Exp. 1

Experiment 1: Freezing Point Depression of Electrolytes Physical Chemistry Laboratory CHEM 445- 021L Cristina Fernandez Nathaly Murillo Due Date: May 4, 2008 Submitted Date: May 4, 2008 Abstract In this experiment the effect on freezing point depression relative to the concentration of an electrolyte (HCl) was measured using a Dewar flask. It was found that as the molality of HCl increases the freezing point of the solution decreases in a linear fashion, meaning the freezing point depression increases with increasing molality. The experimental data was shown to be consistently lower than that of an ideal electrolyte. The equation fitting an ideal electrolyte is ΔTF= 3.72m, the experimental data fits the equation ΔTF= 3.5336m. Osmotic coefficients and activity coefficients were determines for these data. The osmotic coefficients did not follow any tangible pattern but the activity coefficients were found to decrease with increasing molality. Last, using the same methods as the experimental data, osmotic coefficients were calculated for a given set of data for NaOH. The given data followed the trends of that of the experimental data. The activity coefficients were measured in three different ways for the given data set, first using the experimental equation, second using the DHLL equation and third using the Debye-Hückel-Guggenheim equation. The results showed that the first two ways of determining the activity coefficients are more accurate than the DebyeHückel-Guggenheim equation due to the inclusion of more parameters other than molality.

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Introduction Colligative properties are unique properties of solutions that depend only in the solvent used and the concentration of the sample, in other words, they do not depend on the chemical composition of the solution. The freezing point depression is one colligative property greatly used. The freezing point depression for non-electrolytes is described by the following equation: ΔTF = Kf m

(1)

In Equation (1), the freezing point depression constant, KF, for water is 1.860 °/molal and m is the molality. The osmotic coefficient, g, is the ratio of the experimental freezing point depression of electrolytes solutions with the value of ideal strong electrolytes and it is represented by the following equation:

(2) The osmotic coefficient is less than 1 because the real electrolytes solutions do not behave ideally due to the interionic forces. The osmotic coefficient depends on the dilution; as the solution becomes more dilute , g approaches 1 as expressed by the following equation: Limit{g}m0 = 1

(3)

It is know theoretically that the osmotic coefficient is greatly affected by the ionic charges as well as the ionic concentrations, and the equation that defines this relationship is the ionic strength:

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(4) Also, the average activity coefficient of the electrolyte can be calculated using the osmotic coefficient, g, at the temperature of the freezing solution. The equation to calculate the average activity coefficient is the following: (5) Experimental Procedure 1. Freezing Point of Water: The Dewar flask was filled half full with distilled water, and then ice until the flaks was nearly full. The water and ice were stirred to ensure that the solution was mixed well and also to prevent temperature gradients. Using a differential mercury thermometer the freezing point of water was determined. The magnifying lens was used to read the temperature with an accuracy of ± 0.00X°. The temperature was recorded three times while the slurry was being stirred vigorously to obtain a constant value. This procedure was repeated with another batch of distilled water and ice. The value for the freezing point of water used in the proceeding calculations was the average of the recorded temperature values. 2. Freezing Points of Solutions: Approximately 5 mL of HCl were added to the water/ice slurry while being stirred continuously until a constant temperature was obtained. The freezing point of the solution was recorded three times (with an accuracy of ± 0.00X°), and then ~ 50 mL of aliquot were removed and transfer to a labeled and weighed snap jar, with cap. The jar was allowed to return to room temperature and then weighed.

