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EXPT 5: Determination of Partial Molar Volumes Group 9: Francheska Biolena, Precious Caree Regunton, Marian Justine Yorobe Chem 156.1 – WAD Instructor: Sarah Sibug

Submitted: August 9, 2013 Performed: July 27, 2013

I. THEORETICAL FRAMEWORK The volumes of two solutions, when mixed together, are generally not additive A significant mathematical difference occurs between the extensive and intensive properties of mixtures. These properties can be treated as mathematical functions. Equation 1 shows a function f (x1, x2,… xN) which is considered to homogeneous of degree k. k f (λx1, λx2,…, λxN) = λ f (x1, x2,…, xN) (eq.1) All extensive properties, which are amount-dependent, are homogeneous of degree 1. This can be illustrated by volume for which 1 V (λn1, λn2, …, λnN) = λ V (n1, n2, …, nN) = λV (n1, n2, …, nN) (eq. 2) where n1, n2, … are amounts of substances. Hence, increasing the amounts of every substance λ-fold would result to a total volume increased λ-fold. On the other hand, all intensive properties, or those that are amount-independent, are said to be homogeneous of degree zero. This is illustrated by the temperature for which 0 T (λn1, λn2, …, λnN) = λ T (n1, n2, …, nN) = T(n1, n2, …, nN) (eq. 3) According to Euler’s Theorem, when equation 1 applies, kf (x1, x2,…, xN) = ∑ Therefore, for the volume of a mixture (k=1), V=( )

n1 + (

)

= ̅ 1 n1 + ̅ 2n2 + … + ̅ N nN

I

(

)

n2 + … + (

(eq.4)

)

nN (eq. 5)

where nj corresponds to the amounts of all other substances that are held constant when the amount of one of the substances is varied (Alberty, 2005). These derivatives are referred to as Partial Molar Volumes, which is indicated by the use of an overbar. ̅i = ( ) (eq. 6) The Partial Molar Volume is then defined as the change in V when 1 mole of i is added to an infinitely large amount of solution at constant temperature and pressure. It is an intensive property that determines the contribution of a given substance to the total volume of the solution, as it is observed that the volumes of two solutions, when mixed together, aren’t additive. This particular behavior is attributed to the intermolecular forces and interaction of the components of each solution. It is very important to understand the concept of partial molar volume, as it provides information on the solutesolvent interaction and solute structure of the solution. Also, it is the most essential quantity in the analysis of the pressure effect on chemical reactions (Kusatsu, 2007). The goal of the experiment is the determination of the partial molar volumes of water and ethyl alcohol in water-ethanol mixtures.

Page 1 of 3 Experiment 5 | Group 9 | Chem 156.1

II. RESULTS A. Determination of Partial Molar Volume of Ethanol Table 1. Determination of Partial Molar Volume of C2H5OH

Figure 1. Moles of ethanol vs volume of solution

Flask #

1

2

3

4

VH2O (ml)

15

15

15

15

VC2H5OH (ml)

9

10

11

8

mC2H5OH (g)

7.498

7.893

8.682

6.314

molC2H5OH (moles)

0.1628

0.1713

0.1885

0.1370

Vol sol’n (ml)

24.00

24.50

25.10

22.50

Sample computation: Moles in Trial #1 = 9 mL x ρC2H5OH / MW C2H5OH = 0.1628 moles Partial Molar Volume = 51.42 ml/mol B. Determination of Partial Molar Volume of Water Table 2. Determination of Partial Molar Volume of Water

Figure 2. Moles of ethanol vs volume of solution

Flask #

1

2

4

5

VH2O (ml)

9

11.60

10.50

7

VC2H5OH (ml) mH2O (g)

15

15

15

15

8.958

11.45

10.45

6.967

0.4971

0.6354

0.5800

0.3866

23.40

28.10

24.70

20.80

molH2O (moles) Vol sol’n (ml)

Sample computation: Moles in Trial #1 = 9 mL x ρH2O / MW H2O = 0.1628 moles Partial Molar Volume = 27.05818 ml

III. INTERPRETATION OF DATA AND CONCLUSIONS Based from the gathered data, the partial molar volume of ethanol and water is 51.42 ml/mol and 27.05818 ml/mol, respectively. It is determined by the slope of the line based from the linear regression gathered from the two compounds at 25 degrees. Errors from this experiment can be rooted from the incorrect addition of volume of ethanol or water by the students, or by the vaporization of the ethanol due to temperature. In order to avoid errors from this experiment, larger quantities of the compounds are recommended for a smaller margin of error. More replicates and flasks with varying amounts of the compounds are recommended for higher precision and accuracy. Also, other solutions with similar structures (benzene and toluene) can be used for this experiment in order to explore more on this topic.

