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# Thermodynamics of gallium arsenide formation

## Problem

Element 31, gallium, a silvery-white metal at room temperature, has numerous applications to science. In medicine, it is best known for the gallium scan, which uses a radioactive isotope of gallium injected into blood vessels that localize to sites of inflammation and infection. However, the most common application of gallium is in the electronics industry. Gallium arsenide, the gallium compound most frequently used in electronics manufacturing, is found in microwave circuits, LEDs, and solar cells, just to name a few applications.
An important complicating factor in the manufacture of gallium arsenide is contamination of the final product with silicon, formed from the quartz (silicon dioxide) reaction vessel used in the oxidation of gallium. The reaction processes are given below:
Reaction 1: Elemental gallium reacts with silicon dioxide to form gallium (I) oxide and silicon monoxide in a reversible reaction.
Reaction 2: Gallium (I) oxide reacts with elemental arsenic to form gallium oxide and gallium arsenide in a reversible reaction.
For Reaction 1, the following thermodynamic data are obtained from the experiment.
ln K at 298 K = -72
K at 298 K = 5.38*10${}^{-32}$
ΔH${}^{o}$ reaction at 298 K = 171,070 cal/mole
ΔH${}_{fgallium\left(I\right)oxideat298K}^{o}$ = -17,420 cal/mole
Figure 1: ln K vs. temperature (in oC) for Reaction 1 (curve 1). Curve 2 and Curve 3 are irrelevant to this passage.
What is the electron configuration of elemental gallium?