June 5, 1950

Dr. G. E. Burch

School of Medicine

Tulane University

1430 Tulane Avenue

New Orleans 12, La.

Dear George:

My wife and I had a pleasant trip home. We spent a day at the Petrified Forest National Monument in Arizona. We remember with much pleasure our visit with you in New Orleans.

Since getting home I have worked out a staple theory of the interaction of sodium and potassium in the flame photometer. First, I have checked some old experimental work by H. A. Wilson, described in a paper in 1922 in the Journal of the American Chemical Society by H. A. Wilson and A. A. Noyes, from which it is evident that the electrons in the flame are due almost entirely to the ionization of the sodium and potassium atoms.

We may assume that in a flame containing both sodium and potassium there are present sodium atoms in various states (the normal state and various excited states), potassium atoms in various states, sodium ions, potassium ions, and electrons. The distribution of the unionized sodium atoms among the various states is a function of the temperature, but not of the amount of sodium or potassium present. This means that the intensity of the sodium radiation can be taken as proportional to the number of sodium atoms in the normal state and all the various excited states, provided that the temperature remains constant. The same thing is true for potassium. However, there is an equilibrium between the unionized sodium and sodium ions and electrons. This can be expressed by the equation

Na [in equilibrium with] Na^{+}+e^{-}

The equilibrium constant for this equation can be taken as K1, which is given by the equation

[Na^{+}][e^{-}]
_________=K_{1}
[Na]

Similarly the equilibrium constant for the ionization of potassium can

Dr. Burch

be expressed by the equation

[K^{+}][e^{-}]
_________=K_{1}
[K]

The total amount of sodium, [Na_{t}], is equal to the unionized sodium plus the sodium Ions, [Na] + [Na^{+}]. Similarly the total amount of potassium, [Kt ] is equal to [K] + [K^{+}]

Electrical neutrality requires that the concentration of electrons be equal to the sum of the concentrations of sodium ion and potassium ion:

[Na^{+}] + [K^{+}] = [e^{-}]

Now let us introduce I_{1}, the intensity of the sodium lines, as proportional to the number of unionized sodium atoms, that is,

I_{1} = k_{1} [Na]

We also introduce a similar expression for I_{2}, the intensity of the potassium line.

Now by manipulating the quantities, we can derive an equation for the total amount of sodium and for the total amount of potassium in terms of the intensities of the sodium line and the potassium line. This equation is the following:

[Na_{t}] = _I_{1}
_ {1 +_____K_{1}
_____}

We can derive a similar expression for the total amount of potassium.

Not having the observed intensities at hand for your experiments, but instead the apparent amounts of sodium and potassium given by mixtures of the two, making use of the calibrations with sodium alone or potassium alone, I have changed this equation somewhat, for comparison with experiments. Namely, I have replaced I_{1} in the equation by the apparent concentration of sodium, and I_{2} by the actual concentration of potassium which was added. Similarly in the equation for the total amount of potassium I replaced I_{1} in the correction term by the actual amount of sodium that was added.

Dr. Burch

It turns out that one can in this way develop an equation that agrees moderately well with your experimental data - better than agreement between the experiments reported in columns 3 and 4. I have not spent much time in an effort to get the best agreement, but I have found that for the experiments in which you had a large amount of added sodium with relatively small amounts of potassium the following equation works reasonably well:

For example, in the series in which the actual potassium, concentration was 0.200 milliequivalents per liter and the sodium concentration varied from 0 to 50 milliequivalents per liter, the values of K

app

were found to vary From 0.200 to 0.515. When corrected by this equation, the values all lie Between 0.19 and 0.22 milliequivalents per liter. With 1.2 milliequivalents per liter of potassium actually present, the sodium concentration varying between 0 and 50 milliequivalents per liter, the apparent values ranged from 1.21 to 1.65 milliequivalents per liter. When corrected by this same equation, the apparent values ranged from 1.19 and 1.23. I think that similar agreement would be obtained for the other values in your table. Also a similar equation can be used to correct the values from the sodium determination in the presence of added potassium.