Nathaly Murillo Kevin Brew 04/20/08 Experiment 2: Partial Molal Volume Abstract Densities of a small range of concentrations of aqueous potassium chloride and aqueous sodium chloride were recorded with a density meter so that the partial molal volumes, and ultimately, the partial molal volumes at infinite dilution, could be calculated. For potassium chloride and sodium chloride, the partial molal volumes at infinite dilution of the salts were calculated to be 25.18 mL/mol and 15.19 mL/mol, respectively. These differ from literature values by 6.23% and 26.85%, respectively. Error sources include inadequate mixing of the solutions, evaporation and the small range of the solutions. Introduction: Amagat’s law states that volumes are approximately additive. However, this does not apply to solutions whose concentrations are to be known to a high degree of accuracy. Preparation of a solution with accurate molality is generally done by adding an amount of water to a measured amount of salt and
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Nathaly MurilloKevin Brew 04/20/08
Experiment 2: Partial Molal Volume
Abstract
Densities of a small range of concentrations of aqueous potassium chloride and
aqueous sodium chloride were recorded with a density meter so that the partial molal
volumes, and ultimately, the partial molal volumes at infinite dilution, could be
calculated. For potassium chloride and sodium chloride, the partial molal volumes at
infinite dilution of the salts were calculated to be 25.18 mL/mol and 15.19 mL/mol,
respectively. These differ from literature values by 6.23% and 26.85%, respectively.
Error sources include inadequate mixing of the solutions, evaporation and the small range
of the solutions.
Introduction:
Amagat’s law states that volumes are approximately additive. However, this does
not apply to solutions whose concentrations are to be known to a high degree of accuracy.
Preparation of a solution with accurate molality is generally done by adding an amount of
water to a measured amount of salt and obtaining the weight of water by difference. In
1770 Millero reported that volume decreases when salts are added to a specific volume of
water. This effect was explained as electrostriction: the volume contracts due to
interaction of the polar solvent around the ions. However, this phenomenon occurs in
non-ionic solutions well, reflecting differences in intermolecular forces. Thermodynamics
explains this deviation from ideal behavior through partial molal quantities. The most
important partial molal quantity is chemical potential:
(1)
For this experiment, partial molal volume will be measured:
(2)
In high pressure systems, partial molal volume is related thermodynamically to chemical
potential by the following:
(3)
The partial molal volume considers the change in molal volume with the increase in
moles of material:
Since partial molal volumes are functions of concentration but not the total number of
moles, equation 4 can be expressed as:
where V is total volume. Taking component 1 to be water and component 2 to be the salt,
the volume of solution can be determined with static amounts of solvent (water) and
varying amounts of salt. Since molality is the concentration of solute per kg of solvent, it
is intuitive to take the amount of water fixed at 1000 g. With the molality of the solution
and the molecular weight of the salt used and the measured density of the solution, the
volume can be calculated:
The graph of experimental data for volume as a function of molality can be fit with a
power series, yielding a fit equation whose derivative with respect to molality yields the
partial molal volume as a function of molality or amount of salt added:
Replacing equation 7 into equation 5, taking n1 = 55.508 mol of water
(1000g/18.015g/mol), n2 = m, and rearranging, the partial molal volume of solvent can be
expressed as:
Since both partial molal volumes are functions of concentration, they can be expressed at
infinite dilution for a single value. At infinite dilution for the partial molal volume of
water, the effects of solvated ions on the solvent are null. The partial molal volume of salt
at infinite dilution reflects the effects of electrostriction on water due to the solvated ions.
The values of partial molal volumes at infinite dilution depend on the equation used to fit
the data and how well is extrapolates to m = 0. Thus, it is imperative that density be
measured accurately because slight deviations can result in poor results.
Procedure:
Five solutions of KCl with varying molalities between 0.05 m and 2.00 m were
prepared by weighing salt by difference in a jar with lid. 20 mL of distilled water was
added to the jar and the mass was recorded. This was used to calculate the molality of the
solution. The DMA 4500 was turned on and its temperature was adjusted to 25.00°.
Distilled Water was injected and then the air line was reconnected and the pump was
turned on. The density was then taken. Once the density read that of air (between 0.0011-
0.0014 g/mL), a syringe of distilled water was put into the injection port and distilled
water was injected. The density for water was recorded at least 3 times for different
portions until consistency (within 0.0001g/mL). Then the syringe was rinsed twice with
small portions of the KCl solution and was then filled with the solution. The solution was
injected partially and density was recorded. This was repeated until 3 consistent values of
density were reported for the solution, again using different portions. The syringe was
rinsed with another solution of KCl and the density was measured as before. This was
repeated for the remaining KCl solutions. Then the entire procedure was repeated using
NaCl instead of KCl.
