Experiment 4 The Determination of Partial Molar Enthalpy

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Experiment 4 THE DETERMINATION OF PARTIAL MOLAR ENTHALPY A Laboratory Report in Partial Fulfilment of the Requirements in Chem116 Laboratory

ARELLANO, LORY MAE DAGONDON, VANESSA OLGA (Group 5)

Chem116 Laboratory – Physical Chemistry I Laboratory Section 1 Performed on October 5, 2015 Submitted on October 22, 2015

ARNOLD C. GAJE Laboratory Instructor

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ABSTRACT The main focus of this experiment is to estimate the values of the partial molar enthalpy of mixing of glycerol-water mixtures. In order to do so, (8) eight glycerol-water mixtures were prepared. Tasks dictated by the laboratory manual were distributed to each of the groups in the class to minimize the use of reagents and equipment. The molar change in enthalpy of mixing of these glycerol-water mixtures was determined with the use of a constant pressure calorimeter. These obtained values of molar enthalpy change were plotted against the mole fraction of glycerol. An outlier was determined in the curve. Personal errors that might cause this outlier were acknowledged. The outlier was omitted from the data analysis. The partial molar enthalpy of glycerol and water were estimated by drawing a tangent at a specific point in the plotted curve which designates the given concentration. The y-intercepts at both ends of the tangent line represent the partial molar enthalpies. The estimated values for the partial molar enthalpy of glycerol and water are 135 J/mol and 460 J/mol, respectively.

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INTRODUCTION In a solution made my mixing substance 1 of specific number of moles with substance 2 of a specific number of moles, the enthalpy change associated with these two substances is a function of the number of moles of the components present in the formed mixture.

[1]

∆ H=∆ H ( T , P , n1 , n2 )

Where ∆H is the enthalpy change T is temperature P is pressure n1 is the number of moles of substance 1 n2 is the number of moles of substance 2 Expressing equation [1] intro partial derivatives to determine the infinitesimal change contributed by each of the parameters which ∆H is dependent to yields: [2]

d ∆ H=

( ∂∂T∆ H )

dT +

P , n1 ,n2

( ∂∂∆PH )

(

dP+

T , n1 ,n2

∂ ∆H ∂ n1

)

P , T ,n2

(

d n1 +

∂∆ H ∂ n2

)

d n2 P ,n1 , T

In constant temperature and pressure, equation of [2] would be reduced to: [3]

d ∆ H=

(

∂∆ H ∂ n1

)

n2

d n1 +

(

∂∆H ∂ n2

) dn

2

n1

The infinitesimal enthalpy change with respect to the infinitesimal change of the number of moles of a particular component in a mixture such that the other variables to which the enthalpy change is dependent on remain constant is referred to as the partial molar enthalpy. Partial molar enthalpy, as it is a ratio of two extensive properties just like other partial molar quantities, is an intensive property describing the heat change when a mole of the component is added to a volume of solution at a given concentration. Partial molar ´ enthalpy can be denoted by ∆ H . Equation [3] now becomes:

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[4]

´ 1 d n1 +∆ H ´ 2 d n2 d ∆ H=∆ H

Integrating equation [4] would result to:

[5]

´ 1 n 1+ ∆ H ´ 2 n2 ∆ H=∆ H

Dividing each term on equation [5] by the total number of moles of component 1 and components 2 would result to:

[6]

´ ´ 1 X 1+ ∆ H ´ 2X2 ∆ H=∆ H

´ where ∆ H

is the molar enthalpy

X1 and X2 are the mole fractions of component 1 and component 2 respectively.

Equation [6] suggests that the molar enthalpy of mixing is a function of the mole fraction of the two components present in the mixture. It must be noted that the partial molar properties of a component in a mixture or solution are not equal to their corresponding properties in their pure form that is the components form prior to mixing. This is due to the differences between the intermolecular forces in the solution and those in the pure components (Levine, Ira, 2009). The experiment is designed to estimate the partial molar enthalpies of each of the components of the glycerol-water mixture. This was done by obtaining the change in enthalpy of the mixture through constant pressure calorimeter so as to calculate for the molar change in enthalpy. The equation [6] can be further manipulated such that the relationship between the molar change in enthalpy and one component in the mixture is linear.

