The predicted geometry of the inorganic molecule SO3 sulfur trioxide can be determined using the VSEPR Valence Shell Electron Pair Repulsion theory. First, let's determine the number of valence electrons for SO3. Sulfur has 6 valence electrons, and each oxygen atom has 6 valence electrons. Since there are three oxygen atoms, the total number of valence electrons is 6 Sulfur + 3 * 6 Oxygen = 24 valence electrons.Now, let's distribute the valence electrons in the Lewis structure. Sulfur is the central atom, and it forms double bonds with each of the three oxygen atoms. Each double bond consists of 4 electrons 2 pairs , so 3 double bonds will have 12 electrons 6 pairs . The remaining 12 electrons 6 pairs are placed as lone pairs on the oxygen atoms 2 lone pairs on each oxygen atom .In SO3, the central sulfur atom has 3 regions of electron density 3 double bonds with oxygen atoms and no lone pairs. According to the VSEPR theory, this arrangement corresponds to a trigonal planar molecular geometry with bond angles of approximately 120 degrees.As for the polarity of SO3, we need to consider the electronegativity difference between sulfur and oxygen atoms and the molecular geometry. Oxygen is more electronegative than sulfur, so there is a dipole moment charge separation in each S-O bond. However, due to the symmetrical trigonal planar geometry, these dipole moments cancel each other out, resulting in a nonpolar molecule.In conclusion, the predicted geometry of the SO3 molecule is trigonal planar, and its polarity is nonpolar.