[tex] m(\text{Cl}) = 0.979 \; \text{g} [/tex]
Explanation
The [tex] 1.750 \; \text{g} [/tex] sample contains only the atoms of
Thus no matter what natural numbers [tex] x [/tex] and [tex] y [/tex] are, [tex] m(\text{Fe}_x\text{Cl}_y) = m(\text{Fe}) + m(\text{Cl}) [/tex] shall holds.
Recall that zinc [tex] \text{Zn} [/tex] is more reactive than iron as seen in the reactivity series; Adding zinc to the solution would reduce all iron atoms (regardless of the oxidation state, [tex] +2 [/tex] or [tex] +3 [/tex]) to their elementary form, hence displacing them out of the solution. [tex] 0.771 \; \text{g} [/tex] of iron was obtained and therefore [tex] m(\text{Fe}) = 0.771 \; \text{g} [/tex].
Thus
[tex] \begin{array}{lll}m(\text{Cl})& =& m(\text{Fe}_x\text{Cl}_y) - m(\text{Fe})\\ & = &1.750 \; \text{g}- 0.771\; \text{g}\\ &=&0.979\; \text{g}\end{array} [/tex]