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The aliquot was then transferred to an Erlenmeyer flask to be titrated with NaOH and calculate the exact amount of HCl in each solution. Once the amount of HCl in the solution was found, one was able to back calculate to find the exact weight of the water. This data were used to calculate the molality of HCl in the solution, mol{HCl}/Kg{H2O}. The entire procedure was repeated to obtain the freezing point and concentrations of 10 solutions of HCl, keeping in mind that the freezing point depressions should had covered a range from ~0.1 to 1°C. To avoid refilling the buret with NaOH during the titrations, ~25mL of aliquot were removed instead of 50mL as the concentration of HCl increased due to the addition of ~5mL HCl. Results and Discussion Table 1a contains the data gathered during the experiment which consist of the freezing points of each solution of HCl and their averages. Table 1b contains freezing point depressions (ΔTf), the weight of each solution of HCl, the volume of the NaOH solution used to titrate each HCl solution, the mmols of HCl titrated, and the molality of each solution. Before the first recorded value of the freezing point of HCl, three values were obtained but these were discarded due to a misunderstanding of the experimental procedure. For the omitted values water and ice were added after every 50mL extraction of the HCl solution which resulted in different freezing point temperatures due to dilution of the solution and a temperature change due to the ice. These values were as follow: 5.000°C, 4.458°C, and 4.400°C. Another value was omitted between the first and second recorded value due to a lack of indicator in the titrated solution. The freezing point for this value was 4.355°C. Water and ice were added to solutions # 8 and # 9 since the freezing point started rising instead of declining due to lack of ice and too little solution.

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This could have lead to some experimental error. For all solutions at least triplicate freezing point values were obtained, but for some solutions more values were acquired due to inconsistent temperature readings. Figure 1 shows the linear relationship between the molality and the freezing point depression of HCl for the data obtained experimentally, and also as it would appear if the solution were an ideal electrolyte. It should be noted that the experimental freezing point data is always lower than the ideal freezing point depression. This is due to interionic interactions between the ions which are not taken into account in the equation for an ideal electrolyte. To compensate for this, activity coefficients must be determined. Table 2 contains the data used to calculate the osmotic coefficient, g. This was calculated using Equation (2), which is the ratio between the experimental and ideal values of the freezing point depression. It is a measure of the deviation between ideal and real strong electrolytes. In an ideal solution, as the molality approaches 0, the osmotic coefficient should reach 1. The value for solution # 1 was omitted since it yielded an osmotic coefficient greater than one which may result in an activity coefficient greater than one. Figure 2 depicts the quadratic relationship between the osmotic coefficients of HCl solution and the square root of the molality of the HCl solution. The square root of the molality was used in order to fit the equation g= 1+ am1/2 + bm. The value for all solutions was plotted first which lead to the following values: a=0.4051± 0.3234 and b=-1.7214 ± 0.8538. Since the value for solution # 1 does not agree with our data, it was omitted which lead to the following values of a and b: a=0.3628± 0.3884 and b= -1.5872 ± 1.0696. This omission leads to better activity coefficient values.

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In Table 3a the activity coefficients, γ, were calculated without solution #1. In Table 3b the values for the activity coefficients in solution #1 were included. The difference between the two is noted as Table 3b leads to activity coefficient values greater than 1. Using the equation g= 1+ am1/2 + bm and Equation (5), an equation for the activity coefficient was derived assuming that μ is equal to the molality of the solution (m). The resulting equation is as follows: Ln{γ} = 3am1/2 + 2bm

(6)

Using the same concepts used for the HCl solutions, the osmotic coefficient and the activity coefficients for the given set of data for NaOH in Table A were calculated. These data are shown in Table 4. Also included are calculations for the activity coefficients using the DHLL, Equations (7), and the Debye-Hückel-Guggenheim, Equations (8): (7)

(8) The activity coefficients were first calculated using Equation (5) and g= 1+ am1/2 + bm. The values for a and b were as follow: a=-0.3221±0.0420 and b= 0.3019 ± 0.0532. In Figure 3 the experimental values for the activity coefficients and those found using Equation (7) and (8) were plotted against molality. These values are different from each others since they take different elements into account. Equation (5) uses the osmotic coefficient when calculating the activity coefficients. Equation (7) only uses the square root of μ or the molality for 1,1 electrolytes in this case. Equation (8) takes the charge of the ions and the ratio between the square root of μ and 1+μ1/2. Because Equation (7) only

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takes μ into account, it is not as accurate as the values obtained experimentally using Equation (5) or Equation (8). Those values obtained using Equation (8) better represent the experimental values. Tables and Figures Table 1a: Experimental Freezing Point Values of HCl Solutions. Freezing Point of HCl Solution Solution # Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8 Average Freezing Point

