NOTES
1327
Table I: Results of Comparison Experiments Washer correction, cal
Adjustment to 0.96 g of NFs, cal
temp rise,
0
Ignition energY , cal
0.9621 0.9698 0.9382 0.9746 0.9757
0.24 0.21 0.22 0.22 0.18
24.74 29.69 23.30 16.33 16.33
0.86 4.03 -8.97 6.01 6.46
0.49399 0.49488 0.49740 0.49143 0.49103
Mass of NFa,
Corrected Calories per expt.
O C
1657.19 1658.47 1660.43 1662.06 1661.19 Av 1659.87
Table I1 : Results of Hexafluoroethsne Experiments Ignition energy. cal
Adjustment to 0.96 g of NFa, oal
At,
-AEr/M,
g
Washer correction, cal
O C
CaVg
1.3769 1.3523 1.3448 1.3407 1.3511
21.53 21.53 21.53 21.53 21.53
0.21 0.20 0.21 0.20 0.20
6.42 -3.70 -5.72 -5.39 -4.57
0.75203 0.75604 0.75578 0.74940 0.75365
of CzFs,
Mass of NF3,
g
1.1701 1,1702 1.1625 1.1481 1.1727
Mass
ments was thermally equivalent to the final state in the C2F6 experiments. The calorimeter starting temperature was selected so that the final temperature in each series was 25.00'. I n the C2Fe series, however, CF4 and additional N2 were present as well as H F vapor. The comparison experiments therefore did not exactly duplicate the final state in the CzFe experiments. Further work on this aspect of the method is planned. The effect of the additional gases on the thermal state of the H F vapor is probably small. Employing atomic weights of 12.0111 and 18.9984 for carbon and fluorine, respectively, there is derived for the reaction CZF6(g)
+ 2/3NF3(g)
2CF4(g)
+
+ '/aNz(g)
AEr2ss = -104.3 kcal/mole Calculating to constant pressure conditions
756.0 758.9 761.5 752.4 749.6 Av 755.7
*
102 2 kcal as the most reliable value for the CFS-H bond dissociation energy, which gives for the enthalpy of formation of CF3 radical -114.6 f 2.5 kcal/ mole. The present work yields an enthalpy of formation of CzF6 of -318.2 i 2 kcal/mole. From these data is calculated a CF3-CF3 bond dissociation energy of 89 =k 4.5 kcal. Tschuikow-Roux6 measured 93 4 kcal by direct observation of the dissociation of C2F6 in a shock tube, in agreement within experimental error. Other work listed by Tschuikow-Roux2 leading to much higher or lower values now appears to be in error.
*
Acknowledgment. This work was supported by the United States Air Force under Contract No. AF04(611)-7554(4). ( 5 ) E. Tschuikow-Roux, J. Chem. Phys., 43, 2251 (1965).
AHrzos = -103.9 kcal/mole
The over-all uncertainty is estimated as i1kcal/mole.
Conclusions
Schmidt Number Correction for
Although accurate heats of formation for fluorocarbons cannot be computed because of the uncertainty in the true value for aqueous HF, a consistent set based on the most recent selections at the National Bureau of Standards4 allows some comparisons to be made. The selected enthalpies of formation (all in kcal/mole) are -29.8 for NF3(g), -221 for CF*(g), and - 164.5 for CHFa(g). Tschuikow-Row2 selected
the Rotating Disk by John Newman Department of Chemical Engineering, University of California, Berkeley, California (Received October 18, 1966)
According to Levich,1$2the rate of mass transfer to a rotating disk is given by Votume 70,Number 4 April 1966
NOTES
1328
Table I: Comparison of Values for i( 1 - t)/nF(c-
- c~)& Gregory and Riddiford
Eq 5 “Exact”’
SC
100 200 500 800 1000 1200 1400 a
eb
0.026874 0.017188 0.009471 0.006964 0.006016 0.005338 0.004824
0.026892 0.017194 0.009472 0.006965 0.006017 0,005338 0.004824
Levich
€b
0.069 0,038 0.015 0.010 0.009 0.007 0,005
0.026970 0.017226 0.009488 0.006975 0.006024 0.005346 0.004830
“Exact” refers to a numerical evaluation of eq 1, and thus is still subject to error.
€b
0.36 0.22 0.18 0.16 0.14 0.15 0.14
0.028799 0.018137 0.009850 0.007200 0.006205 0.005495 0.004988
7.16 5.52 4.00 3.39 3.13 2.94 2.79
* E is per cent deviation.
in eq 1 for large Schmidt numbers and integrates analytically, then one obtains i(1 - t) nF(c, co)d% -
-
where
0.10265(D)ly4 V
+.
,
.]
1 (2)
i is the current density, t is the transference number, c is the concentration of the reactant, y is the distance from the disk, Q is the rotation speed, v is the kinematic viscosity of the fluid, F is Faraday’s constant, and n is the number of electrons produced when one reactant ion or molecule reacts. Equation 1 applies to two cases: (a) when the reactant is an ion in a solution with excess indifferent electrolyte or the reactant is a neutral molecule; then t = 0, and D is the diffusion coefficient of the reactant ion or molecule; (b) when the reactant is one of two ionic species in the solution; then D is the diffusion coefficient of the salt. For large Schmidt numbers, Levich1g2 neglected all but the first term in eq 2, so that with this approximation eq 1yields i(1 - t ) nP(c, - c d -
6
= 0.6205S~-’/~
(3)
where Sc = v/D. For a Schmidt number of 1000, accurate evaluation of eq 1 gives a value about 3% lower than eq 3. Gregory arid Riddiford3 evaluated eq 1 numerically and fitted the results empirically with the equation i(1 - t ) o.554Sc-2/a (4) nF(c, - c ~ ) l / s z ; = 0.8934 0 . 3 1 6 X ~ - ~ . ~ ~
+
This representation agrees with eq 1 within 1% for S c > 250 according to Gregory and Riddiford, although Table I shows that the agreement actually is better. It should be noted that if one expands the exponential The J O U Tof~Physical ~ Chemistry
+
0.62048Sc-”/” 0.2980S~-’/~ 0.14514S~-*’~ (5)
+
where terms of order Sc-’ have been neglected in the denominator. This expression adequately approximates eq 1 for Sc > 100, in which region the maximum deviation is about 0.1%. Thus an analytic approach yields a result essentially no more complicated than that of Gregory and Riddiford and a t the same time does not sacrifice accuracy. The results of these several formulas are compared in Table I. (1) V. Levich, Acta Physicochim. U R S S , 17, 257 (1942). (2) V. G. Levich, “Physicochemical Hydrodynamics,” PrenticeHall, Inc., Englewood Cliffs, N. J., 1962. (3) D.P. Gregory and A. C. Riddiford, J . Chem. SOC., 3756 (1956).
The Acid-Catalyzed Oxygen Exchange of Acetylacetone in Dioxane-Water Solutions Measured by Oxygen-17 Nuclear Magnetic Resonance by Z. Luz and Brian L. Silver The Weirmann Institute of Science, Rehovoth, Israel (Received November 16, 1966)
Rates of oxygen isotope exchange are usually st,udied using l80as tracer.’ This almost always requires sepa~
~
~~
(1) D. Samuel and B. L. Silver, Adoan. Phys. Org. Chem., 3, 123 (1965).
