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CHM170L Physical Chemistry 1 Laboratory 4th Quarter SY 2009-2010

Measurement of Density and Determination of Partial Molar Volume and Ethanol-Water System

Nieva, Aileen D.1, Arceo, Mary Anne V., Cuales, Jelline C., Kim, Sung Min, Ngan, Emil Joseph T., Rivera, Jainie Lynne B.21Professor, School of Chemical Engineering, Chemistry and Biotechnology, Mapua Institute of Technology; 2Student (s), CHM170L/A41, School of Chemical Engineering, Chemistry and Biotechnology, Mapua Institute of Technology

ABSTRACTDue to intermolecular interactions, the total volume measured when two real liquids (e.g. ethanol and water) are mixed deviates from the total volume calculated from the individual volumes of the two liquids (volume contraction). To describe this non-ideal behavior in the mixing phase, one defines partial molar quantities which are dependent on the composition of the system. This experiment intends to measure the density of a liquid, having different concentrations of ethanol-water solutions with the use a pycnometer. Molecules that are mixed with different molecules would interact differently, that is why in this experiment, partial volumes are also considered due to ethanol and water mixture. It prepared with different solutions having 10% of increment of concentrations. Densities have been calculated using the mass of each sample and the known volume of the pycnometer. As the volume of water increased (volume of ethanol decreased), the density of the ethanol-water system has been observed to increase. The values of these can be experimentally determined.

INTRODUCTIONDensity

The density of a material is defined as its mass per unit volume. The symbol of density is (the Greek letter rho).

Mathematically: Density = Mass Divided By Volume

where:

(rho) is the density,

m is the mass,

V is the volume.

Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity (SG) or relative density (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas.

Pycnometer A pycnometer (from Greek: (puknos) meaning "dense"), also called pyknometer or specific gravity bottle, is a device used to determine the density of a liquid. A pycnometer is usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as water or mercury, using an analytical balance.

If the flask is weighed empty, full of water, and full of a liquid whose specific gravity is desired, the specific gravity of the liquid can easily be calculated.

Partial Molar Property

A partial molar property is a thermodynamic quantity which indicates how an extensive property of a solution or mixture varies with changes in the molar composition of the mixture at constant temperature and pressure, or for constant values of the natural variables of the extensive property considered. Essentially it is the partial derivative with respect to the quantity (number of moles) of the component of interest. Every extensive property of a mixture has a corresponding partial molar property.

The partial molar volume is broadly understood as the contribution that a component of a mixture makes to the overall volume of the solution. However, there is rather more to it than this:

When one mole of water is added to a large volume of water at 25 C, the volume increases by 18 cm3. The molar volume of pure water would thus be reported as 18 cm3 mol-1. However, addition of one mole of water to a large volume of pure ethanol results in an increase in volume of only 14 cm3. The reason that the increase is different is that the volume occupied by a given number of water molecules depends upon the identity of the surrounding molecules. The value 14 cm3 is said to be the partial molar volume of water in ethanol.

In general, the partial molar volume of a substance X in a mixture is the change in volume per mole of X added to the mixture.

The partial molar volumes of the components of a mixture vary with the composition of the mixture, because the environment of the molecules in the mixture changes with the composition. It is the changing molecular environment (and the consequent alteration of the interactions between molecules) that results in the thermodynamic properties of a mixture changing as its composition is altered.

METHODOLOGYThe materials used are the following: 25 mL pycnometer

Chain Balance

Analytical Balance

250 mL beaker

Stirrer

10 or 25 mL graduated cylinder

The Reagents used are the following:

Ethanol (C2H6O)- also known as ethyl alcohol or grain alcohol, is a flammable, colorless chemical compound, one of the alcohols that is most often found in alcoholic beverages. In common parlance, it is often referred to simply as alcohol.

Distilled water- is water that has many of its impurities removed through distillation. Distillation involves boiling the water and then condensing the steam into a clean container.