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´ (∆ H ´ 1−∆ H ´ 2) X ´ 1+ ∆ H ´2 ∆ H=

[7]

Equation [7] is in the form of the linear equation y=mx +b where the expression ´ 1−∆ H ´2 ∆H

is m or the slope of the line and

´2 ∆H

which is the partial molar enthalpy

of component 2 is just the y intercept. However, it must be noted that both the partial molar enthalpy of component 1 and 2 are dependent on the mole fraction of the components in the

mixture. This resulted to a nonlinear graph of

´ ∆H

vs.

X´ 1 . Estimated values of partial

molar enthalpies at a given concentration were still obtained by the intercept method (Chua, Ortillo, Araullo, et al, 1996). Partial molar properties such as partial molar enthalpy are essential in determining values of any extensive properties which define the state of the system in consideration. The values of partial molar properties are maintained in constant temperature and pressure which are the conditions in which values of the said extensive properties can be obtained (P. Atkins, 2006). MATERIALS AND METHODS MATERIALS 1. Acid Buret (50 mL) Acid buret is a common device in analytical chemistry, particularly those associated with titration as it is capable of measuring accurate amounts of a solution with unknown concentration. In the experiment, it was utilized to measure accurate amounts of distilled water to be added to glycerol. Figure 1. Acid Buret

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2. Beaker (250 mL) Beaker is a common glassware in laboratories used to contain solutions subject for stirring, mixing, heating or to simply hold the said solution. In the experiment, it served as a container for the measured glycerol to be placed in the calorimeter. Figure 2. 250 mL Beaker 3. Coffee cup calorimeter Coffee cup calorimeter is an improvised calorimeter made up of two styrofoam cups and a stopper such that it can function as a constant pressure (isobaric) calorimeter which in turn would make its measured heat be equal to the change in enthalpy of the system in consideration. It is usually accompanied by thermometer and a stirrer. It is the main device used in the experiment to measure the heat and, therefore, the change of enthalpy of the glycerol-water mixtures. Figure 3. Coffee cup calorimeter 4. Iron stand and Iron clamp Iron stand and iron clamp are instruments used mainly as support for glass wares and other devices. In the experiment, the iron clamp was attached to the iron stand so as to support the thermometer (part of the calorimeter hardware) stringed on the iron clamp. Figure

4.

Iron

stand

and

Iron

clamp 5. Graduated Cylinder (100 mL)

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A graduated cylinder is a glass ware used to measure accurate volumes of liquids. In the experiment, it was used to measure large accurate volumes of glycerol. Figure 5. Graduated Cylinder 6. Pipet (10 mL) Pipet is a graduated glass tube used to suction accurate small volumes of liquids. It is usually accompanied by an aspirator. In the experiment, it was used to measure out small amounts of glycerol. Figure 6. 10 mL Pipet 7. Thermometer Thermometer is a device used to measure temperature. In the experiment, it was part of the calorimeter hardware such that it can measure the temperature changes in the glycerol-water mixture the system contained in the calorimeter.

Figure 7. Thermometer METHODS Molar enthalpies of eight (8) glycerol-water mixtures were determined. Data obtained in each mixture were used to estimate partial molar enthalpies of each component in the mixture at a given concentration. Labour was divided within the seven (7) groups in the class for reasons concerning the scarcity of reagents and instruments such as coffee cup calorimeters. Each group was paired with another group to determine the molar enthalpies of two mixtures assigned to them

