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A proposal for a normalized stoichiometry
Chemical Engineering Science, 1962, Vol. 17, pp. 573-577.
Pergamon Press Ltd., London.
Printed in Great Britain.
The use of the “ time reaction ” in residence time studies . (Received 30 November 1961) BETWEENan acidified solution of potassium iodate and a solution of sodium sulphite containing a little starch paste there occurs the remarkable chemical process known as the “time reaction”. On mixing the solutions there is no visible change during an induction period but when this is complete there is a very sudden liberation of iodine and this leads to an almost instantaneous colouration of the starch. The moment at which the colouration occurs can be adjusted over a range from a few seconds to upwards of a minute by suitable choice of the concentrations [l]. It seems that this reaction might be useful in certain kinds of residence time study. Thus if the concentrations of the solutions were adjusted to give the blue colour, say, 20 sec. after mixing, then anywhere in a flow apparatus where the blue colour was visible would be known to correspond to a time of passage from the point of mixing of 3 20 sec. Such a method would obviously be applied most simply to systems in which the reagents were initially perfectly mixed during a very short interval of time. However, it might be applicable also to a study of the process of mixing itself; but here its theory would be more complex since the time required for the blue colour to develop would be a function of the local concentrations and these would generally be. unknown. In order to try out the potentialities of the method we photographed the blue colour in the wake behind a sphere. The latter was of 1.6 cm diameter and was suspended in a 4 cm diameter glass tube mounted vertically. At the base of the tube there was a very small centrifugal mixing chamber having four small jets for the introduction of a concentrated iodate solution, and a further four small jets (alternately placed with the first four) for the introduction of the sulphite
solution, together with a larger jet for the [introduction of a diluting stream of water. The concentrations used were such that the blue colour developed in 12 sec. Immediately above the mixing chamber and at the entrance to the experimental tube were three layers of stainless steel gauze whose purpose was to eliminate the rotary motion created in the mixing chamber and also to assist in the setting up of a uniform velocity profile. The sphere was suspended at about 5 cm above the highest gauze. In order to obtain photographs free from the distortion arising from the lens effect of the glass tube a rectangular Perspex box was fitted round the tube and filled with water. Fig. 1 shows a typical photograph taken at an approach velocity of 4 cm/set. The wake was illuminated with rear diffuse tungsten lighting, and adequate contrast between the blue colouration and the white background was achieved by exposing a high contrast panchromatic emulsion through a red filter. The photograph demonstrates those regions in the wake of the sphere where the residence time was 312 sec. We shall not offer any interpretation-and especially as the hydrodynamic conditions were very far from being those of a sphere in an infinite fluid stream-and we present this note only in order to put forward the method to any who may wish to take it up. K. G. DENBIGH, N. DOMBROWSKI A. J. KISIEL, E. R. PLACE The Department of Chemical Engineering and Chemical Technology Imperial College, London. S. W.7.
REFERENCE
[l]
PONOMAREVA E. N. Zh. Anal. Khim. 1952 7 163.
A proposal for a normalized stoichiometry (Received 6 January 1962) THERE exists a sometimes bothersome ambiguity in the writing of chemical equations. In the generalized expression
111
4W2
” (1)
the set of V~‘S is arbitrary within Hence, for example, we might write
a multiplying
factor.
Ns + 3Hz + 2NHs
(2)
fNe + Hz -+ 5NHs
(3)
+
fHz + NH3
(4)
etc. Of course, this arbitrariness poses no particular problem if one only wishes to contemplate the qualitative chemistry of the reaction or is concerned only with the ratios of changes in moles. However, there are at least two classes of commonly encountered applications requiring more explicit stipulation of the set of YK’S. Firstly, the value for the change in the De Donder extent of reaction depends on the vk’s
or dt = $,
or
573
all k
Shorter Communications Secondly, conventional the Vk’s
e.quilibrium expressions K = fj
depend on
arbitrary starting set of
Vk’s,
denoted by
Vk', form
[u&‘k
k=l
For a process involving a particular reaction, a value for extent of reaction (or for reaction rate v = d[/dB) is meaningless without concurrent stipulation of the Yk’s. Similarly, in an equilibrium computation, it is mandatory that the equilibrium constant, K (or, equivalently, the standard free energy change) be based on the same set of Yk’S as used in the right-band side of equation (6). In these two examples the multiplicative arbitrariness of the V~‘Scannot be ignored. There perhaps would be merit to an absolute stoichiometry, which, if universally used, would eliminate this ambiguity. We propose a system of writing chemical equations based on the normalization to unity of the sum of the absolute values of the vk’s.
Then compute_the set of
Vk’s
satisfying equation (7) by.