Experimental Procedure

A. Calibration of Pycnometer and Density Measurement using Pycnometer

1. Prepare different concentration (10% by volume increments) of ethanol-water solutions.

2. Weigh and clean, dry pycnometer and label it as empty.

3. Fill the pycnometer with the sample to the brim and wipe dry the outside.

4. Re-weigh the pycnometer and label it as pycnometer with sample.

5. Remove the sample and dry the pycnometer in the oven.

6. Repeat procedure 3 to 5 for the remaining samples.

7. Determine the total volume of the pycnometer.

CalculationsThe initial calculation should include:

1. mass of the solution inside the pycnometer

2. volume of the solution, based on the volume of the pycnometer

3. density of the solution inside the pycnometer

4. mole fraction of ethanol in the solution

5. average molar mass of the solution

6. molar volume of the solution

B. Specific Gravity Measurement using Chain Balance

1. Prepare different concentration (10% by volume increment) of ethanol-water solutions.

2. Measure the specific gravity of the solution using the chain balance.

C. Evaluation of partial molar volume of ethanol-water system

Plot the molar volume versus mole fraction and get the equation of the curve. Use the equation to evaluate the partial molar volumes of the component (1 and 2) of the binary mixture using partial differential equation.

Set up of Apparatus

Drying of Pycnometer inside the ovenRESULTS AND DISCUSSIONMeasured Surface Tension of Water:Trial 1 85.9 dynes/cm

Trial 2 85.3 dynes/cm

The first thing to do is to get the Erlenmeyer flask and measure 5 mL of n-butanol and dilute it to the mark with water. Water surface tension was 72.0 dynes/cm at 25C and 67.9 dynes/cm at 50C temperature. The temperature of the water is 32 C, and its surface tension was 98.18 dynes/cm. The surface tensions literature value was computed using interpolation. The instrument used to get the surface tension of the liquids was Du Nuoy tensiometer. It consists of a platinum-iridium ring supported by a stirrup attached to the upper part of the instrument. The ring is placed at the surface of a liquid with air. It is then pulled upward until it breaks free of the liquid and moves into the second liquid or into the air. The force that is just required to break the ring free of the liquid/air interface is proportional to the surface tension. Doing three trials, we obtained 85.967 dynes/cm. This gives us a difference of 12.133 dynes/cm.

The n-butanol solutions surface tension with different concentration was also measured. Different values of surface tension were recorded due to the difference in its concentration. Addition of more n-butanol lowered the surface tension of the solution.

CONCLUSION AND RECOMMENDATIONDensity determination by pycnometer is a very precise method. It uses a working liquid with well-known density, such as water. We used distilled water, for which temperature dependent values of density H2O.The pycnometer is a glass flask with a close-fitting ground glass stopper with a capillary hole through it. This fine hole releases a spare liquid after closing a top-filled pycnometer and allows for obtaining a given volume of measured and/or working liquid with a high accuracy.First we filled pycnometer with distilled water. According to equation = m /V, the volume of water that is filling the pycnometer and the stopper is V=; where mH2O is experimentally determined weight of water (empty pycnometer weight subtracted).

We repeated the procedure for the liquid with ethanol and determine its weight mL (measured weight minus weight of empty pycnometer). Volume V obtained in this measurement is the same as the volume of water it follows alternated equation V=.Combining yields a relation that provides the density of measured liquid

Sample table

A. Calibration of the pycnometer

Weight of empty pycnometer:

29.5359g30.3821

Weight of pyhnometer + water:

57.4688g58.1792

Temperature of water, T: 28C

28C

Density of water at T: 0.966g/cm3 0.966g/cm3

Volume of pycnometer: 28.045cm3 27.909cm3

V1, cm3V2, cm3m1M2X1Mavgmix, g/cm3V, cm3/molVmix, cm3/mol

03000.51520460.752063.17022.9404

3270.16610.46370.263738.620.780049.51371.8796

6240.33220.4110.446333.510.804041.68341.3825

9210.49840.3590.580129.770.825036.08201.1617

B. Molar volumes of ethanol-water mixture at different concentrations

Temperature, C: 28C

28CDensity of pure ethanol:0.966g/cm30.966Density of distilled water: 28.045g/cm3 28.909For the partial molar volumes of each component (VPM, i) as a function of the mole fraction of the ethanol. The partial molar volume of the solvent (water) at a given mole fraction of the solute can be obtained from the y intercept at XB = 0 (yXB=0) of the slope of a line tangent to the curve of the plot, VMIX/nT vs. XB, using equation Calculating the partial molar volume

