THE RATE OF SOLUTION OF MAGNESIUM I N ACIDS' MARTIN KILPATRICK LabOTatOTU
AND
J. HENRY RUSHTON
of Physical Chemistry, University of Pennsylvania, Philadelphia, P a . Received J u n e 2.4, 1988
In a preliminary paper (16) the authors have treated the problem of the rate of solution of magnesium in acids from the point of view of the extended theory of acids and bases ( 5 , 18). The present paper is a continuation of that study with an attempt to consider the problem from the point of view of the diffusion rate theory as well as from that of the Bronsted-Kilpatrick theory. It will be demonstrated that in either case it is necessary to consider the extended theory of acids as an important factor. Consider first the reactions which take place when magnesium reacts with a strong acid such as hydrogen chloride. When hydrogen chloride dissolves in water, we have HC1
+ HzO
+ C1-
and the reaction goes practically to completion to the right. The reaction can, therefore, involve the water, the hydrogen ion (H80+),or the chloride ion. The metal itself is composed of magnesium ions (Mg++) and free electrons (10). Equation 1 gives one possible primary reaction. HaO+
+e
+ HzO
+H
(1)
This might be followed by the reactions Mg++ (solid) 2H
Mg++ (dissolved) -+
Hz
the hydrogen escaping in the gaseous state. It is also possible for the primary reaction (3) to be Mg* -I- C1- -+ MgC1+ or MgC& (solid)
which would be followed by reactions 1 and lb. 1 Abstracted from the thesis of John Henry Rushton presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy, April, 1933. 269
270
MARTIN KILPATRICK AND J. HENRY RUSHTON
Centnerszwer (8) considers the reaction to be between the metal and the molecular acid, but his computations are based upon the application of the classical law of mass action to solutions of strong electrolytes and cannot be accepted (14). If equation 1 is accepted as more probable, then in accordance with the extended theory of acids, any proton carrier should react with the metal, and for weak acids there should be a reaction with the molecules, as well as with the hydrogen ions. For example, in the case of acetic acid, CHaCOOH
+ HzO + HaO’ + CHICOO-
and since this reaction does not go to completion to the right, in addition to the water reaction, two reactions are possible HaO+ CHaCOOH
+ e -+ HzO + H + e + CHaCOO- + H
In fact, in accordance with the forkal definition of an acid,
+
Acid % Base Proton A + B + H +
(4)
Where A represents an acid and B its conjugate base, we have the general double acid-base reaction (6), A + e - + B + Acid 1 Base 2 Base 1
A Acid 2
where A can be H30+, CH3COOH, CHzCICOOH, C5HsNH+, €LO, etc. The water reaction is readily detectable at higher temperature as will be shown later. The question of which is the rate-controlling process has been discussed recently by Hammett (11) in connection with the work of Bronsted and Kane on sodium amalgams. Hammett concludes that if it could be proved that diffusion was not a factor in the determination of the reaction velocity in the experiments of Bronsted and Kane and of Kilpatrick and Rushton, these experiments would be strong evidence for reaction 1 as the ratedetermining step. King and Braverman (17) conclude that while the “old diffusion theory’’ is not satisfactory without modification, certain results are definitely contradictory to the Bronsted-Kilpatrick theory. King and Braverman are vague as to the modification. In explanation of the dissolution of metals, Palmaer (20) accepts the theory of local elements of de la Rive (9), and definitely rejects the diffusion theory. The theory of local elements seems to be well founded for impure metals, but does not apply to pure magnesium. In the first experimental section the dissolving of magnesium in strong acids will be described. The temperature coefficient of the reaction, the
c
RATE O F SOLUTION O F MAGNESIUM IN ACIDS
271
relation of the rate to the concentration and volume of the solution and to the surface of the metal, the effect of stirring, and the effect of viscosity will be discussed. EXPERIMENTAL PART