Analysis and Results
Weights, molalities, and densities for water, sodium chloride and potassium
chloride were recorded in Table 1. It must be noted that instead of using 0.5 to 2.0 molal
solutions as the procedure indicated, 0.01 to 0.5 molal solutions for sodium chloride and
0.06 to 0.5 molal solutions for potassium chloride were used. With the data obtained,
Figure 1, which shows the relationship between density and molality for each salt, was
produced. The graphs indicate a quadratic relationship between density and molality; as
molality increases, density increases as well. R-squared values of 0.99872 for sodium
chloride and 0.99346 for potassium chloride indicate that the data obtained is precise.
Table 2 contains the calculated volume as a function of molality, V{m}, partial
molal volume of water, V1, the partial molal volume of the salts, V2, and the apparent
partial molal volume, φ. The volume as a function of molality was calculated using
equation 6, the partial molal volume of water using equation 8, the partial molal volume
of the salts using equation 7 and the apparent molal volume using equation 11. It is to be
noted that the partial molal volume of water is somewhat constant across different
molalities but the partial molal volume of the salts decreases greatly with increasing
molality.
Figure 2 represents the relationship between the partial molal volume of the salt
and molality; both graphs show a quadratic relationship. As molality increases, partial
molal volume of the salt increases as well. R-squared values for figure 2 are not as high
as those for figure 1 but still show about 90% reliability.
Table 3 is a summary of the values for an infinite dilution using three different
methods of calculation. By taking the derivative of the fit equation for volume versus
molality in the form V = A + B*m+C*m2. An expression for the partial molal volume is
obtained. This is V2 = B + 2*C*m. The infinite dilution can be found as a limit of
molality approaching 0. This results in the infinite dilution of V2 being equal to the fit
parameter B. A second method to find V2 at infinite dilution is to take the limit of m 0
again, but use the fit equation obtained in figure 3. A third method is to do the same but
use figure 4. This data shows that method 2 is the most reliable with only a 8.6%
deviation from the literature value for NaCl and a 6.2% deviation for KCl.
In figure 3, φ is plotted against m1/2 for both salts. It was found that there is a
linear relationship between φ and m1/2 for NaCl but a quadratic relationship for KCl. This
could be due to the small range of molalities used. The values for R-squared are not as
desirable as those in previous graphs, values of 0.5847 for NaCl and 0.96381 for KCl
were acquired. The quadratic relationship for KCl, although more accurate, does not fit
the mason equation (12) which is clearly linear.
φ =φº + am1/2 + bm (12)
If the salt solutions followed the Debye-Huckel theory, the equation for φ{m} would
provide a single slope of 1.868 for all 1,1-electrolites at 25ºC. This slope changes
depending on charge and temperature. The relationship between φ-1.86m1/2 and m1/2 is
shown in figure 4. φº is the intercept at m=0. The value φº for NaCl was found to be
14.24 and 25.18 for KCl. This means a deviation from the literature value of 14.3% and
6.2% respectively. The graph for NaCl is linear whereas KCl is quadratic. Once again,
KCl does not fit the equation (13) provided.
φ =φº + 1.868m1/2 + bm (13)
Table 4 presents information on the differences between the partial molal values of KCl
and NaCl, and between KBr and NaBr at an infinite solution. It is noted that the
difference between the partial molal volumes and the apparent molal volumes of KCl and
NaCl decreases with decreasing molality. We determined that since both KCl and KBr,
and NaCl and KBr are 1,1 electrolytes the difference between them would be equal. The
literature indicates a difference of 6.9 between the partial molal volumes of ions of Cl and
Br. The reason for the disparity between the literature value and the experimental values
Figure 1: Density vs Molality for NaCl and KCl Solutions
Table 2: Volumes as a function of molality, V{m}, partial molal volumes of water, V1, the partial molal volumes of the salts, V2, and the apparent partial molal volumes, φ for KCl and NaCl
Figure 2: Volume vs Molality for NaCl and KCl Solutions
Table 3: Values for Infinite Dilutions via 3 different methodsV2{Method 1} V2{Method 2} V2{Method 3} Literature
NaCl 34.13 15.19 14.24 16.63KCl 64.30 25.18 25.18 26.85% Deviation from literature for NaCl 105.26049 8.64396 14.37589% Deviation from literature for KCl 139.47266 6.23039 6.23099
Figure 3: φ vs m1/2 for NaCl and KCl Solutions
Figure 4: φ-1.86m1/2 vs m1/2 for NaCl and KCl Solutions
Table 4: Differences between partial and infinite molal volumes for KCl-NaCl and KBr-NaBr
m {KCl} m{NaCl} V2{KCl} V2{NaCl} V2{KCl}-V2{NaCl} V2{KBr}-V2{NaBr} φ{KCl} φ{NaCl}φ{KCl}-φ{NaCl}