Which series of reactions correctly represents the chemical relations related to iron and its compound?

First, we write down the four proposed sequences exactly as given so that we can examine each step:

Option A :   $$Fe \;\rightarrow\; FeSO_4 \;\rightarrow\; Fe_2(SO_4)_3 \;\rightarrow\; Fe$$

Option B :   $$Fe \;\rightarrow\; FeO \;\rightarrow\; FeSO_4 \;\rightarrow\; Fe$$

Option C :   $$Fe \;\rightarrow\; FeCl_3 \;\rightarrow\; FeCl_2 \;\rightarrow\; Fe$$

Option D :   $$Fe \;\rightarrow\; Fe_3O_4 \;\rightarrow\; FeO \;\rightarrow\; Fe$$

Now we test every step of every option against the well-known reactions of iron and its compounds.

In Option A the first step is the ordinary reaction of iron with dilute sulphuric acid:

$$Fe + H_2SO_4(dil.) \;\rightarrow\; FeSO_4 + H_2\uparrow$$

That step is correct. The second step claims that ferrous sulphate is converted into ferric sulphate simply by adding more $$H_2SO_4$$ and $$O_2$$. In reality, direct oxidation of $$FeSO_4$$ in acid gives a mixture containing $$Fe_2(SO_4)_3$$, so this might still be acceptable. But the third step says that heating $$Fe_2(SO_4)_3$$ yields metallic iron:

$$Fe_2(SO_4)_3 \;\xrightarrow{\text{heat}}\; Fe$$

This is impossible. The correct thermal decomposition is

$$2\,Fe_2(SO_4)_3 \;\rightarrow\; 2\,Fe_2O_3 + 6\,SO_3$$

No free iron is produced, so Option A fails.

In Option B the first step proposes the formation of $$FeO$$ by simply heating iron in oxygen:

$$2\,Fe + O_2 \;\xrightarrow{\text{heat}}\; 2\,FeO$$

Actually, ordinary oxidation of iron in air gives a mixture dominated by $$Fe_3O_4$$, not pure $$FeO$$. Hence even the first arrow is doubtful. Moreover, the last step claims that heating $$FeSO_4$$ alone produces metallic iron:

$$FeSO_4 \;\xrightarrow{\text{heat}}\; Fe$$

The true decomposition is

$$2\,FeSO_4 \;\rightarrow\; Fe_2O_3 + SO_2 + SO_3$$

Again no iron metal appears, so Option B is incorrect.

Option C starts correctly because iron combines with chlorine on heating to give ferric chloride:

$$2\,Fe + 3\,Cl_2 \;\xrightarrow{\text{heat}}\; 2\,FeCl_3$$

The next step claims that further heating of $$FeCl_3$$ in air converts it into $$FeCl_2$$:

$$2\,FeCl_3 \;\xrightarrow{\text{heat, air}}\; 2\,FeCl_2 + Cl_2$$

In reality, heating $$FeCl_3$$ in air does not reduce it; instead it hydrolyses to give $$Fe_2O_3$$ with the liberation of $$HCl$$ or $$Cl_2$$. Therefore the second arrow is wrong, so the whole chain cannot be correct even though the last displacement $$Zn + FeCl_2 \rightarrow ZnCl_2 + Fe$$ would otherwise work.

Finally we analyse Option D. The first arrow describes the partial oxidation of iron on strong heating in oxygen:

$$3\,Fe + 2\,O_2 \;\xrightarrow{\text{heat}}\; Fe_3O_4$$

This is precisely what happens; the black oxide $$Fe_3O_4$$ (magnetite) is produced. Now we supply carbon monoxide at about 600 °C. The blast-furnace reduction of magnetite proceeds in two stages. At the lower temperature the reaction is

$$Fe_3O_4 + CO \;\xrightarrow{600^{\circ}\!C}\; 3\,FeO + CO_2$$

Thus the second arrow $$Fe_3O_4 \rightarrow FeO$$ with $$CO$$ as the reducing agent is fully justified. When the partly reduced ore ($$FeO$$) meets hotter rising CO (≈700 °C or above) a further reduction occurs:

$$FeO + CO \;\xrightarrow{700^{\circ}\!C}\; Fe + CO_2$$

So the final step $$FeO \rightarrow Fe$$ is perfectly valid. Every arrow in Option D is therefore correct, and the overall sequence accurately reproduces the industrial route found in a blast furnace.

Since Options A, B and C each contain at least one impossible or incorrect transformation, while every step in Option D is chemically sound, Option D is the only correct choice.

Hence, the correct answer is Option D.