1

2

3

4

5

6

7

8

9

4.413 4.413 4.413

4.355 4.355 4.355

4.318 4.318 4.318

4.270 4.270 4.270

4.240 4.245 4.245 4.245

4.200 4.200 4.200

4.165 4.165 4.165

4.130 4.150 4.205 4.155 4.150 4.145 4.145 4.145

4.120 4.120 4.120 4.115 4.115

4.413

4.355

4.318

4.270

4.244

4.200

4.165

4.153

4.118

Table 1b: Primary Data for HCl Solutions. Solutio n#

1 2 3 4 5 6 7 8 9

• • •

Average Freezing Point of Solution (ºC)

ΔTf {expt'l} (ºC)

Weight of Solution (g)

Volume {NaOH} (mL)

mmol HCl

Molality {HCl} (n/Kg)

4.413 4.355 4.318 4.270 4.244 4.200 4.165 4.153 4.118

0.155 0.213 0.250 0.298 0.324 0.368 0.403 0.415 0.450

49.7878 24.9999 25.0005 24.9732 24.9458 24.9938 24.9428 24.6739 28.6414

20.319 14.290 16.900 21.160 22.310 25.500 28.500 31.230 35.040

2.032 1.429 1.690 2.116 2.231 2.550 2.850 3.123 3.504

0.0409 0.0573 0.0678 0.0850 0.0897 0.1024 0.1147 0.1271 0.1229

m = N{NaOH} = 0.1 Relative Freezing Point of Water = 4.568 ºC Equations to calculate the molality of HCl: o V{NaOH} (L) * m{NaOH}* (mol HCl/mol NaOH) = mol of HCl in solution o mol HCl* MW{HCl}= weight of HCl (g) o Calculate the weight of the water :  (Weight of solution)- (weight of HCl)= weight of water o m{HCl} = mol{HCl}/Kg{H2O}

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Table 2: Primary Data Used to Calculate the Osmotic Coefficient, g. Solutio n#

m {HCl} (n/Kg)

m^(1/2)

ΔTf {calc.}

ΔTf {expt'l}

g{m}

**1 2 3 4 5 6 7 8 9

0.0409 0.0573 0.0678 0.0850 0.0897 0.1024 0.1147 0.1271 0.1229

0.2022 0.2393 0.2603 0.2915 0.2995 0.3200 0.3387 0.3566 0.3505

0.152 0.213 0.252 0.316 0.334 0.381 0.427 0.473 0.457

0.155 0.213 0.250 0.298 0.324 0.368 0.403 0.415 0.450

1.018 0.999 0.991 0.942 0.971 0.966 0.944 0.877 0.984

** This data point was omitted in the following calculations because it is greater than 1 and it may result in activity coefficients greater that are greater than 1. • For aqueous HCl solutions, ν = 2. Table 3a: Activity Coefficients Obtained with one Data Point Omitted. Solutio n#

m {HCl} (n/Kg)

ΔTf {calc.}

ΔTf {expt'l}

(ºC)

(ºC)

**1 2 3 4 5 6 7 8 9

0.0409 0.0573 0.0678 0.0850 0.0897 0.1024 0.1147 0.1271 0.1229

0.152 0.213 0.252 0.316 0.334 0.381 0.427 0.473 0.457

0.155 0.213 0.250 0.298 0.324 0.368 0.403 0.415 0.450

g{m}

Activity Coefficient γ

1.018 0.999 0.991 0.942 0.971 0.966 0.944 0.877 0.984

N/A 0.334 0.304 0.265 0.256 0.235 0.217 0.201 0.206

**This data point was omitted because it yielded an activity coefficient greater than 1. • Derived equation for activity coefficients: Ln{γ} = 3am1/2 + 2bm (6)

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Table 3b: Activity Coefficients Obtained using Solution # 1 Data. No Data Points were Omitted. Solutio n#

m {HCl} (n/Kg)

ΔTf {calc.}

ΔTf {expt'l}

(ºC)

(ºC)

1 2 3 4 5 6 7 8 9

0.0409 0.0573 0.0678 0.0850 0.0897 0.1024 0.1147 0.1271 0.1229

0.152 0.213 0.252 0.316 0.334 0.381 0.427 0.473 0.457

0.155 0.213 0.250 0.298 0.324 0.368 0.403 0.415 0.450

g{m}

Activity Coefficient γ

1.018 0.999 0.991 0.942 0.971 0.966 0.944 0.877 0.984

1.111 1.098 1.087 1.064 1.057 1.037 1.017 0.996 1.003

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All the data were included and they yielded activity coefficients were greater than 1. Table 4: Analysis of Literature Data for NaOH and Activity Coefficients using Different Equations. m{NaOH} (n/Kg)

m^(1/2)