Page 2 of 3 Experiment 5 | Group 9 | Chem 156.1

IV. GUIDE QUESTIONS 1. Add the measured volume of the liquids used in the experiment. How do the computed volumes compare with the observed volumes of the mixtures? Table 3: Comparison of the Computed Volume of Solution and Measured Volume of Solution for the Determination of Partial Molar Volume of C2H5OH

Volume of H2O (mL) Volume of C2H5OH (mL) Volume of Solution (Computed) Volume of Solution (Measured) Discrepancy (mL)

1 15.0 9.0

2 15.0 10.0

3 15.0 11.0

4 15.0 8.0

24.5

25.0

26.0

23.0

24.0

24.5

25.1

22.5

0.5

1.5

0.9

0.5

The computations above show us that the substances are not pure and ideal. A contraction is experienced when volumes are mixed especially when water is involved. Volume is an intensive property meaning it is amount-dependent. So, as the amount increases by λ-fold the total volume also increases by λ-fold. Furthermore, volume is a function or dependent on temperature, pressure and number of moles of the substance. 3. The following data were obtained from liquids A and B: Moles of A 0.15 0.25 0.45 0.45 0.45 0.45 Moles of B 0.45 0.45 0.45 0.35 0.25 0.15 Vol of mixture (mL) 48.9 55.1 67.5 58.7 49.9 41.1

mixtures of 0.35 0.45 61.3

a. Calculate the partial molar volumes of A and B V = naVa + nbVb, Va

Table 4: Comparison of the Computed Volume of Solution and Measured Volume of Solution for the Determination of Partial Molar

Volume of H2O (mL) Volume of C2H5OH (mL) Volume of Solution (Computed) Volume of Solution (Measured) Discrepancy (mL)

1 9.00

2 11.5

3 11.0

4 10.5

5 7.00

15.0

15.0

15.0

15.0

15.0

24.0

26.5

26.0

27.0

22.0

23.4

25.1

25.1

24.7

20.8

0.6

1.4

0.9

2.3

1.2

Volume of H2O

In both parts of the experiment, it is shown above that the measured volume of the solution was smaller than the computed volume. This discrepancy is due the interaction of water and ethanol in the solution. There are two factors that cause the decrease in volume of the solution. They are the intermolecular forces between the substances and the nature of the substance mixed. In this case, the attractive force of ethyl alcohol and water was stronger since both are polar. Moreover, water in liquid form has an open structure which can be filled by the nonpolar part of the alcohol. This arrangement contributes to the discrepancy observed in this experiment (New Mexico Institute of Mining and Technology,2005).

Using linear regression of moles of A against volume of mixture and moles of B against volume of mixture, partial molar volume of the liquid A and liquid B can be obtained respectively. Hence, the partial molar volume of liquid A is 62 mL/mol while liquid B has a partial molar volume of 88 mL/mol. b. What will be the volume of a mixture that contains 60 mole %A? 60 mole % A can be defined as mole fraction of A (XA) XA = 0.60 The equation V = XAVA + XBVB, where V is the average molar volume of A-B solution, XA and XB are the mole fractions of A and B, respectively and VA and VB are the partial molar volumes of A and B. V = XaVA + XBVB V = (0.60)(62mL/mol A) + (1.00– 0.60)(88mL/mol B) V = 72.4 mL per mole of A-B solution

V. REFERENCES 2. Explain the significance of the observations made in no 1?

Alberty, R., Bawendi, M., Silbey, R. (2005) Physical Chemistry. New Jersey, USA: John Wiley & Sons. Page 3 of 3

Experiment 5 | Group 9 | Chem 156.1

Kusatsu, S, (2007). Molecular theory of partial molar volume and its applications to biomolecular systems. Condensed Matter Physics 2007. Vol. 10 No 3(51), pp. 343-361. Accessed August 5, 2013. Retrieved from http://www.icmp.lviv.ua/journal/zbirnyk.51/004/art04.pdf New Mexico Institute of Mining and Technology. (2005). Measurement of Partial Molar Volumes. Accessed July 29, 2012. Retrieved from infohost.nmt.edu/~jaltig/PartVol.pdf

