The Determination of Partial Molar Enthalpy

EXPERIMENT 4 THE DETERMINATION OF PARTIAL MOLAR ENTHALPY

INTRODUCTION

A partial molar property is a thermodynamic quantity which indicates how an extensive property of a solution or mixture varies with changes in the molar composition of the mixture at constant temperature and pressure. Similar to the volume, the enthalpy of a solution is a function of temperature, pressure and composition. The partial molar enthalpy of mixing of a component is the heat change when one more of that component is added to a large volume of solution at a specific concentration. The excess molar enthalpy is identical with the molar enthalpy change on mixing and therefore is often termed as the heat of mixing.

INTRODUCTION

The enthalpy of mixing is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution. It is most often expressed in kJ/mol at constant temperature. A chemical reaction involves the breaking of some chemical bonds and the formation of the other chemical bonds. The breaking of bonds requires an input of energy and the formation of bonds gives off energy, so that nearly every constant-temperature chemical reaction is accompanied by energy and enthalpy changes. If the system gives off heat when a reaction takes place at constant temperature, the reaction is called exothermic. If the system absorbs heat at constant temperature, the reaction is called endothermic.

INTRODUCTION

In general, the value of a partial molar property of a constituent in a solution is not equal to the value for the pure substance.

OBJECTIVES

• To determine the molar enthalpy of mixing (H) for the different mixtures of glycerol and water. • To use the data to estimate the partial molar enthalpies of mixing or the two components in a mixture.

SCHEMATIC DIAGRAM

Measure out the specified volume of glycerol into the Dewar flask through a pipet and allow it to equilibrate for two minutes before recording its constant temperature using a Fischer thermometer. Add the specified volume of water through a buret them immediately cover the flask and mix the solution by swirling. Add the specified volume of water through a buret them immediately cover the flask and mix the solution by swirling. For every minute, in three minutes, get the time temperature data and record the constant temperature obtained.

Rinse and dry the Dewar flask thoroughly before continuing on a new measurement. Repeat the last four steps for all the specified mixtures of glycerol and water.

DATA

Table 1. Composition of Glycerol- Water Mixtures No. mL mL Mol Mol glycero water glycero water l l (n1) (n2) 1 2 3 4

2.77 13.83 27.67 20.85

67.54 30.69 27.29 11.94

0.038 0.19 0.38 0.29

3.752 1.705 1.516 0.66

5 6 7 8

34.49 38.66 36.76 25.01

8.53 4.17 2.27 0.38

0.47 0.53 0.50 0.34

0.47 0.23 0.126 0.021

CALCULATIONS

Mole fraction of glycerol and water

Where: X1=mole fraction of glycerol X2=mole fraction of water n1= mole of glycerol n2= mole of water

CALCULATIONS

Mean heat capacity

: C(water) = 75.3 J/K mol : C(glycerol) = 207.5 J/K mol

CALCULATIONS

The molar enthalpy of mixing

Where: ∆H= Molar Enthalpy C=Mean heat Capacity ∆T= Change in temperature

Mole fraction of glycerol (X1)

Mole fraction of water (X2)

(J/K mol)



n1

n2

T (K)

0.010032 0.989968

0.038

3.75

0.1

0.100529 0.899471

0.19

1.7

0.9

88.52

79.668

0.202128 0.797872

0.38

1.5

0.9

101.74

91.566

0.305263 0.694737

0.29

0.66

2.3

0.47

0.47

1.5

0.697368 0.302632

0.53

0.23

1.8

167.4921 301.4858

0.793651 0.206349

0.5

0.13

2.3

180.2206 414.5075

0.941828 0.058172

0.34

0.021

0.7

199.8097 139.8668

0.5

0.5

(J/mol)

76.62619 7.662619

115.6558 266.0083 141.4

212.1

CALCULATIONS

• If you set the X1 in the general equation to zero, you can obtain this formula for H2:

• For H1, this is a possible equation:

CALCULATIONS

H

H1

H2

7.662619

-562.1942422

7.740267

79.668

-377.3747368

88.52

91.566

-216.8668421

114.4575

266.0083

45.86350272

382.8908

212.1

27.07659574

424.2

301.4858

136.5218669

996.2139

414.5075

306.7355206

2008.767

139.8668

262.8672844

2404.377

CALCULATIONS

• Draw a graph of the molar enthalpy of mixing (H) vs. mol fraction of glycerol (X1) and determine the value of H1 and H2 for a mixture of 0.45 mol fraction of water. y = 259.55x + 73.991 y= 259.55 (0.55) + 73.991

:X1=.55

y= 261.7435 J/mol = H

CALCULATIONS

CALCULATIONS

H vs X1 3000 2500 2000 1500 H

H2 H1 mixing

1000 500 0 0

1

2

3

4

-500 -1000 X1

5

6

7

8

9

DISCUSSIONS

To simplify matters, the volumes for both glycerol and water had to be cut down to smaller portions and so we came up with the ones in the Table 1 since we knew that by doing so, the mole fractions for both would not be altered. We also had to make use of pure glycerol which was more viscous for the later part of the experiment because we ran out of the less viscous glycerol and that could be another reason for the discrepancy in the temperature of each mixture. The molar enthalpy of mixing at 0.45 mol fraction of water is 261.7435 J/mol. Its H1 is481.6522 J/mol while its H2 is 1.03352x10-13 J/mol.

CONCLUSION

In this experiment, we learned that the temperature of glycerol and the temperature of the solution vary more visibly when the amount of glycerol is much greater than the amount of water in a mixture and makes the temperature of solution higher than that of the glycerol. This also shows that the mixture of glycerol and water generally undergoes endothermic process because of the positive values that we obtained in our data. All differences from the expected results can be accounted to the personal errors that we committed while performing the experiment when we did not maintain the consistency of the glycerol that we used and perhaps while adding the volumes of each substance into the Dewar flask.