Four separate methods were used to follow the reaction. The amount reacted was determined at definite intervals of time by first, weighing the metal, second, measuring the volume of hydrogen evolved, third, titrating the solution, or fourth, measuring the amount of acid required to maintain a definite hydrogen-ion concentration as shown by an indicator. The last method was used in the study of the water reaction. The apparatus used differed for the several methods mentioned above for following the reaction. The majority of the experiments were followed by measurement of the volume of hydrogen evolved. Samples of gas given off in reactions with hydrochloric, acetic, chloroacetic, and formic acids were analyzed for gases other than hydrogen. Hydrogen was found to be the only gas evolved. Two types of apparatus were employed, one for experiments at 0" and 25"C., and another for experiments at higher temperatures. Figure 1illustrates the apparatus used in the 25°C. thermostat. Figure 2 shows the apparatus used for work at temperatures higher than 25°C. The reaction chamber of these two pieces of apparatus differed both in size and shape. The 25°C. reaction flask was either a 300-cc. Florence flask or a special cylindrical flask as shown in the diagram. This special flask was used so that the level of the solution could be adjusted to various sizes of metal bars. The reaction vessel in the vapor thermostat was cylindrical and of very much smaller capacity. Several runs were made in the vapor thermostat by passing water a t 25°C. through the vapor chamber of the thermostat. In this way parallel experiments were made in the two distinctly different reaction vessels and the results checked with each other. In each of the two pieces of apparatus the gas given off during the reaction was led to a water-jacketed gas buret, where the volume could be read at atmospheric pressure. In the vapor thermostat the metal bar was first placed in the reaction vessel and allowed to come to temperature while a solution mas placed in the delivery tube. Upon reaching thermal equilibrium, stopcock A was set so that when stopcocks B and C were opened the solution drained into the rpaction vessel and the total volume of the system remained unchanged. Stopcock A was then turned so that the gas was delivered to the buret. As soon as the pressure in the gas buret could be made equal to atmospheric pressure, stopcock C was closed. By this method no gas was lost at any part of the reaction. Various liquids were used for work a t the different temperatures.
272
MARTIN KILPATRICK AND J . HENRY RUSHTON
Any part of the cylindrical bar of magnesium above the solution, or where reaction was not desired, was covered with collodion. No special
FIG. 1. APPARATUSFOR EXPERIMENTS AT 25°C.
AND AT
0°C.
methods were used to make the metallic surface active. It was found unnecessary to do this in the case of magnesium. The surface of the metal exposed varied from 7 to 35 cm.2 The metal cylinder was held in
RATE OF SOLUTION OF MAGNESIUM IN ACIDS
273
solution by a small steel rod threaded into one end of the bar. The steel rod was passed through a steel cap containing mercury, forming a s e d (see detail in figure 1) (13). The end of the steel rod was attached directly to an electric motor whose speed could be controlled by a small resistance.
n
\
FIQ.2. APPARATUS FOR EXPERIMENTS AT ELEVATED TEMPERATURES The opposite end of the motor shaft was connected to an electric tachometer with a scale reading directly in revolutions per minute. To measure the rate of reaction by weight determinations, a set of stirrers was built. Six shafts were run simultaneously from a main shaft driven by an electric motor whose speed was controlled by a rheostat. Bars of
274
MARTIN KILPATRICK AND J. HENRY RUSHTON
metal were threaded onto the Bakelite shafts coupled to the main shaft. Six experiments were run simultaneously, the bars washed, dried, and weighed. Other weight determinations were made using the apparatus shown in figure 1. TABLE 1 Data for two hydrochloric acid experiments NUMBER TIUE
Hydrogen evolved Ht ce
1 2 3 4 5 6 7 8 9 10 11 12 13 14
6.0 11.4 16.8 22.0 26.6 31.5 36.0 40.3 44.4 48.4 52.2 55.8 59.2 62.6 65.7 68.8 71.7 74.5 77.2 79.8
15
NUMBER
- Ht
22t
H Q- Hi
.
minutes
16 17 18 19 20
Ho
li
5'
cc.