“k = &“;;“k,,9
(8)
a11k
As an example, if this operation is performed with any .of the three sets of Yk's implied by equations (2) to (4) one obtains the following normalized equation: #Ne + tHa = 3NH3
(9)
Such a scheme as proposed here lacks the apparent simplicity of assigning a value of unity to some one of the Yk'S.tinversely, it removes the arbitrariness of selection of the species which is to have unit value of Vk.
k&-i =1 h any
c.
case it iSan easy matter t0 select the SetOf Vk's satisfying equation (7). For a particular reaction, with any actual
J.
PINGS
Chemical Engineering Laboratory California Institute qf Technology Pasadena.
REFERENCE [l]
PRKJOGINE I. and DEFAY R. Chemical Thermodynamics, 10. Longmans
Green, New York, 1954.
Isopiestic binary vapour liquid equilibria system chloroform (l)-wbutanol(2) (Received 8 January 1962) THX vapour liquid equilibrium data of the system, chloroform (l)-n-butanol(2) have been determined at 760 mm Hg total pressure using a modified Colburn equilibrium still [6, 91. The chemicals used in the present investigation are of E. MERCK grade and they have been further purified by distilling in a laboratory fractionating column and collectlng the fractions at their respective boiling points. Specific gravity has been used for analysing the liquid and vapour samples. Calculations The activity coefficients are calculated for all the runs from experimental vapour liquid equilibrium data using the equation: ZrPyr Yr = 0 Pl x1 where yr P &” xi, yr
= = = =
Activity coefficient of component “i” Total pressure. Vapour pressure of component “i” Mole fractions of the it” component in liquid and vapour respectively. Zt = Vapour phase non-ideality correction factor given by Zt = explo
(Pi” - P)(YI - 134 2.303RT
where UC= fig = R = T=
Liquid molal volume. Second virial coefficient. Gas constant. Absolute boiling temperature.
ANTOINE type of vapour pressure equations [l, 41 and the critical constants of the components [3,5] have been taken from literature. Liquid molal volumes have been calculated at the desired temperatures by the method of LYDERSEN, GREENKORN and HOUGEN [7] using the values of pure liquid density at 30°C. The second virial coefficients, ,9, have been calculated at the desired temperatures using the relation given by WOHL
DOI i.e.
,8 = g
(0197 - O.O12T, - TF
- gj
where T = Reduced temperature. T,, P, = Critical temperature and pressure respectively. Discussion and Correlation of Results This system shows positive deviations from Raoult’s law. Thermodynamic consistency of the experimental data has been tested by means of REDLICH and Usran area plot applying Herington Criteria [2]. Neither an axeotrope nor a tendency for its formation is observed for this system.
Pergamon Press Ltd., London.
Printed in Great Britain.
The use of the “ time reaction ” in residence time studies . (Received 30 November 1961) BETWEENan acidified solution of potassium iodate and a solution of sodium sulphite containing a little starch paste there occurs the remarkable chemical process known as the “time reaction”. On mixing the solutions there is no visible change during an induction period but when this is complete there is a very sudden liberation of iodine and this leads to an almost instantaneous colouration of the starch. The moment at which the colouration occurs can be adjusted over a range from a few seconds to upwards of a minute by suitable choice of the concentrations [l]. It seems that this reaction might be useful in certain kinds of residence time study. Thus if the concentrations of the solutions were adjusted to give the blue colour, say, 20 sec. after mixing, then anywhere in a flow apparatus where the blue colour was visible would be known to correspond to a time of passage from the point of mixing of 3 20 sec. Such a method would obviously be applied most simply to systems in which the reagents were initially perfectly mixed during a very short interval of time. However, it might be applicable also to a study of the process of mixing itself; but here its theory would be more complex since the time required for the blue colour to develop would be a function of the local concentrations and these would generally be. unknown. In order to try out the potentialities of the method we photographed the blue colour in the wake behind a sphere. The latter was of 1.6 cm diameter and was suspended in a 4 cm diameter glass tube mounted vertically. At the base of the tube there was a very small centrifugal mixing chamber having four small jets for the introduction of a concentrated iodate solution, and a further four small jets (alternately placed with the first four) for the introduction of the sulphite
solution, together with a larger jet for the [introduction of a diluting stream of water. The concentrations used were such that the blue colour developed in 12 sec. Immediately above the mixing chamber and at the entrance to the experimental tube were three layers of stainless steel gauze whose purpose was to eliminate the rotary motion created in the mixing chamber and also to assist in the setting up of a uniform velocity profile. The sphere was suspended at about 5 cm above the highest gauze. In order to obtain photographs free from the distortion arising from the lens effect of the glass tube a rectangular Perspex box was fitted round the tube and filled with water. Fig. 1 shows a typical photograph taken at an approach velocity of 4 cm/set. The wake was illuminated with rear diffuse tungsten lighting, and adequate contrast between the blue colouration and the white background was achieved by exposing a high contrast panchromatic emulsion through a red filter. The photograph demonstrates those regions in the wake of the sphere where the residence time was 312 sec. We shall not offer any interpretation-and especially as the hydrodynamic conditions were very far from being those of a sphere in an infinite fluid stream-and we present this note only in order to put forward the method to any who may wish to take it up. K. G. DENBIGH, N. DOMBROWSKI A. J. KISIEL, E. R. PLACE The Department of Chemical Engineering and Chemical Technology Imperial College, London. S. W.7.
