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1.0 mole of Fe reacts completely with 0.65 mole of O2 to give a mixture of only FeO and Fe2O3.
The mole ratio of ferrous oxide to ferric oxide is x: y, then (x+y) is

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Solution

2Fe+O22FeOa molea2 molea4Fe+3O22Fe2O3b3b4b2
a+b=1...(i)
a2+3b4=0.65...(ii)
On multiplying equation (ii) by 2, we get
[a2+3b4=0.65]×2
a+3b2=1.30...(iii)
Subtracting equation (iii) from equation (i), we get
[a+b=1][a+3b2=1.30]
b=0.6 mole
Now, placing the value of b=0.6 in equation (i), we get,
a=0.4
moles of FeO=a=0.4
moles of Fe2O3=b2=0.3
ratio = 4 : 3
Now, x+y=4+3=7

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