ΔTf{expt'l} (ºC)

ΔTf{calc.} (ºC)

g{m}

γ using Equation (5)

γ using Equatio n (7)

γ using Equation (8)

0.010 0.020 0.050 0.100 0.126 0.253 0.500 0.510

0.100 0.141 0.224 0.316 0.355 0.503 0.707 0.714

0.036 0.070 0.173 0.346 0.430 0.860 1.700 1.740

0.037 0.074 0.186 0.372 0.469 0.941 1.860 1.897

0.968 0.941 0.930 0.930 0.917 0.914 0.914 0.917

0.905 0.871 0.814 0.763 0.745 0.693 0.659 0.658

0.894 0.853 0.778 0.701 0.671 0.568 0.452 0.448

0.903 0.870 0.814 0.763 0.745 0.687 0.628 0.626

• • •

Primary data obtained from Table A in lab manual. Equation that fits the data for g= 1+ am1/2 + bm is: y=0.3019x2 – 0.3221x + 0.9937 Derived equation for activity coefficients: Ln{γ} = 3am1/2 + 2bm (6)

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Figure 1. ΔTf {experimental} ΔTf {calculated} Linear ( ΔTf {experimental}) Linear (ΔTf {calculated})

Freezing Point Depression of HCl (ΔTf ) vs. Molality of HCl 0.5

y = 3.72x 2 R =1

0.45 0.4

y = 3.5336x 2 R = 0.9891

0.35

ΔTf (°C)

0.3 0.25 0.2 0.15 0.1 0.05 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

molality (n/kgH2O)

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Figure 2.

Osmotic Coefficient of HCl vs. Square Root of Molality of HCl (mol/Kg of water)

1.400

1.200

2

y = -1.7214x + 0.4051x + 1.0005 2 R = 0.5716

osmotic coefficient {g}

1.000 with outlier value without outlier value Poly. (with outlier value) Poly. (without outlier value)

0.800

0.600 2

y = -1.5872x + 0.3628x + 1 2 R = 0.4823

0.400

0.200

0.000 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

m^(1/2)

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Figure 3. Osmotic Coefficient of NaOH vs. Square Root of Molality of NaOH NaOH values

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Poly. (NaOH values)

0.99 0.98 0.97

g

0.96 0.95 2

y = 0.3386x - 0.3564x + 1 2 R = 0.9361

0.94 0.93 0.92 0.91 0.9 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

m^(1/2) (mol/kgH2O)

Conclusion A linear relationship was found between the electrolyte concentration and the freezing point depression. Because of ionic interactions between the molecules the experimental data yields a consistently lower freezing point depression than if the solution were ideal. The equation for an ideal electrolyte is: y= 3.72x, for the experimental data the equation is: y= 3.5663x. Y being the freezing point depression and x being the molality. The osmotic coefficient, or, the ratio between the experimental and ideal values of the freezing point depression, measures the deviation between ideal and real strong electrolytes. In an ideal solution, as the molality approaches 0, the osmotic

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coefficient should reach 1. There is no clear pattern to the degree of deviation in our data. The calculation of the activity coefficients demonstrates a decrease of the activity coefficients as the molality increases if the experimental equation is used to determine the activity coefficients. Using the same methods used to calculate the data obtained experimentally, a given set of data for NaOH was calculated. For this set of data, a linear relationship between freezing point depression and molality was found. The data for the osmotic coefficient did not follow a tangible pattern either. For this set of data three different ways to calculate the activity coefficients were used. Using the experimental equation, the activity coefficients were also found to decrease as the molality increases. Using the DHLL equation, the activity coefficients were found to decrease as molality increases, just like with the experimental equation. These two ways of calculating activity coefficients are the most alike since they take more than molality into account. The Debye-Hückel-Guggenheim only takes into account molality, making this the most deviant data.

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