Final answer:
The Lewis structure of BrCl₄⁻ includes a bromine atom surrounded by four chlorine atoms with two lone pairs on bromine, giving a total of six electron domains. This results in an octahedral electron domain geometry and a square planar molecular geometry according to VSEPR theory.
Step-by-step explanation:
To draw the Lewis structure of BrCl₄⁻, we must first determine the total number of valence electrons. Bromine (Br) has 7 valence electrons, each Chlorine (Cl) atom has 7, and the extra electron from the negative charge gives us a total of 36 valence electrons. Br is the central atom with four Cl atoms surrounding it. Each Br-Cl bond uses up 2 electrons, so we have 4 Br-Cl single bonds leaving us with 28 electrons. Those leftover valence electrons are placed as lone pairs around the Br atom (2 pairs) and the Cl atoms to satisfy the octet rule.
Using the VSEPR theory, we determine the electron domain geometry by counting bonding regions and lone pairs on the central atom. In BrCl₄⁻, bromine has six electron domains (four bonding domains from the Br-Cl bonds and two lone pairs), which corresponds to an octahedral electron domain geometry. However, the molecular geometry - the shape made by the actual placement of the atoms - is different. Since there are two lone pairs, these will repel each other and adopt positions that minimize repulsion, distorting the geometry into a square planar shape.
The molecular geometry, also known as the molecular shape, can be described by the AXmEn notation, where 'A' represents the central atom, 'X' the number of atoms bonded to 'A', 'm' the number of attached atoms, and 'En' the number of lone pairs on 'A'. For BrCl₄⁻, this would be AX4E2, with 'E' representing the electron pairs. This leads to a square planar molecular geometry.