Page 4 of 3 Experiment 5 | Group 9 | Chem 156.1

View more...
Submitted: August 9, 2013 Performed: July 27, 2013

I. THEORETICAL FRAMEWORK The volumes of two solutions, when mixed together, are generally not additive A significant mathematical difference occurs between the extensive and intensive properties of mixtures. These properties can be treated as mathematical functions. Equation 1 shows a function f (x1, x2,… xN) which is considered to homogeneous of degree k. k f (λx1, λx2,…, λxN) = λ f (x1, x2,…, xN) (eq.1) All extensive properties, which are amount-dependent, are homogeneous of degree 1. This can be illustrated by volume for which 1 V (λn1, λn2, …, λnN) = λ V (n1, n2, …, nN) = λV (n1, n2, …, nN) (eq. 2) where n1, n2, … are amounts of substances. Hence, increasing the amounts of every substance λ-fold would result to a total volume increased λ-fold. On the other hand, all intensive properties, or those that are amount-independent, are said to be homogeneous of degree zero. This is illustrated by the temperature for which 0 T (λn1, λn2, …, λnN) = λ T (n1, n2, …, nN) = T(n1, n2, …, nN) (eq. 3) According to Euler’s Theorem, when equation 1 applies, kf (x1, x2,…, xN) = ∑ Therefore, for the volume of a mixture (k=1), V=( )

n1 + (

)

= ̅ 1 n1 + ̅ 2n2 + … + ̅ N nN

I

(

)

n2 + … + (

(eq.4)

)

nN (eq. 5)

where nj corresponds to the amounts of all other substances that are held constant when the amount of one of the substances is varied (Alberty, 2005). These derivatives are referred to as Partial Molar Volumes, which is indicated by the use of an overbar. ̅i = ( ) (eq. 6) The Partial Molar Volume is then defined as the change in V when 1 mole of i is added to an infinitely large amount of solution at constant temperature and pressure. It is an intensive property that determines the contribution of a given substance to the total volume of the solution, as it is observed that the volumes of two solutions, when mixed together, aren’t additive. This particular behavior is attributed to the intermolecular forces and interaction of the components of each solution. It is very important to understand the concept of partial molar volume, as it provides information on the solutesolvent interaction and solute structure of the solution. Also, it is the most essential quantity in the analysis of the pressure effect on chemical reactions (Kusatsu, 2007). The goal of the experiment is the determination of the partial molar volumes of water and ethyl alcohol in water-ethanol mixtures.

Page 1 of 3 Experiment 5 | Group 9 | Chem 156.1

II. RESULTS A. Determination of Partial Molar Volume of Ethanol Table 1. Determination of Partial Molar Volume of C2H5OH

Figure 1. Moles of ethanol vs volume of solution

Flask #

1

2

3

4

VH2O (ml)

15

15

15

15

VC2H5OH (ml)

9

10

11

8

mC2H5OH (g)

7.498

7.893

8.682

6.314

molC2H5OH (moles)

0.1628

0.1713

0.1885

0.1370

Vol sol’n (ml)

24.00

24.50

25.10

22.50

Sample computation: Moles in Trial #1 = 9 mL x ρC2H5OH / MW C2H5OH = 0.1628 moles Partial Molar Volume = 51.42 ml/mol B. Determination of Partial Molar Volume of Water Table 2. Determination of Partial Molar Volume of Water

Figure 2. Moles of ethanol vs volume of solution

Flask #

1

2

4

5

VH2O (ml)

9

11.60

10.50

7

VC2H5OH (ml) mH2O (g)

15

15

15

15

8.958

11.45

10.45

6.967

0.4971

0.6354

0.5800

0.3866

23.40

28.10

24.70

20.80

molH2O (moles) Vol sol’n (ml)

Sample computation: Moles in Trial #1 = 9 mL x ρH2O / MW H2O = 0.1628 moles Partial Molar Volume = 27.05818 ml

III. INTERPRETATION OF DATA AND CONCLUSIONS Based from the gathered data, the partial molar volume of ethanol and water is 51.42 ml/mol and 27.05818 ml/mol, respectively. It is determined by the slope of the line based from the linear regression gathered from the two compounds at 25 degrees. Errors from this experiment can be rooted from the incorrect addition of volume of ethanol or water by the students, or by the vaporization of the ethanol due to temperature. In order to avoid errors from this experiment, larger quantities of the compounds are recommended for a smaller margin of error. More replicates and flasks with varying amounts of the compounds are recommended for higher precision and accuracy. Also, other solutions with similar structures (benzene and toluene) can be used for this experiment in order to explore more on this topic.

