Answer: The empirical formula of the metal sulfide is [tex]CoBr_{2}[/tex].
Explanation:
Given: Mass of metal = 20.38 g
Mass of metal sulfide = 31.47 g
Moles is the mass of a substance divided by its molar mass.
So, moles of cobalt (molar mass = 59 g/mol) are as follows.
[tex]Moles = \frac{mass}{molarmass}\\= \frac{20.38 g}{59 g/mol}\\= 0.345 mol[/tex]
Moles of bromine (molar mass = 80 g/mol) are as follows.
[tex]Moles = \frac{(31.47 - 20.38) g}{80 g/mol}\\= \frac{11.09 g}{80 g/mol}\\= 0.138 mol[/tex]
Now, the ratio of number of moles of cobalt and number of moles of bromine are as follows.
Moles of Co : Moles of Br = 1 : 2
Hence, the empirical formula is [tex]CoBr_{2}[/tex].
Thus, we can conclude that the empirical formula of the metal sulfide is [tex]CoBr_{2}[/tex].
