Abstract
The kinetics for the hydrothermal decomposition of sodium amalgam was studied in the presence of water and caustic soda on graphite electrodes containing iron.
Regression analysis of over 1000 data points in a linear regression analysis yielded the following rate expression, explaining 89% of the variance in the data, leaving 11% of the variance unexplained: r=−d(Na)/dt=187.8 (T)^{−2/3} exp (− 196.9/RT) (Na)^{3/4} (NaOH)^{−1/5}.
The decomposition rate of sodium amalgam is strongly limited by the rate of diffusion of sodium metal atoms in the mercury, and also the activity of water at the active cathodic sites on the catalyst. The activation energy for charge transfer for this process is low at 196.9 cal mol^{−1} or 8.5 mV.
The range of variables studied was: temperature −25, 50 and 85° C; caustic concentration −10, 30 and 50 wt.%; amalgam concentration −0.1,0.2 and 0.3 mol.%, and finally with iron concentrations in the graphite matrix of − 215.9, 929.5 and 6180 ppm.
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Abbreviations
 R :

1.987 cal (K mol)^{−1} = ideal gas law constant
 ¯R :

MM distance between nearest neighbours in the crystal lattice of the electrode used to calculate the Madelung constant
 r :

i/nF = −d(Na)/dt = reaction rate giving loss of amalgam in mol min^{−1}
 T :

(273 + ° C) = absolute temperature (K)
 (Na):

C _{Na} = moll^{−1} = concentration of sodium in mercury
 (NaOH):

C _{NaOH} = moll^{−1} = concentration of sodium hydroxide in water solution
 Z^{+}, Z^{−} :

charges on cation and anion, respectively
 (M):

active centre on the iron promoter catalyst
 i :

total net current density
 i _{+} :

anode partial current density
 i _{−} :

cathode partial current density
 i _{0} :

exchange current density, ati _{+} =i _{−} =i _{0}, whereη → 0, and the mutually compensating anodic and cathodic current densities are present at the equilibrium potential
 η :

overpotential on the electrode,EE ^{0}
 A:

Arrhenius coefficient, constant
 \(D_{{\text{Na}}^ \circ } \) :

diffusion coefficient of sodium metal in mercury in cm^{2} min^{−1}
 ¯K :

rate constant, temperature and activation energy dependent
 k:

rate constant, independent of temperature and activation energy
 a _{Na} :

(Na) =C _{Na} = activity of sodium in mercury and to a good approximation equal to its concentration
 a _{w} :

activity of water in presence of caustic
 x :

distance normal to the catalyst surface (cm)
 dx :

change in distance normal to the catalyst surface
 t :

time at which sample is collected and reaction is quenched
 t_{0} :

initial time zero
 a, b :

the order of the reaction, or the exponential power to which the concentration is raised, as opposed to the molecularity of the reaction, or the molecules/collision. The order is empirical and the molecularity is theoretical
 Y :

ln( d [Na]/dt) = lnk +nlnTE _{a}/RT +aln(Na) +bln(NaOH), the linear least squares curve fitting program equation
 B _{0,1,2,3,4} :

coefficients for the linear least squares curve fitting program
 x _{i} :

sample measurementi
 d :

x _{i}¯X = deviation from the average
 σ :

standard deviation, √Σd^{2}/¯n
 σ ^{2} :

variance, or the mean squared deviation from the mean, Σd ^{2}/¯n
 ¯X :

arithmetic mean,x _{1} +x _{2} + ... x_{n}/¯n
 ¯n :

total number of measurements.
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Dotson, R.L., Jenkins, A. Kinetics and mechanism for the hydrothermal decomposition of sodium amalgam promoted on graphite electrodes containing iron. J Appl Electrochem 7, 517–530 (1977). https://doi.org/10.1007/BF00616764
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Keywords
 Iron
 Graphite
 Mercury
 Activation Energy
 Regression Analysis