Che121l Experiment 1 Partial Molar Volumes

EXPERIMENT 1 PARTIAL MOLAR VOLUMES

OBJECTIVES To differentiate absolute density from relative density. To measure the density of liquid mixtures using a pycnometer. To determine the partial molar volumes of a binary system of liquids from density measurements. THEORY Conditions of constant temperature and pressure are exceptionally convenient experimentally and so a wide range of extensive thermodynamic properties that define a system can be explored. Theoretically, any extensive property that defines a system, when varied with respect to the amounts (ni) of the components that comprise the system at constant temperature and pressure give rise to interesting intensive properties called partial molar quantities. For instance, Y is an extensive property of a mixture; a partial molar quantity can be defined based on, say, the ith component of the mixture: Yi =

𝜕𝑌 𝜕𝑛 𝑖 𝑇,𝑝,𝑛 𝑗

where, Yi is the partial molar quantity based on the ith component, while nj represents the amount of the rest of the components of the mixture. The most important of these partial molar quantities is the partial molar free (Gibbs) energy also known as the chemical potential. In this experiment, however, the partial molar volume is in focus, because it is much easier to measure experimentally compared to Gibbs energy. The partial molar volume is a good indicator of non-ideality (similar to the compression factor for real gases) in mixtures. It is a common assumption that when two liquids are mixed, the volumes simply add up. This, however, is only true for ideal solutions—those that are formed from components that have very similar structures and hence similar forces of attraction operating among molecules. Very similar forces of attraction lead to minimal expansion or contraction in the volume of the mixture formed from the components. Any amount of deviation from ideal behavior is measured in terms of the enthalpy of mixing or a quantity called the partial molar volume.

Experiment 1: Partial Molar Volumes

For a binary liquid mixture composed of liquid A and liquid B, VA =

𝜕𝑉 𝜕𝑛 𝐴 𝑇,𝑝,𝑛 𝐵

VA is said to be the partial molar volume of A in a mixture with B. This quantity tells us how the volume of the mixture changes as the amount of A is varied. For example, for a waterethanol system, when one mole of water is added to huge volume of ethanol at 25° the volume increases by 14 cm3. Hence, it is said that the partial molar volume of water in ethanol is 14 cm3/mol in this case. The scenario is different when one mole of water is added to a huge amount of water at 25°C, which gives rise to a volume increase of 18 cm3. This is expected since the environment that receives the additional one mole of water is also a pool of water molecules as opposed to a pool of ethanol molecules! Apparently, the partial molar volume of water in the ethanol mixture will be near 18 cm3/mol if the mixture is largely water, but its value will be near 14 cm3/mol if ethanol is present in very large amounts compared to water. Hence, it can be said that the partial molar volumes of the components of a binary mixture of A and B vary with the composition of the mixture because the environment of each type of molecule changes as the composition changes from pure A to pure B. In this experiment, the partial molar volumes of water and alcohol will be determined by density measurements using a pycnometer (Figure 1.1).

Figure 1.1 Empty Pycnometer A pycnometer is a flask with tight-fitting glass stopper with a fine hole through it. A pycnometer is used for measuring the density of a solution using a reference liquid, such as water. Essentially, it is the specific gravity that is determined first. This is accomplished by accurately measuring the mass of the reference liquid using the pycnometer and an CHE121L Physical Chemistry 1 Laboratory

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Experiment 1: Partial Molar Volumes

analytical balance. Then, the mass of the liquid is also determined using the same pycnometer. The specific gravity of the solution is then determined by: 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

SG = 𝑚𝑎𝑠𝑠

𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛 𝑐𝑒 𝑙𝑖𝑞𝑢𝑖𝑑

The density values derived from the specific gravity values will be used to determine the partial molar volumes (such as Vm,A, the molar volume of A). When the partial molar volumes of the components are already determined, the total volume of the mixture with known composition can be determined as: V = nAVm,A + nBVm,B

MATERIALS Pycnometer Erlenmeyer flasks Water Mixture of unknown concentration

analytical balance thermometer alcohol sample (1-propanol, 2-propanol) acetone

PROCEDURE A. Calculation of approximate volumes necessary to prepare a mixture of given concentration 1. Calculate the necessary volumes of your alcohol sample and water to prepare 50 mL solutions with the following mole fractions: 0.20, 0.40, 0.60, and 0.80. 2. Record your data in Table 1.1 Table 1.1. Calculated Volumes of Liquids to Be Mixed for Specified Mole Fractions Sample xB xA VB, cm3 VA,cm3 1 2 3 4 NOTE: xB can be taken here as the mole fraction of your alcohol sample. V B is the calculated volume of alcohol necessary to prepare the solution based on the xB. The subscript A refers to the solvent, which is water in this case.

