S. F. Sun and Peter M. Serpentino st. John's University Jamoico, New York 11439
The Determination of Partial Specific Volume A physical chemistry experiment
In the thermodynamic analysis of multicomponent solutions (I), the quantity, partial specific volume, 0, appears in many equations such as in the calculations of solventsalute and solute-solute interactions from the measurements of osmotic pressure and light scattering. More importantly, the quantity ii appears in the determination of molecular weight of macromolecules (e.g., proteins, enzymes, and nucleic acids) via ultracentrifuge sedimentation. Usuallv all the other narameters in the sedimentation equations can be measured accurately within 10.5%. The auantitv hardest to measure is 0 . Yet accurate molecularweight determinations require accurate values of U. In this note we describe a method for the accurate determination of partial specific volume of a protein (2). The method is so simple that it is worthy of inclusion in the reoertoire of undermaduate . ohvsical chemistrv laboratory experiments. The operation of the experiment reauires oatience and careful handling, which orovide good (raining in laboratory techniques. Theory For a two-component system the total volume of a solution can he expressd in terms of partial specific volumes,
where V i s the total volume of the solution in ml, w is the weight in grams, and the subscripts 1 and 2 refer to the components. Component 1 is usually designated a s the solvent (or solvent mixture) and component 2 as the solute. Equation l may be rearranged
For dilute solutions in general, we may approximate 01 (solvent component) by p , - l , where p l is the density of the solvent at anv given temnerature. Based on this assumption, the qu&&y D2 now becomes an apparent partial specific volume and is customarily desimated as 6 such h a t
Thus to determine 4 there are only four quantities to he measured: wl, wz, PI, and V. The values of w~ and wz are known from the prepared solution, while the value of p l can be calculated from data in the "International Critical Tables" (3), or experimentally determined using the same pycnometer. The measurements are then reduced to the determination of V. Experimental Crystalline bovine serum albumin of high purity which is commercially available is chosen for study. The sample solution is prepared by dissolving the protein in 0.1 M KC1 (or NaC1) solution in the concentration of about 0.75 g/lW g solvent. KC1 (or NaCI) is used because it is known not to affect the conformation of bovine SeNm albumin and 0.1 M corresponds to an ionic strength of 552
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Journal of Chemical Education
0.1, a customary value for biopolymer research studies. The pycnometers are fashioned by fastening capillary necks of about 1 mm i.d. to 25-ml volumetric or Erlenmeyer flasks as shown in the figure. A reference mark is engraved an the neck. IF no cathetometer is available, an accurate linear on the neck. The most scale may be engraved important part in constmetion is the selection of a capillary with a uniform diameter. The volume Vof the solution can he determined directly by reading the reference mark h, and the meniscus h, using the fallowing equation AV (4) V = V, + (h, - ha), LI ,"
h.
Pycnometer
where V, is the volume of the pycnameter to the reference mark and AV/Ah is the change in the volume with respect to the height of the capillary. For each pycnometer at a given temperature Vo and aV/Ah are constants. These two values may be determined by calibration with distilled deionized water. (The value of AV/Ah may also be obtained by the determination of mean radius as in capillary rise experiments.) A water bath in which the temperature should be controlled to =k 0.05'C and an analytical balance which is sensitive to the nearest 10.' g must be available. design.
Results and Discussion The table gives the results of representative experiments. The temperature, ionic strength, and pH describe the conditions under which measurements are taken. Bovine serum alhumin is believed to be in its native form a t the conditions specified (temperature 25% ionic strength 0.1, and pH 5.2). The literature value of 0z for albumin in its native form is 0.734 (4). The average value reported in this paper is also 0.734, indicating that the method is viable. The error in the value of 02 is dependent upon the errors of each of the three variables, total volume V, weight of the solvent WI, and weight of the protein wz in the solution. From the maximum error analysis the qeatest error is found to he from the weight of the protein wz in the so-
Determination of Apparent Partial Specific Volume of Bovine Serum Albumin at 2S0C, Ionic Strength 0.10, and pH 5.2 Pvmom-"
eterNo: 3
8
-.
"9.
w2, g
w,, g
ha, cm t+, cm
P,,
g/ml ml/gi
0.1880 25.774 26.248 29.898 1.00483 0.734 0.2019 27.740 26.404 31.092 1.00483 0.733
aPycnameter 3: pycnometer 8:
AV VO,25.756 ml; -, 0.00892 ml/cm;
Ah Vo, 27.716 m1; --,i;. 0.00830 ml/cm AV
U,"
For proteins the quantity 6 is virtually independent of their concentrations; hence, + E 6.
lntion. In order to obtain an accurate value of oz, the error in dry-weight of the of protein should not be greater than 1 ppt ( 5 ) . Correction for salt binding to the protein may be made ( 6 ) , but it is not absolutely necessary.
Literature Cited Ul Casassa,E.F.,andEisenberg,H..Aduon.PmfsinChem.. 19.287(1%4). (z1 vanH ~ I ~ ~ . K and . E .sun. . s.F..J . A ~ * , . cham.sot. w.ffi(19621. (31 "In~rnati~nalC1iticalT~bles."McCraw-HillBmkCo..lne..NauYork.1933. (41 Oayholf, M. 0.. Perlmann, G. E.. and Mselnnes. D. A,, J. Amer. Chem. Soc., 71. 251s(19521. (51 Hunter. M. J . . JPhya. Chem., 7l.3717119671. (61 Cararsa, E.F.,and Eirenbrrg, H.. J. Phys Chem., 65,427l19611
Volume 5 1 , Number 8, Augusf 1974
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