REFERENCE
[l]
PONOMAREVA E. N. Zh. Anal. Khim. 1952 7 163.
A proposal for a normalized stoichiometry (Received 6 January 1962) THERE exists a sometimes bothersome ambiguity in the writing of chemical equations. In the generalized expression
111
4W2
” (1)
the set of V~‘S is arbitrary within Hence, for example, we might write
a multiplying
factor.
Ns + 3Hz + 2NHs
(2)
fNe + Hz -+ 5NHs
(3)
+
fHz + NH3
(4)
etc. Of course, this arbitrariness poses no particular problem if one only wishes to contemplate the qualitative chemistry of the reaction or is concerned only with the ratios of changes in moles. However, there are at least two classes of commonly encountered applications requiring more explicit stipulation of the set of YK’S. Firstly, the value for the change in the De Donder extent of reaction depends on the vk’s
or dt = $,
or
573
all k
Shorter Communications Secondly, conventional the Vk’s
e.quilibrium expressions K = fj
depend on
arbitrary starting set of
Vk’s,
denoted by
Vk', form
[u&‘k
k=l
For a process involving a particular reaction, a value for extent of reaction (or for reaction rate v = d[/dB) is meaningless without concurrent stipulation of the Yk’s. Similarly, in an equilibrium computation, it is mandatory that the equilibrium constant, K (or, equivalently, the standard free energy change) be based on the same set of Yk’S as used in the right-band side of equation (6). In these two examples the multiplicative arbitrariness of the V~‘Scannot be ignored. There perhaps would be merit to an absolute stoichiometry, which, if universally used, would eliminate this ambiguity. We propose a system of writing chemical equations based on the normalization to unity of the sum of the absolute values of the vk’s.
Then compute_the set of
Vk’s
satisfying equation (7) by.
“k = &“;;“k,,9
(8)
a11k
As an example, if this operation is performed with any .of the three sets of Yk's implied by equations (2) to (4) one obtains the following normalized equation: #Ne + tHa = 3NH3
(9)
Such a scheme as proposed here lacks the apparent simplicity of assigning a value of unity to some one of the Yk'S.tinversely, it removes the arbitrariness of selection of the species which is to have unit value of Vk.
k&-i =1 h any
c.
case it iSan easy matter t0 select the SetOf Vk's satisfying equation (7). For a particular reaction, with any actual
J.
PINGS
Chemical Engineering Laboratory California Institute qf Technology Pasadena.
REFERENCE [l]
PRKJOGINE I. and DEFAY R. Chemical Thermodynamics, 10. Longmans
Green, New York, 1954.
Isopiestic binary vapour liquid equilibria system chloroform (l)-wbutanol(2) (Received 8 January 1962) THX vapour liquid equilibrium data of the system, chloroform (l)-n-butanol(2) have been determined at 760 mm Hg total pressure using a modified Colburn equilibrium still [6, 91. The chemicals used in the present investigation are of E. MERCK grade and they have been further purified by distilling in a laboratory fractionating column and collectlng the fractions at their respective boiling points. Specific gravity has been used for analysing the liquid and vapour samples. Calculations The activity coefficients are calculated for all the runs from experimental vapour liquid equilibrium data using the equation: ZrPyr Yr = 0 Pl x1 where yr P &” xi, yr
= = = =
Activity coefficient of component “i” Total pressure. Vapour pressure of component “i” Mole fractions of the it” component in liquid and vapour respectively. Zt = Vapour phase non-ideality correction factor given by Zt = explo
(Pi” - P)(YI - 134 2.303RT
where UC= fig = R = T=
Liquid molal volume. Second virial coefficient. Gas constant. Absolute boiling temperature.
ANTOINE type of vapour pressure equations [l, 41 and the critical constants of the components [3,5] have been taken from literature. Liquid molal volumes have been calculated at the desired temperatures by the method of LYDERSEN, GREENKORN and HOUGEN [7] using the values of pure liquid density at 30°C. The second virial coefficients, ,9, have been calculated at the desired temperatures using the relation given by WOHL
DOI i.e.
,8 = g
(0197 - O.O12T, - TF
- gj
where T = Reduced temperature. T,, P, = Critical temperature and pressure respectively. Discussion and Correlation of Results This system shows positive deviations from Raoult’s law. Thermodynamic consistency of the experimental data has been tested by means of REDLICH and Usran area plot applying Herington Criteria [2]. Neither an axeotrope nor a tendency for its formation is observed for this system.