0.511)mol=−12.548 cm 3 /mol