132.2 126.8 121.4 116.2 111.6 106.7 102.2 97.9 93.8 89.8 86.0 82.4 79.0 75.6 72.5 69.4 66.5 63.7 61.0 58.4
0.0200 0.0380 0.0565 0.0755 0.9038 0.1130 0.1313 0,1500 0.1532 0.1875 0,2062 0.2250 0.2435 0.2622 0.2808 0.2995 0.3180 0.3370 0.3558 0.3743
4.35 8.50 12.20 15.75 19.05 22.05 25.10 27.80 30.35 32.75 35.00 37.10 39.05 40.90 42.60 44.25 45.75 47.175 48.48 49.70
63.65 59.50 55.80 52.25 48.95 45.95 42.90 40.20 37.65 35.25 33.00 30 90 28.95 27.1 25.4 23.75 22.25 20.825 19.52 18.3
0.0285 0.0570 0.0855 0.1140 0.1425 0.1710 0.1995 0.2280 0.2565 0.2850 0.3135 0.3320 0.3705 0.3990 0.4275 0.4570 0.4850 0.5128 0.542 0.570
* Experiment No. 5. Temperature = 25'C.; initial concentration of acid = 0.050 M ; volume of acid = 225 cc.; H O = 138.2 cc.; surface speed = 2150 cm. per minute; metal area = 7.01 cm.2; 57.8 per cent of reaction followed; no sodium chloride present; kat 2000 cm. per minute = 1.36. t Experiment No. 22. Temperature = 25°C.; initial concentration of acid = 0.025 M ; volume of acid = 225 cc.; H o = 68.0 cc.; surface speed = 2670 cm. per minute; metal area = 10.39 cm.2; 65.3 per cent of reaction followed; 0.025 M sodium chloride present; k at 2000 cm. per minute = 1.34. Experiments in the various reaction vessels showed that the rate of reaction as measured by the volume of hydrogen evolved, by the weight of metal dissolved, and by the decrease in acid concentration were in agreement. The shape of the reaction vessel and the length and diameter of the metal cylinder had no effect. The magnesium* itself was for most experiments 2 For this magnesium, the authors wish to thank The Aluminum Company of America.
275
RATE O F SOLUTION O F MAGNESIUM I N ACIDS
of very high purity. The analysis showed no copper, zinc, lead, or free iron, 0.18 per cent of magnesium oxide, 0.02 per cent of silicon, and 0.02 per cent of iron and aluminum. A few experiments made with ordinary C.P. magnesium sticks gave no appreciable difference in rate. METHODS O F EXPRESSING RESULTS
The kinetic equation, based on the hypothesis that the rate depends on the collisions of the acid with the metal and is consequently proportional .40
.oo
I-
N
Ll 0
2
4
8
6
Time ra) ~ x p . ~ esiope* s
‘
1
‘
1
‘
1
10
I t
14
16
18
20
- Minutes
\ / . r z s c m ’ , s r ~ . o icm: ‘‘9 h f i = . o i m p1,1$3 a t 2150 ‘Xi. stlrrinq Spend or
(b) Exp No.22 $lope= ‘‘9&$=
,02850
K=I.3b a t EoooC”/,;,
V~225cm3,S=10.24cmf
K.1.440 atZLIO‘x;nStirrinq spced or K: 1 . 3 4 a t Z o 6 0 C ~ ; ,
FIG, 3. RELATION BETWEEN log
HO
AXD
Ho - HI ACID EXPERIMENTS Nos. 5 ~
TIME FOR HYDROCHLORIC AND
22
to the acid concentration and to the surface of the metal, yields for the velocity constant of the reaction 2.-v c, k = - log St ct
where V is the volume of the solution, S the surface, t the time, COthe initial acid concentration, and Ct the concentration at time t . The same expression can be derived by assuming that the rate is controlled by a process of diffusion, and employing Fick’s law. Consequently the fact that equation 6 fits the data does not distinguish between a chemical process and a process controlled by diffusion. Throughout the paper
276
MARTIN KILPATRICK AND J. HENRY RUSHTON
V is expressed in crnS8,S in ems2,and t in minutes, so that k has the dimension cm. X min.-l. Table 1gives the necessary data for two typical experiments with hydrochloric acid. Figure 3, in which log
HO Ho - Ht
is plotted as ordinate and
TABLE 2
Experiments at W C . Stirring speed = 2000 cm. per minute. Volume of solution = 225 cc. I
EXPERIMENT NO,
kl
AREA OF METAL SURFACE
S
5 4 23 22 3 18 17 13 14 20 19 59 25 26 24
7.01 7.38 10.38 10.39 7.71 13.64 13,65 13.81 13.78 10.42 10.43 25.38 32.42 32.35 32.40
0.04235 0.0403 0.0604 0.0618 0.0456 0.0807 0.0813 0.0786 0.0815 0.0635 0.0635 0,1530 0.1917 0.1925 0.193
TABLE 3
Experiments at R5'C. Stirring speed = 2000 cm. per minute. Unit surface area AVERAGE VALUE OF k2
DUPLICATE EXPERIMENTS
cc
5 3 5 5
.