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by the instructor. One group, however, the one who got the Dewar flask and thus, was spared to use the coffee cup calorimeter which was susceptible to errors, were tasked to do two mixtures. Preparation of Glycerol-Water Mixtures Eight (8) glycerol-water mixtures were prepared by the whole class. The composition of each mixtures were specified in the table 1 (see Appendix I). Preparation of mixture 5 and 6 were assigned to our group. Indicated volumes of glycerol and water for both mixtures 5 and 6 were measured and were transferred to a beaker and graduated cylinder, respectively. For mixture 5, 91.0 mL of glycerol was accurately measured using a 100 mL graduated cylinder. It was then transferred to a labelled beaker. 22.5 mL of distilled water was measured using a 50 mL acid buret and was transferred to a labelled graduated cylinder. Same technique was done for mixture 6: 102.0 mL glycerol and 11.0 mL distilled water were measured. Measuring the temperature change using Coffee cup calorimeter The measured volume of glycerol from mixture 5 was transferred into the coffee cup calorimeter. It was then equilibrated for two minutes noting its temperature per minute. Upon establishing the constant temperature of the glycerol, the measured volume of water was added into the coffee cup (an estimation of 8 seconds was noted before the water was added) and was covered immediately. Before covering it was made sure that the thermometer and the stirrer were assembled on the stopper of the coffee cup calorimeter such that both could not agitate each other during the whole process of measuring the temperature and constant swirling. The time-temperature data and the constant temperature were recorded for every minute until 3 minutes. Same procedure was done for mixture 6. Before proceeding to

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mixture 6, the coffee cup calorimeter was washed and rinsed. For mixture 6, an estimation of 10 seconds was noted before the water was added. The change in temperature is the difference between the constant temperature recorded after mixing the two liquids, glycerol and distilled water and the equilibrated constant temperature of glycerol prior to the addition of distilled water. RESULTS This experiment obtained experimental data essential to estimate the partial molar enthalpies of each components in different glycerol-water mixtures. The following tables show the chronological order of values obtained and calculated so as to estimate partial molar enthalpies. Interpretation of the relationships between these obtained values and target values are shown graphically. Table 1. Indicated volume of glycerol and water in each mixture

Mixture No.

Volume Glycerol (mL)

Volume H20 (mL)

1

3.7

89

2

18.3

40.5

3

36.5

36

4

27.5

15.75

5

45.5

11.3

6

51.0

5.5

7

48.5

3.0

8

33.0

0.5

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One of the first things to do in the experiment is to prepare for the glycerol-water mixtures. These mixtures are made by mixing the indicated volumes of glycerol and water as shown in Table 1. Each mixture has varying volumes for glycerol and water in such a way that a wide range of mole fractions (ranging between 0-1) can be obtained and thus would result to a better set of data points which in turn would allow us to see the key relationships between these values under consideration. Table 2. Calculated values for n1, n2, X1, X2

Mixture No.

n1

n2

X1

X2

1

0.0506

4.9403

0.01

0.99

2

0.2504

2.2481

0.1

0.9

3

0.4994

1.9983

0.2

0.8

4

0.3763

0.8743

0.3

0.7

5

0.6225

0.6273

0.5

0.5

6

0.6978

0.3053

0.7

0.3

7

0.6636

0.1665

0.801

0.199

8

0.4515

0.0278

0.9

0.1

In all glycerol-water mixtures, let glycerol be component 1and water be component 2. Table 2 shows the summary of the calculated values of the number of moles of glycerol, n1; the number moles of water, n 2; the mole fraction of glycerol, X 1; and, the mole fraction of water, X2 in each mixture. From the data in Table 1, the number of moles can be calculated by simple dimensional analysis using densities and molecular weight. Calculations for the number of moles of each component in all mixtures are shown in Appendix 2 (refer to pg. 21). Calculating for the number of moles enables the calculation for the mole fraction

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essential to find the partial molar enthalpies. The calculations for the mole fractions in each mixture are found at the Appendix 2. As expected, the mole fractions are scattered around evidently in the 0-1 range assuring a good set of data points if done correctly, the experimental methods that is. Table 3. Experimental Data: Time-Temperature data for all mixtures Mixture No. 1

