Theo đề có:
\(\%_{Cl\left(MCl_x\right)}:\%_{Cl\left(MCl_y\right)}=\dfrac{1}{1,173}\)
\(\Leftrightarrow\dfrac{35,5x}{M+35,5x}:\dfrac{35,5y}{M+35,5y}=\dfrac{1}{1,173}\)
\(\Leftrightarrow\dfrac{35,5x\left(M+35,5y\right)}{35,5y\left(M+35,5x\right)}=\dfrac{1}{1,173}\)
\(\Leftrightarrow1,173x\left(M+35,5y\right)=y\left(M+35,5x\right)\)
\(\Leftrightarrow1,173xM+41,6415xy-yM-35,5xy=0\\ \Leftrightarrow1,173xM+6,1415xy=yM\left(1\right)\)
Lại có:
\(\%_{O\left(MO_{0,5x}\right)}:\%_{O\left(M_2O_y\right)}=1:1,352\)
\(\Leftrightarrow\dfrac{0,5x.16}{M+0,5x.16}:\dfrac{16y}{2M+16y}=1:1,352\)
\(\Leftrightarrow\dfrac{8x\left(2M+16y\right)}{16y\left(M+8x\right)}=\dfrac{1}{1,352}\)
\(\Leftrightarrow21,632xM+173,056xy-16yM-128xy=0\\ \Leftrightarrow21,632xM+45,056xy=16yM\)
\(\Rightarrow1,352Mx+2,816xy=yM\left(2\right)\)
Từ (1), (2) có: \(1,173xM+6,1415xy=1,352xM+2,816xy\)
\(\Leftrightarrow1,173xM+6,1415xy-1,352xM-2,816xy=0\\ \Leftrightarrow-0,179xM=-3,3255xy\\ \Rightarrow M=18,6y\)
Biện luận với y = 3 => M = 56
Thế y = 3 vào (1) được x = 2
=> CTPT của các hợp chất trên: \(FeCl_2,FeCl_3,FeO,Fe_2O_3\)