I
DEVIATION OF
kz
per cent
37.5 180.0 215.0 225.0
0.02665 0.05550 0.00465 0.00445
0.03575 0.00745 0.00624 0.00595
4.2 1.9 0.5 2.1
time as abscissa, shows that the reaction follows the pseudo monomolecular kl
law, The slope of the line is - ,where 2.3 kl
=
2.3
Ha
log t Ho - Ht
(7)
277
RATE O F SOLUTION O F MAGNESIUM I N ACIDS
ICl may be calculated for a series of solutions, using different volumes of solution and different areas of surface. EFFECT O F SURFACE
Table 2 gives the kl values for a number of experiments in which the same volume of solution was used and the area of the surface of the metal was varied. The values of k l are shown in relation to the surface in figure 4. Over a wide range of surface kl is inversely proportional to the surface. A constant k2 may now be defined kz =
0
kl
or kz =
St
14
10
5
2.3 H@ log -
Surfaca
V O ~Constant Q
(8)
Ho - Ht
20
25
30
cmz
225 cm? i Temperature 25.C.
FIQ.4. RELATION BETWEENkl
AND
SURFACE
The values of ICz are given for varying volumes of solution in table 3 and show that k
=
k2V or k
=
2.3V Ho - log Xt No - Ht
These relations have been determined for solutions having the same constant stirring. Table 4 gives the data used to relate k to the stirring of the solution, It was found that different amounts of stirring resulted with cylinders of metal of different diameters, and in order to measure stirring
278
MARTIN KILPATRICK AND J . HENRY RUSHTON
TABLE 4 Hydrochloric acid experiments at 25°C. EXPIRIMEN'I NO.
33 34 35 36 37 7 6 8 5 4 9 23 22 21 3 1 2 18 17 10 13 14 38 59 53 51 52 50 49 48 47 46 45 11 16 20 25 19 26 24 15 12
SPEED OF JETAL BAR
SURFACE STIRRING SPEED
r.p.m.
sm. per min.
