Assume that 1.588{\rm g} of an alkali metal undergoes complete reaction with the amount of gaseous halogen contained in a 0.500{\rm L} flask at 298{\rm K} and 755 {\rm mm \ Hg} pressure. In the reaction, 22.83{\rm kJ} is released (\Delta H = -22.83{\rm kJ}).
The product, a binary ionic compound, crystallizes in a unit cell with anions in a face-centered cubic arrangement and with cations centered along each edge between anions. In addition, there is a cation in the center of the cube. What is the identity of the alkali metal?