Page 2 of 3 Experiment 5 | Group 9 | Chem 156.1

IV. GUIDE QUESTIONS 1. Add the measured volume of the liquids used in the experiment. How do the computed volumes compare with the observed volumes of the mixtures? Table 3: Comparison of the Computed Volume of Solution and Measured Volume of Solution for the Determination of Partial Molar Volume of C2H5OH

Volume of H2O (mL) Volume of C2H5OH (mL) Volume of Solution (Computed) Volume of Solution (Measured) Discrepancy (mL)

1 15.0 9.0

2 15.0 10.0

3 15.0 11.0

4 15.0 8.0

24.5

25.0

26.0

23.0

24.0

24.5

25.1

22.5

0.5

1.5

0.9

0.5

The computations above show us that the substances are not pure and ideal. A contraction is experienced when volumes are mixed especially when water is involved. Volume is an intensive property meaning it is amount-dependent. So, as the amount increases by λ-fold the total volume also increases by λ-fold. Furthermore, volume is a function or dependent on temperature, pressure and number of moles of the substance. 3. The following data were obtained from liquids A and B: Moles of A 0.15 0.25 0.45 0.45 0.45 0.45 Moles of B 0.45 0.45 0.45 0.35 0.25 0.15 Vol of mixture (mL) 48.9 55.1 67.5 58.7 49.9 41.1

mixtures of 0.35 0.45 61.3

a. Calculate the partial molar volumes of A and B V = naVa + nbVb, Va

Table 4: Comparison of the Computed Volume of Solution and Measured Volume of Solution for the Determination of Partial Molar

Volume of H2O (mL) Volume of C2H5OH (mL) Volume of Solution (Computed) Volume of Solution (Measured) Discrepancy (mL)

1 9.00

2 11.5

3 11.0

4 10.5

5 7.00

15.0

15.0

15.0

15.0

15.0

24.0

26.5

26.0

27.0

22.0

23.4

25.1

25.1

24.7

20.8

0.6

1.4

0.9

2.3

1.2

Volume of H2O

In both parts of the experiment, it is shown above that the measured volume of the solution was smaller than the computed volume. This discrepancy is due the interaction of water and ethanol in the solution. There are two factors that cause the decrease in volume of the solution. They are the intermolecular forces between the substances and the nature of the substance mixed. In this case, the attractive force of ethyl alcohol and water was stronger since both are polar. Moreover, water in liquid form has an open structure which can be filled by the nonpolar part of the alcohol. This arrangement contributes to the discrepancy observed in this experiment (New Mexico Institute of Mining and Technology,2005).

Using linear regression of moles of A against volume of mixture and moles of B against volume of mixture, partial molar volume of the liquid A and liquid B can be obtained respectively. Hence, the partial molar volume of liquid A is 62 mL/mol while liquid B has a partial molar volume of 88 mL/mol. b. What will be the volume of a mixture that contains 60 mole %A? 60 mole % A can be defined as mole fraction of A (XA) XA = 0.60 The equation V = XAVA + XBVB, where V is the average molar volume of A-B solution, XA and XB are the mole fractions of A and B, respectively and VA and VB are the partial molar volumes of A and B. V = XaVA + XBVB V = (0.60)(62mL/mol A) + (1.00– 0.60)(88mL/mol B) V = 72.4 mL per mole of A-B solution

V. REFERENCES 2. Explain the significance of the observations made in no 1?

Alberty, R., Bawendi, M., Silbey, R. (2005) Physical Chemistry. New Jersey, USA: John Wiley & Sons. Page 3 of 3

Experiment 5 | Group 9 | Chem 156.1

Kusatsu, S, (2007). Molecular theory of partial molar volume and its applications to biomolecular systems. Condensed Matter Physics 2007. Vol. 10 No 3(51), pp. 343-361. Accessed August 5, 2013. Retrieved from http://www.icmp.lviv.ua/journal/zbirnyk.51/004/art04.pdf New Mexico Institute of Mining and Technology. (2005). Measurement of Partial Molar Volumes. Accessed July 29, 2012. Retrieved from infohost.nmt.edu/~jaltig/PartVol.pdf

Page 4 of 3 Experiment 5 | Group 9 | Chem 156.1

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