Mixture No. 2

Mixture No. 3

Mixture No. 4

Time (min) 0

Temp. (°C) 25.6

Time (min) 0

Temp. (°C) 25.6

Time (min) 0

Temp. (°C) 28.0

Time (min) 0

Temp. (°C) 27.5

1

26.2

2

26.0

1

27.5

1

27.5

*2

26.2

3

26.0

2

27.5

2

27.5

**-

-

-

-

2.6

29.9

2.11

29.9

***3

26.2

3

29.0

3

30.5

3

30.5

4

26.2

4

29.0

4

30.5

4

30.5

5

26.2

5

29.0

5

30.5

5

30.5

Mixture No. 5

Mixture No. 6

Mixture No. 7

Mixture No. 8

Time (min) 0

Temp. (°C) 26.5

Time (min) 0

Temp. (°C) 27.0

Time (min) 0

Temp. (°C) 27.5

Time (min) 0

Temp. (°C) 28.0

1

26.9

1

27.0

1

27.2

1

28.0

*2

26.9

2

27.0

2

27.0

2

28.0

**2.8

28.5

2.10

27.3

2.4

28.75

***3

29.0

3

27.1

3

28.0

3

28.5

4

29.0

4

27.1

4

28.0

4

28.5

5

29.0

5

27.1

5

28.0

5

28.5

Table 3 summarizes the time temperature data obtained in the experimental method in which a constant pressure calorimeter is used to contain the mixture while a simultaneous

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process of swirling and taking down of temperature per minute in a three minute interval took place. These data were acquired from the class. The row with one asterisk (*) denotes the constant temperature of the glycerol prior to addition of water on that particular time. The row with two asterisks (**) and three asterisks (***) denote the time and temperature recorded on the instant of mixing and the constant temperature of the mixture, respectively. These values are essential for the calculation of the change of T, ∆T. Table 4. Change in Temperature

Mixture No.

Ti °C

Tf °C

∆T

1

26.2

26.2

0

2

26.0

29.0

3

3

27.5

30.5

3

4

27.5

30.5

3

5

26.9

29.0

2.1

6

27.0

27.1

0.1

7

27.0

28.0

1

8

28.0

28.5

0.5

Table 4 shows the temperature change for each mixture. These temperatures and obtained via experimental method and was tabulated in the previous graph. The temperatures in rows with single asterisk (*) and double asterisk (**) are the initial temperature and final temperature, respectively. The difference between these two values would yield to the change in temperature. The change in temperature is needed to calculate the molar enthalpy of mixing.

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´ Table 5. Values for C

and

∆´H

Mixture No.

∆T (K)

Molar enthalpy of Mean heat capacity, ´ mixing, ∆ H (J/ ´ C (J/K mol) mol)

1

0

76.622

0

2

3

88.52

265.56

3

3

101.74

305.22

4

3

114.96

344.88

5

2.1

141.4

296.94

6

0.1

167.84

16.784

7

1

181.19

181.19

8

0.5

194.28

97.14

´ The mean heat capacity, denoted by C , is calculated by the sum of the mole fraction of each component multiplied by the corresponding heat capacities of the components. The heat capacities of water and glycerol are 75.3 J/K mol and 207.5 J/K mol, respectively. Mean heat capacities are calculated so as to calculate for the molar enthalpy of mixing which is just the product of the change in temperature and the mean heat capacities. Values for the molar change in enthalpy in each mixture are tabulated. As shown in table, the values for the molar change of enthalpy increases from mixture 1 until it reached its maximum at mixture 4. After it reached its peak, its value started to fluctuate. However, an outlier was observed in molar change in enthalpy in mixture 6. From the value of 296.94 J/mol, it drastically decreased to 16.784 J/mol and spiked up again at value of 181.19 J/mol. This outlier is best omitted from the data.

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Graph 1.

´ against X 1 Plot of ∆ H

∆‾H vs. X1 400 300 Molar Change in Enthalpy, ∆‾H (J/mol)

200 100 0 0 0.2 0.4 0.6 0.8 1

Mole fraction of glycerol, X1

The molar change in enthalpy is plotted against the mole fraction of glycerol. The graph 1 resulted to curve with its x coordinate ranging from 0-1 (mole fraction of glycerol). This shows that as the mole fraction of glycerol increase from zero, the molar change in enthalpy increases into such a point in the curve that as it approaches the mole fraction of 1 of glycerol, the molar enthalpy decreases. It must be noted that the data point obtained from mixture 6 was omitted.

