April, 1953
VELOCITY OF SOUND IN LIQUIDSAND MOLECULAR WEIGHT
453
VELOCITY OF SOUND I N LIQUIDS AND MOLECULAR WEIGHT BY S. PARTHASARATHY AND N. N. BAKHSHI National Physical Laboratory of India, New Delhi, India Received October 6, 1066
A close examination of Rao’s2 formula v’ls(M/p) = R reveals that in a modified form, it could be made use of in the determination of sound velocities in organic liquids. I n the present work, it has been shown that if, instead of u ’ / ~ ( M / p = ).R against M , only v l / s / p is plotted against M , a family of curves is obtained for the homologous series. The general equation for the family of curves is of the type v ’ l a / p = A -P B / M where A = 13.56 is constant for all the series and B varies from series to series, while a plot of u V r / p against 1 / M shows that curves are transformed to straight lines, which diverge from the same point (0,13.56). It has been tested for some homologous series. The calculated values of sound velocity from the new formulas have been compared with the observed values. The modified form suggests some remarkable regularities in the curves of different homologous series.
Introduction I n 1938, as a result of extensive work on sound velocity, Parthasarathy derived a few empirical rules relating to sound velocity and chemical constitution. Later, Rao2 in 1940 on the basis of Parthasarathy’s work in organic liquids, put forward an empirical formula v’/l(M/p) = R between sound velocity v, molecular weight M and the density p. R, termed the molecular sound velocity by Lagemann,a when plotted against M , gave a parallel set of straight lines. As R is a function of the molecular volume and cube root of sound velocity and as v’18 also does not vary much from member to member in every series, it was thought desirable to examine the relationship eliminating M from both sides of the above equation. Results and Discussion Rao,2 from his formula, viz., v’/a(M/p) = R found that R was a constant, independent of temperature for the same compound. He deduced values for different elements and bonds on an analogy of parachor and showed that R is an additive function. This is evident from the formula itself since molecular volume V is involved in the formula. It was of interest to examine the behavior of the formula if the factor M is removed from the left hand side, i.e., the modified form of the formula becomes (v‘’z/p) = K,a temperature independent constant different from Rao’s R. This could well be derived from the ratio of the temperature coefficient of sound velocity and temperature coefficient of volume expansion. According to Ra0,4 this ratio, i.e. (l/v)(dv/dt)/(l/v)(dv/dl)
=
increase in the length of the chain and in some cases it decreases with the increase in the length of the chain. When v‘/~/lpis plotted against 1 X 10a/M a set of straight lines diverging from a point (0, 13.56) is obtained (see Fig. 1). Their slopes are in the order aliphatic hydrocarbons > 1-olefins, where the series indicates the magnitude of the slope till it comes to aliphatic alcohols for which the line runs approximately parallel to the x-axis. For the other series the gradient changes its sign and follows the order aromatic hydrocarbons > alkyl chlorides > fatty acids. This indicates that the intercept for all the curves is the same whereas the slope varies for each curve.
16
-
15
-
14
-
11
c
hydfocof bono
-3
or (l/v)(dv/dt)/(l/e)(de/dt) = $3 (as V = M / p )
i.e., the ratio of the temperature coefficient of sound velocity to that of the temperature coefficient of density is a constant equal to +3. This constant ( K ) behaves in an entirely different manner. Whereas R increased in every series with an increase in the molecular chain, K does not necessarily behave so. In some series, it increases with the
0
\
5 (1
(1) S. Parthasarathy. several papers in the Proc. Ind. Acad. S c i .
and Cum. Sei.; Bergrnann’s “Der Ultrrtschall,” 1949. (2) M.R. Rao, Ind. J . Phus., 14, 109 (1940). (3) R. T. Lagemann and W. S. Dunbar, THISJOURNAL,49, 428 (1945). (4) M. R. Rao, J . Chem. Phua., fi, 682 (1941).
10 10*/M) Fig. 1.
x
A general equation of the type v‘/a/p
=A
+(B/M)
15
20
S. PARTHASARATHY AND N. N. BAKHSHI
(iii) Aliphatic alcohols: v = 13.56 - (15.O/M)
can be ascribed to these lines where = velocity of sound at temperature t o = density of the liquid at temperature t o p M = molecular weight of the liquid A = a constant which is the same for all the series studied and B = constant for the same homologous series but is different for different series. u
From the above formula, we have calculated B the characteristic constant for each of the homologous series. They are given below TABLEI Series
A
Aliphatic hydrocarbons 1-Olefins Aliphatic alcohols Aromatic hydrocarbons 6 Alkyl chlorides 6 Fatty acids
13.66 13.56 13.56 13.56 13.56 13.56
1 2 3 4
x
B
10-
176 135 15.0 - 79.56 157 -215.2
-
The above formula has been used in predicting the values of velocities of sound for different liquids of the homologous series given in Table 11. Knowing the values of p, M and B for a homologous series as shown in Table I the values of v are calculated. In Table I1 (i to vi) are tabulated the observed and the calculated values of sound velocity obtained in this manner. How well they agree can be seen from the tables. Hence knowing the values of p, M and B for a series, the sound velocity could be predicted with sufficient accuracy by the above formula. TABLE I1 Liquid
Obsd. values u in m / s from Bergmann
(i) Aliphatic hydrocarbons: v = 13.56 Pentane 1008 n-Hexane 1083 n-Heptane 1162 n-Octane 1197 n-Nonane 1248
+
Vol. 57
Calod. values
v in m / r
+ (176/M) 1007 1088 1150 1194 1233
(ii) 1-Olefins: v = 13.56 (135/M) 1-Heptene 1128 1129 1-Octene 1184 1189 1-Nonene 1218 1231 1-Decene 1250 1256 1-Undecene 1275 1279 1-Tridecene 1313 1319 1-Pentadecene 1351 1359
Methyl Ethyl n-Propyl n-Bul,yl n-Amyl n-Hexyl n-Heptyl n-Dctyl n-Nonyl n-Decyl
1123 1180 1223 1268 1294 1322 1341 1358 1391 1402
1112 1140 1224 1255 1305 1324 1351 1373 1384 1395
(iv) Aromatic hydrocarbons: v = 13.56 Benzene Toluene Xylene
1310 1320 1330
( v ) Alkyl chlorides: v = 13.56 n-Propyl n-Butyl n-Hexyl n-0ctyI n-Decyl
1091 1133 1221 1280 1318
- (79.56/M) 1309 1317 1328
- (157/M) 1088 1153 1222 1297 1321
(vi) Fatty acids: w = 13.56 - (215.2/M) Acetic Propionic Butyric Valeric Caproic Oenanthic Caprylic
1150 1176 1203 1244 1280 1312 1331
1146 1179 1209 1256 1286 1320 1323
As regards the constant “A,” it is remarkable to observe that it has the same value in all the series studied. The significance of this constant is still not clear. As an example illustrating further the importance of “A,” it can be mentioned that in another paper6 (under publication) on viscosity and sound velocity, the same constant has appeared in their relationship. Further exploratory work is needed before one can give any meaning to “A.” Work along these lines is being continued in other directions and it is hoped that an insight into intermolecular forces may be obtained through “A*” (5) Relation between velocity of sound and viscosity in liquids, 8. Parthasarathy and N. N. Bakhshi. (Under publication in the Proceedings of the Physical Society of London).
