Determination of the Partial Molar Volume by Density Measurement

Determination of the partial molar volume by density measurement

Purpose In this laboratory experiment, you will measure the partial molar volume of components of a salt solution at 25 °C by determining the density of solutions. The density will be measured using a vibrating cell instrument.

Background In general, the volumes of the components of a solution are not additive. For example mixing 70.0 cm3 water and 30.0 cm3 ethanol results in 97.0 cm3 at 25 oC. The explanation for this result is two-fold. In the solution, the molecules experience different intermolecular forces than in the pure substances. Water and ethanol molecules have different sizes and shapes, consequently the molecules of water and ethanol are going to fit together differently in pure state than in a mixture. Another example involves aqueous solutions of salts. Suppose 250 g of LiCl are added to 1000 g of water. The solution process results in a volume decrease of 55 cm3, about 5%. A quantitative treatment of this behaviour requires the introduction of the partial molar volume. Partial molar volume (SI unit m3/mol) of the ith component is defined by the equation  ∂V    vi    ∂ni  T , p,n j≠i The partial molar volume of a substance is an intensive property (it depends on the composition of the solution, but not on the amount of solution). The volume of a one-phase homogeneous system depends on temperature (T), pressure (p) and on the amounts of the components (ni)

V  VT, p,ni  This is a homogeneous linear function of the amounts of components. Therefore, at constant temperature and pressure the total volume (V) of the system can be written using partial molar volumes of components k  ∂V    V  ∑  dni i1 ∂ni  T , p,n j≠i The total volume (V) of a two component system using partial molar volumes ( v1 and v2) and amounts ( n1 and n2 ) of components

V  n1v1  n2v2 Dividing the equation by the sum of the mole numbers

n  n1  n2 we obtain

v  x1v1  x2v2 Dividing it by the molar volume of solution (v = V/n) x x 1 1 v  2 v v 1 v 2 On the other hand x w i  i v M i where  , wi and Mi are density, mass fraction and molar mass of component i, respectively. Therefore,

 w2 1  1 w2 v1  v2 M1 M 2 when the relation

w1 1- w2 is taken into consideration. Using mass concentration (c) instead of mass fraction (w) c w   an equation can be obtained containing data that are known or can be measured easily

v1 c2v1 c2 1   v2 M1 M1 M 2 Re-arraging the equation there is a linear dependence between density and mass concentration of the 2nd component:

  a bc2 where M a  1 v1 and

v2M1 b 1 v1M 2 Measuring density as a function of mass concentration of the 2nd component, partial molar volumes (v1 and v2) of the components can be calculated. However, the molar volume can change with the concentration (it is expected as general behaviour), the evaluation method above can only be used in a narrow concentration range.

Apparatus The density is measured by a vibrating tube type densitometer. It is based on the electromagnetically induced oscillation of an U-shaped glass tube. A magnet is fixed to the tube and a so-called transmitter induces the oscillation. The period of oscillation is measured by a sensor. The glass tube vibrates at its characteristic frequency. The frequency is a function of the mass. When the tube is filled with a liquid, the mass increases and consequently the frequency decreases. The density and frequency are related to each other by a quadratic function. You will use Mettler Densito 30PX instrument with a reading

2 accuracy of 0.0001 g/cm3. An instruction manual for the instrument is available at the work bench or consult with your mentor.

Procedure  Prepare a series of 12 solutions from the stock solution in 50 cm3 volumetric flasks.  Use burette to measure the necessary volumes of the stock solution given by the instructor.  Fill up the volumetric flasks with distilled water, but keep the solution level below the mark.  Put the flasks into thermostat at 25 °C.  Put also a small baker with distilled water into the thermostat. This thermostated water will be used to fill the flasks up to the mark.  After 20 mins fill the volumetric flasks up to the mark. Use Pasteur pipette.  Measure the density of the solutions at least 3 times by Mettler Densito 30PX densitometer. Values may scatter only within the range of 0.0003 g/cm3.  Record the temperature displayed by the densitometer, as well.  Record measured data in the form of a suitable table.  Aftermaking the measurements clean the densitometer carefully with distilled water.

Calculations 1. Plot the measured density vs. mass concentration. 2. Fit linear on the datapoints resulting the slope ( b ), the y-axis intercept ( a ), and their standard deviations σ a and σ b . 3. Calculate the 95% confidence interval of a and b by

a  t0,05, f  a and

b  t0,05, f b applying Student’s t-distribution for the system of the given degree of freedom (f). 4. Calculate the partial molar volume of water M H2O v  H2O a 5. Calculate the partial molar volume of the solute

vH OM 2 v  1- b 2 2 M H2O 6. Calculate the error of partial molar volumes by error propagation law of Gauss

vH O M H O v  2 a  2 a H2O a a2 and

2 2 2 2  v   v   M 2vH O   M  v   2 b   2 v    2 b  1b 2 v  2 b  v H2O   M   M H2O     H2O   H2O   H2O  N.B. Take care on suitable units and the number of significant digits.

Results to be given  The plot density vs. mass concentration with fitted straight line and the parameters determined.  Partial molar volume of H2O and the solute with their error.  Range of concentration and temperature of measurement.

Test questions 1. What is the working principle of the Mohr–Westphal-balance? 2. Define the partial molar volume! 3. List three partial molar quantities and give their dimension! 4. Does the partial molar volume of water depend on the solute concentration at constant temperature and pressure? Support your answer! 5. List the main parts of a thermostat and give their task! 6. If you measure density using picnometer how do you determine its volume? 7. If you determine the partial molar volues in a binary solution using picnometers do we have to thermostate the picnometes and the volumetric flasks? 8. What is the working principle of the vibrating cell densitometer? 9. Describe when and how do you fill the volumetric flasks to the mark! 10. How do you fill the vibrating cell densitometer with the liquid to be measured? 11. Why do we work in a narrow concentration range?

Miklós Riedel and Maria Ujvári February 2016