This graph can be described by the equation [7]:

´ (∆ H ´ 1−∆ H ´ 2) X ´ 1+ ∆ H ´2 ∆ H= .

Using this expression, the partial molar enthalpies at any given concentration can be estimated. Graph 2 (see the attached graphing paper) is the plot of the molar change in enthalpy against the mole fraction of glycerol made manually. To estimate the partial molar enthalpies, a tangent line in a certain point in the curve must be drawn.

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DISCUSSION The experiment’s main focus is to determine the effect of the composition of each of the component in the glycerol-water mixture on the molar enthalpy of mixing. Eight (8) sets of glycerol-water mixture were prepared accordingly. The molar enthalpies of each mixture were evaluated by simple calorimetric techniques. In order to get the change in molar enthalpy of mixing, it must be first noted that partial molar properties or quantities vary with parameters such as temperature, pressure and the composition of each of the component present in the mixture.

Thus to evaluate the molar enthalpy of mixing, pressure and

temperature must be kept constant. With the use of the coffee cup calorimeter which imposes constant pressure, the molar enthalpies of mixing were obtained. Table 5 show the complete values of the molar enthalpy of mixing in all mixtures. The values of partial molar enthalpies for both water and glycerol were estimated using the intercept method. In order to get the estimated values of the partial molar enthalpies of each component, the plot of the enthalpy of mixing against the mole fraction of glycerol was examined. It must be noted that partial molar enthalpies are dependent on the mole fraction of a particular components, may it be glycerol or water. The graph of the molar enthalpy of mixing against the mole fraction of a particular component yielded a curve, a contradiction with equation [7] which suggests that is a straight line. This is because both the partial molar enthalpies of glycerol and water are dependent on the mole fraction, as stated previously. At a given concentration there is point in the curve that will give rise to a tangent

line. The slope of the tangent will give the value

( ∆ H´ 1 −∆ H´ 2 )

. Therefore, the intercept of

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this tangent line at

X1

´ = 0 will give the value of ∆ H 2 . The intercept on the other side of

the tangent line at

X1

´ = 1 will give the value ∆ H 1 .

Graphs 1 show the behaviour of the partial molar enthalpies of with varying concentration. It was observed that the molar enthalpy of mixing at the X 1=0 increases until such a point in the curve where it fluctuates and starts to decrease as it approaches X 1=1. X1=0 means that the mixture has no component of glycerol and therefore would mean that it no contribution to the molar enthalpy of mixing. Similarly, as X 1=0, the value of X1=1 which means that the value of the molar enthalpy of mixing is due only to water component. As the value of X1 increases, the molar enthalpy of mixing increases. This means that the glycerol and water are mixed and both contribute to the molar enthalpy of mixing. Graph 2 shows the same graph as graph 1 except it is done manually and a tangent line identified at X1=0.55 in the curve. To estimate the partial molar enthalpies of glycerol and water, the intercepts of the tangent line in both sides of the graph must be determined. Using the graph, a rough estimation can be made. This estimation can induce personal errors. These personal errors root on the judgement based analysis done. However, this will give us the idea of how much of the concentration of each of the components in the mixture contributes to the molar change in enthalpy of mixing. The estimated value for the partial molar enthalpy of water is 460 J/mol and the estimated partial molar enthalpy of glycerol is 135 J/mol. These values suggest that water has a higher contribution to the molar change in enthalpy of mixing at that specific concentration. This method in determining the values of the partial molar enthalpies is known as the method of intercepts. CONCLUSION