B. Preparation of Liquid Mixtures 1. Measure the mass of an empty and dry volumetric flask (with the stopper) using an analytical balance. 2. Add the calculated volume of water for xwater = 0.20 determined in Part A (Table 1.1) and measure the mass again. 3. Add the alcohol, mix thoroughly, and weigh the sample again. 4. Record all data in Table 1.2. CHE121L Physical Chemistry 1 Laboratory

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Experiment 1: Partial Molar Volumes

Table 1.2. Calculation of the Actual Mole Fractions of Prepared Solutions Sple

A (1) (2) (3) (4) B

Empty flask m0 , g

Flask + Soln A mA*, g

Flask + A+B mB*, g

mA*– m0

mB* – mA*

mA/MA

mB/MB

nB/(nA +nB)

mA , g

mB, g

nA, mol

nA, mol

xB

--

--

--

--

--

--

--

0

--

--

--

--

--

--

--

1

5. Calculate the actual mole fraction of the solution prepared based on the mass determinations. 6. Repeat the procedure for the other three solutions. (Don’t forget to label the flasks). 7. Put all solutions in a thermostated bath for at least 3 minutes before measuring the densities (Part C). 8. Record the temperature of the bath. C. Measuring the Mass of the Reference Liquid Using a Pycnometer 1. Measure the mass of a clean and dry pycnometer. 2. Fill the pycnometer with water and measure its mass. Important: a. Always start with a clean and dry pycnometer. b. Ensure that there are no bubbles every time the pycnometer is filled with a liquid. c. The pycnometer should always be filled to the same level. Put the cover while the excess liquid runs out. Dry the pycnometer using lint-free paper. d. Ensure that the temperature is the same throughout the measurements. 3. After each measurement, clean the pycnometer using technical acetone. 4. Record observations. D. Density Measurements 1. Perform measurements of the mass of solutions prepared in Part B using the same procedure outlined in Part C. 2. Do the same for the pure alcohol sample. 3. Record data in Table 1.3 4. Calculate the densities of each mixture using the formula: 𝑑=

CHE121L Physical Chemistry 1 Laboratory

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑚𝑖𝑥𝑡𝑢𝑟𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

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Experiment 1: Partial Molar Volumes

Table 1.3. Calculation of Densities and Molar Volumes Sple

xB (from Table 1.2)

xA = 1 – xB

A (1) (2) (3) (4) B

0

1.00

1.00

0

M (average) g/mol

Mass of pycnometer + sample, g

Mass of liquid g

Density g/mL

Molar Volume (Vm) mL/mol

E. Partial Molar Volume Calculation 1. Plot the density of the mixture against the mole fraction using your data in Table 1.3. 2. Measure the density of your unknown solution and calculate its concentration (in mole fraction). Note: The density of your unknown solution can be computed using the average molar mass of the mixture. 3. Compare the density of your unknown to the literature value. Explain the difference.

Figure 1.2 Tangent Method in Determining Molar Volumes

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Experiment 1: Partial Molar Volumes

4. Determine the partial molar volume of water and the partial molar volume of the alcohol at the specified molar concentration (ask your laboratory instructor) using the tangent method (See Figure 1.2). 5. Compare your values with the molar volumes of the pure compounds. Draw your conclusions.

POSTLAB PROBLEMS: 1. Calculate the partial molar volume of zinc chloride in 1 molar ZnCl2 solution using the following data: Mass percent 2 6 10 14 18 of ZnCl2 Density/ 1.0167 1.0532 1.0891 1.1275 1.1665 g cm–3 2. The partial molar volumes for a carbon tetrachloride (1) – benzene (2) solution at 25°C are shown in the following table: X1 0.0 0.3 0.5 0.7 1.0 –1 V1/L mol 0.1793 0.1122 0.1001 0.0983 0.09719 –1 V2/L mol 0.08927 0.09844 0.1064 0.1092 0.1123 (a) What is the molar volume of an equimolar solution? (b) What is the volume change on mixing 1 and 2 to form one mole of an equimolar solution? (c) Account for the value of the molar volume of mixing.

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