Once the y intercepts have been found, they can then be used to calculate the partial molar volume of a binary mixtureSample ComputationPlot of Molar Volume VS Mole Fraction

0.4463-2.312515.74891.312559.5367

0.5801-117.05780.968859.1889

0.6825-0.484417.57430.656358.8899

The partial molar volume of the ethanol at this same mole fraction can then be determined for the y intercept of the tangent line at XB = 1 (yXB=1).

The figure illustrates the volume contraction that occurs on mixing of ethanol and water. From the corresponding polynomial and its first derivate, e.g. for xA = xB = 0.5, one obtains the partial molar volumes VA = 63.17 ml / mol (ethanol) and VB = 15.75 ml / mol(water) by substitution in equations These values are definitely less than the molar volumes of the pure substances at 273.15 K

Dependence of the mean molar mixing volumes MV on the composition of different ethanol-water mixtures described by the mole fraction xA of ethanol (T =293.25 K)The partial molar volumes of the components of a mixture vary with the composition of the mixture, because the environment of the molecules in the mixture changes with the composition. It is the changing molecular environment (and the consequent alteration of the interactions between molecules) that results in the thermodynamic properties of a mixture changing as its composition is altered.REFERENCES

1. Masterton, W. and Hurley, C. 2001. Chemistry Principles and Reactions, 4th ed. New York: Harcourt.

{Accessed: 06-11-10}

2. Knight, S.B, Crockford, H.B., Fundamentals of Physical Chemistry 2nd ed., Wiley International, 1964, {Accessed: 06-11-10}

Online References: {Accessed: 06-011-10}

http://www.everyscience.com/Chemistry/Physical/Mixtures/a.1265.phphttp://www.colby.edu/chemistry/PChem/lab/PartMolalV.pdfhttp://en.wikipedia.org/wiki/Partial_molar_property

APPENDICES

Appendix 1: Problem Solving using Computers

Excel can be very useful in the exploratory analysis of data:

Use a spreadsheet to do the calculations in the next 5 parts viewing your data in graphs to detect errors, unusual values, trends and patterns summarising data with means and standard deviations

Appendix 2: Useful Information

A partial molar property is a thermodynamic quantity which indicates how an extensive property of a solution or mixture varies with changes in the molar composition of the mixture at constant temperature and pressure, or for constant values of the natural variables of the extensive property considered. Essentially it is the partial derivative with respect to the quantity (number of moles) of the component of interest. Ethanol has a specific gravity of 0.78, so it is 0.78 times as dense as water.

Temperature dependence

The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or weights were determined. It is nearly always the case that measurements are made at nominally 1 atmosphere (101.325 kPa the variations caused by changing weather patterns) but as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances variations in density caused by pressure are usually neglected at least where apparent specific gravity is being measured.

Measurement of concentration

If the pycnometer is weighed empty, full of water, and full of a liquid whose specific gravity is desired, the specific gravity of the liquid can easily be calculated.

Partial molar properties are useful because chemical mixtures are often maintained at constant temperature and pressure and under these conditions; the value of any extensive property can be obtained from its partial molar property. They are especially useful when considering specific properties of pure substances (that is, properties of one mole of pure substance) and properties of mixing.

Appendix 3: Further Reading

Masterton, W. and Hurley, C. 2001. Chemistry Principles and Reactions, 4th ed. New York: Harcourt.

MsExcel: For more information on how to use MsExcel to calculate and plot data.

Thermometer

Pycnometer

Liquid sample

Digital balance

Experiment 02 Group No. 4 15 June 2010

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