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To estimate the partial molar enthalpies of glycerol and water in a mixture is the main goal of this experiment. To do so, coffee cup calorimeter was used to get the molar enthalpy of mixing. Series of calculation were done to achieve the goal of this experiment. These calculations root from the concepts governing partial molar quantities. It is essential to know that partial molar quantities, such as partial molar enthalpy, depend on the number of moles of each component in a mixture. The molar change in enthalpy is not equal to the summation of the change in enthalpy of each of the component at its pure form. The same principle applies for other molar quantities. Thus, it is important to know the effect of each component in a mixture to the change in enthalpy of mixing. The plot of the molar change in enthalpy against the mole fraction of glycerol yields a curve in which a tangent line at a certain point in the x-axis (concentration) will enable the partial molar enthalpies to be estimated. The intercepts on each side of the graph of the tangent line represents the partial molar enthalpies of each component in the mixture. This can be estimated by graphing manually and identifying the tangent line at a certain point in the graph and trace the tangent line until such time that it reaches its intercepts at both sides of the graph. CONTRIBUTION OF AUTHORS The experiment was conducted by the two members of the group 5, Ms. Dagondon and Ms. Arellano, together with group 1. All the members of the two groups participated and were efficient in the experiment. The distribution of duties between the groups was properly followed by each of the members. This laboratory report was made solely by Ms. Dagondon. Ms. Arellano had her fair share of laboratory report duties since it was her that made the laboratory report for the third experiment and her only.

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REFERENCES Atkins, P. & De Paula, J. (2006). Atkins’Physical Chemistry, (8 th ed.). Great Britain: Oxford Chang, R. (2007). Physical Chemistry for the Biosciences. United States: McGraw-Hill. Levine, I. Physical Chemistry, 5th edition, McGraw Hill companies Inc., 1978 edition. Physical Chemistry Laboratory Committee. Experiments in Physical Chemistry Part One. Institute of Chemistry, University of the Philippines, Diliman Quezon City, 1996 edition. APPENDICES APPENDIX 1. TABLE AND VALUES Table 1. Indicated volume of glycerol and water in each mixture

Mixture No.

Volume Glycerol (mL)

Volume H20 (mL)

1

3.7

89

2

18.3

40.5

3

36.5

36

4

27.5

15.75

5

45.5

11.3

6

51.0

5.5

7

48.5

3.0

8

33.0

0.5

Table 2. Calculated values for n1, n2, X1, X2

Mixture No.

n1

n2

X1

X2

1

0.0506

4.9403

0.01

0.99

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2

0.2504

2.2481

0.1

0.9

3

0.4994

1.9983

0.2

0.8

4

0.3763

0.8743

0.3

0.7

5

0.6225

0.6273

0.5

0.5

6

0.6978

0.3053

0.7

0.3

7

0.6636

0.1665

0.801

0.199

8

0.4515

0.0278

0.9

0.1

Table 3. Experimental Data: Time-Temperature data for all mixtures Mixture No. 1

Mixture No. 2

Mixture No. 3

Mixture No. 4

Time (min) 0

Temp. (°C) 25.6

Time (min) 0

Temp. (°C) 25.6

Time (min) 0

Temp. (°C) 28.0

Time (min) 0

Temp. (°C) 27.5

1

26.2

2

26.0

1

27.5

1

27.5

*2

26.2

3

26.0

2

27.5

2

27.5

**-

-

-

-

2.6

29.9

2.11

29.9

***3

26.2

3

29.0

3

30.5

3

30.5

4

26.2

4

29.0

4

30.5

4

30.5

5

26.2

5

29.0

5

30.5

5

30.5

Mixture No. 5

Mixture No. 6

Mixture No. 7

Mixture No. 8

Time (min) 0

Temp. (°C) 26.5

Time (min) 0

Temp. (°C) 27.0

Time (min) 0

Temp. (°C) 27.5

Time (min) 0

Temp. (°C) 28.0

1

26.9

1

27.0

1

27.2

1

28.0

*2

26.9

2

27.0

2

27.0

2

28.0

**2.8

28.5

2.10

27.3

2.4

28.75

***3

29.0

3

27.1

3

28.0

3

28.5

4

29.0

4

27.1

4

28.0

4

28.5

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5

29.0

5

27.1

5

28.0

5

28.5

Table 4. Change in Temperature

Mixture No.