0 0 0 0 0 600 600 800 800 800 900 800 800 800 1000 1000 1000 800 800 850 1200 1200 2210 2250 2550 2550 2550 2550 2550 2550 2550 2550 2550 1850 1850 2800 2000 2800 2000 2000 3100 3100
0
0 0 0 0 1550 1590 2000 2150 2170 2200 2650 2670 2700 2730 2940 2940 3060 3080 3090 4700 4500 5570 5840 6240 6270 6240 6270 6300 6300 6300 6320 6320 7330 7350 9520 9550 9580 9670 9740 11800 12200
k AT EXPERIMENT SPEED
k AT 2000 CM. PER MINUTE STIRRING SPEED
PER CENT 01 REACTION FOLLOWED
INITIAL CONCENTRAPION OF ACID
noles per liter
0.235 0.232 0,231 0.225 0.229 1.418 1,504 1.46 1.38 1,245 1.495 1.403 1.442 1.31 1.44 0.932 0.932 1.485 1.502 1.268 1.695 1.690 1.30 1.68 1.87 1.87 1.70 1.78 1.78 1.94 1.99 1.78 2.00 1.99 1.98 2.15 2.080 2.162 2.125 2.100 2.472 2.460
1.51 1.61 1.46 1.36 1.23 1.46 1.31 1.34 1.20 1.33 0.83 0.83 1.33 1.34 1.08 1.28 1.33 0.97 1.22 1.34 1.35 1.22 1.28 1.34 1.38 1.42 1.28 1.41 1.37 1.37 1.37 1.33 1.37 1.34 1.34 1.47 1.46 iv. = 1.33
.
10.7 27.0 30.8 41.2 56.0 62.4 59.8 62.3 57.8 41.1 62.3 12.0 65.3 12.5 39.0 82.5 82.5 66.5 66.7 61.2 61.8 64.4 99.2 99.5 100 I
100.
99.3 98.0 98.0 98.5 98.7 100. 98.7 11.6 11.4 9.5 100. 1.0
100. 100. 1.5 1.5
0.050 0,050 0.050 0.050 0.050 0.050 0.025 0.051 0.050 0 075 0.050 0.1235 0.025 0.075 0,1235 0.012 0,012 0.050 0.050 0.050 0,050 0.050 0.010 0.050 0.050 0.050 0.025 0.025 0.025 0.050 0,050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 I
.
279
RATE OF SOLUTION OF MAGNESIUM IN ACIDS
the surface velocity R was employed by multiplying the circumference of the cylinder by the revolutions per minute. When the logarithm of the surface speed was plotted against the corresponding logarithm of k, it was found that the following relation held over a wide range of supface speeds, k = aR*
(9)
and a
.C .7 8
pi
1
2
IS
3
4
5
6
1 6 9 1 0
15
*.I
SURFnCESPfED
(a) HCI
R
cM/mi~ XIf'
K - aR" K - ,139 R'294
(b)
FIG. 5. LOGARITHMIC RELATIONBETWEENk
H(CtHa4) AND
K* 4 R" K: 0,7sR'~'~
STIRRINGSPEED
TABLE 5 Hydrochloric acid experiments at 25°C. NUMBER OF DUPLICATE EXPERIMENTS
METHOD
8 35 8
Weight Volume Titration
AVERAGE VALUES OF k AT 2000 CM. PER MINUTE BTIRRINQ
AVERAGE DEVIATION
per cent
1.309 1.335 1.312
8.5
6.0 7.2
the value of IC when R = 1. The values of a and n for magnesium and hydrochloric acid are 0.139 and 0.362, respectively. Acetic acid behaves in a similar way, the essential difference being the value of a in equation 9. Many experiments were performed at surface speeds in the neighborhood of 2000 em. per minute. To make all experiTHE JOCRNAL OF PHYSICAL CHEMISTRY, VOL. XXXVIII, NO.
3
280
MARTIN KILPATRICK AND J. HENRY RUSHTON
ments comparable, the values of k have been calculated to 2000 c’m. per minute by equation 9 and are given in table 5. The maximum deviation TABLE 6 V a l u e s for hydrochloric acid experiments at 25%’. All rate data a t stirring speed of 2000 cm. per minute NUMBER OP DUPLICATE EXPERIMENTS
CONCENTRATION OF ACID
AVERAGE MILLIEQUIVALENTS REACTED PER LITER PER CM.2 PER MINUTE OVER 1/10 REACTION
AVERAQE DEVIATION
M
4 2 10 25 6 4
per cent
0.010 0.012 0.025 0.050 0.075 0.1235
0.01062 0.00966 0.03246 0.06405 0.08605 0.15440
7.2 9.4 5.7 6.5 6.6
7.3
.I4
e ‘.E .E > E
ct \