Ti °C

Tf °C

∆T

1

26.2

26.2

0

2

26.0

29.0

3

3

27.5

30.5

3

4

27.5

30.5

3

5

26.9

29.0

2.1

6

27.0

27.1

0.1

7

27.0

28.0

1

8

28.0

28.5

0.5

´ Table 5. Values for C

and

∆´H

Mixture No.

∆T (K)

Molar enthalpy of Mean heat capacity, ´ mixing, ∆ H (J/ ´ C (J/K mol) mol)

1

0

76.622

0

2

3

88.52

265.56

3

3

101.74

305.22

4

3

114.96

344.88

5

2.1

141.4

296.94

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6

0.1

167.84

16.784

7

1

181.19

181.19

8

0.5

194.28

97.14

Graph 1.

´ against X 1 Plot of ∆ H

∆‾H vs. X1 400 300 Molar Change in Enthalpy, ∆‾H (J/mol)

200 100 0 0 0.2 0.4 0.6 0.8 1

Mole fraction of glycerol, X1

APPENDIX 2. CALCULATIONS Number of moles of glycerol, n1 −1 −1 Formula: n1=(vol . glycerolmL )(density of glycerol g mL )( MW of glycerol g mol )

Where density of glycerol is 1.26 g ml-1

Mixture 1:

n2= (3.7 mL Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 ) =0.0506 mol

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Mixture 2:

n2= (18.3 mL Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 )=0.2504 mol

Mixture 3:

n2= (36.5 ml Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 )=0.4994 mol

Mixture 4:

n2= (27.5 mL Glyc erol ) ( 1.26 g mL−1) ( 92.09 g mol−1) =0.3793 mol

Mixture 5:

n2= ( 45.5 mL Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 ) =0.6225 mol

Mixture 6:

n2= (51.0 mL Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 )=0.6978mol

Mixture 7:

n2= ( 48.5 mL Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 ) =0.6636 mol

Mixture 8:

n2= (33.0 mL Glycerol ) ( 1.26 g mL−1 ) ( 92.09 g mol−1 )=0.4515mol

Number of moles of water, n2 Formula: n2=(vol . water mL)( density of water g mL−1)(MW of water g mol−1)

Where density of glycerol is 1.00 g ml-1

Mixture 1

−1 −1 : n2= ( 89.0 mL ) ( 1.0 g mL )( 18.015 g mol ) =4.9403 mol

Mixture 2:

n2= ( 40.5 mL ) ( 1.0 g mL−1 ) ( 18.015 g mol−1 )=2.2481 mol

Mixture 3:

n2= (36.0 mL ) ( 1.0 g mL−1 )( 18.015 g mol−1 ) =1.9983 mol

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Mixture 4:

n2= (15.75 mL ) ( 1.0 g mL−1) ( 18.015 g mol−1 ) =0.8743 mol

Mixture 5:

n2= (11.3 mL ) ( 1.0 g mL−1 ) ( 18.015 g mol−1 )=0.6273 mol

Mixture 6:

n2= (5.5 mL ) ( 1.0 g mL−1) ( 18.015 g mol−1 ) =0.3053 mol

Mixture 7:

n2= (3.0 mL ) ( 1.0 g mL−1 )( 18.015 g mol−1 ) =0.1665 mol

Mixture 8:

n2= ( 0.5 mL ) ( 1.0 g mL−1 )( 18.015 g mol−1) =0.0278 mol

Mole fraction of glycerol, X1 n1 n1 +n 2

Formula:

X 1=

Mixture 1:

X 1=

0.0506 =0.01 0.0506+ 4.9403

Mixture 2:

X 1=

0.2504 =0.1 0.2504+ 2.2481

Mixture 3:

X 1=

0.4994 =0.2 0.4994+ 1.9983

Mixture 4:

X 1=

0.3763 =0.3 0.3763+0.8743

Mixture 5:

X 1=

0.6225 =0.5 0.6225+0.6273

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Mixture 6:

X 1=

0.6978 =0.7 0.6978+0.3052

Mixture 7:

X 1=

0.6639 =0.8 0.6636+0.1665

Mixture 8:

X 1=

0.4515 =0.9 0.4515+0.0278

Mole fraction of water, X2 n2 n1 +n 2

Formula:

X 2=

Mixture 1:

X 2=

4.9403 =0.99 0.0506+4.9403

Mixture 2:

X 2=

0.2504 =0.9 0.2504+ 2.2481

Mixture 3:

X 2=

1.9983 =0.8 0.4994+ 1.9983

Mixture 4:

X 2=

0.8743 =0.7 0.3763+0.8743

Mixture 5:

X 2=

0.6273 =0.5 0.6225+0.6273

Mixture 6:

X 2=

0.3052 =0.3 0.6978+0.3052

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Mixture 7:

X 2=

0.1665 =0.2 0.6636+ 0.1665

Mixture 8:

X 2=

0.0278 =0.1 0.4515+0.0278

Change in Temperature

Formula:

∆ T =T final−T initial

Mixture 1:

∆ T =26.2 ℃−26.2 ℃=0 ℃

Mixture 2:

∆ T =29.0 ℃−26.0℃=3 ℃

Mixture 3:

∆ T =30.5 ℃−27.5℃=3 ℃

Mixture 4:

∆ T =30.5 ℃−27.5℃=3 ℃

Mixture 5:

∆ T =29.0 ℃−26.9℃=2.1 ℃

Mixture 6:

∆ T =27.0 ℃−27.1℃=0.1 ℃

Mixture 7:

∆ T =28.0 ℃−27.0℃=1 ℃

Mixture 8:

∆ T =28.5 ℃−28.0℃=0.5 ℃

´ Mean Heat capacity, C

Formula:

´ C=X 1 C glycerol + X 2 C water

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Where

Mixture 1:

Mixture 2:

Mixture 3:

Mixture 4:

Mixture 5:

Mixture 6:

Mixture 7:

Mixture 8:

C glycerol=207.5

(

J J J + ( 0.99 ) 75.3 =76.622 K mol K mol K mol

(

J J J + ( 0.9 ) 75.3 =88.52 K mol K mol K mol

(

J J J + ( 0.8 ) 75.3 =101.74 K mol K mol K mol

(

J J J + ( 0.7 ) 75.3 =114.96 K mol K mol K mol

(

J J J + ( 0.5 ) 75.3 =141.4 K mol K mol K mol

(

J J J + ( 0.3 ) 75.3 =167.84 K mol K mol K mol

´ ( 0.1 ) 207.5 C=

´ ( 0.1 ) 207.5 C=

´ ( 0.2 ) 207.5 C=

´ ( 0.3 ) 207.5 C=

´ ( 0.5 ) 207.5 C=

´ ( 0.7 ) 207.5 C=

(

)

(

´ ( 0.9 ) 207.5 C=

´ C´ ∆ T ∆ H=

(

)

)

(

)

)

(

)

)

(

)

)

(

)

´ ( 0.801 ) 207.5 C=

´ Molar enthalpy, ∆ H

Formula:

J J ∧C water =75.3 K mol K mol

)

(

)

J J J + ( 0.199 ) 75.3 =181.19 K mol K mol K mol

)

(

)

J J J + ( 0.1 ) 75.3 =194.28 K mol K mol K mol

)

(

)

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Mixture 1:

Mixture 2:

Mixture 3:

Mixture 4:

Mixture 5:

Mixture 6:

Mixture 7:

Mixture 8:

(

´ 75.3 ∆ H=

J J ( 0 K )=0 K mol mol

(

´ 88.52 ∆ H=

)

J J ( 3 K )=265.56 K mol mol

)

´ 101.74 ∆ H=

(

J J ( 3 K )=305.22 K mol mol

(

J J ( 3 K )=344.88 K mol mol

(

J J ( 2.1 K )=296.94 K mol mol

´ 114.96 ∆ H=

´ 141.4 ∆ H=

)

)

)

(

J J ( 0.1 K )=16.784 K mol mol

´ 181.19 ∆ H=

(

J J (1 K )=181.19 K mol mol

(

J J ( 0.5 K )=97.14 K mol mol

´ 167.84 ∆ H=

´ 194.28 ∆ H=

)

) )

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