To identify the metal displacement reaction from the given options, we need to understand what defines a displacement reaction. A metal displacement reaction is a type of redox reaction in which a more reactive metal displaces a less reactive metal from its compound.
Let's analyze each option:
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$2KClO_3 \xrightarrow{\Delta} 2KCl + 3O_2$: This reaction is a decomposition reaction where potassium chlorate decomposes to form potassium chloride and oxygen gas. No metal displacement occurs here.
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$Cr_2O_3 + 2Al \xrightarrow{\Delta} Al_2O_3 + 2Cr$: Here, aluminum (Al), which is more reactive than chromium (Cr), displaces chromium from its oxide (Cr2O3) to form aluminum oxide (Al2O3) and free chromium. This is a metal displacement reaction.
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$Fe + 2HCl \to FeCl_2 + H_2 \uparrow$: This is a single displacement reaction where iron displaces hydrogen from hydrochloric acid to form iron(II) chloride and hydrogen gas. Although this involves the displacement of a non-metal (hydrogen), it is not classified purely as a metal displacement reaction as it involves an acid.
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$2Pb(NO_3)_2 \to 2PbO + 4NO_2 + O_2 \uparrow$: This is another decomposition reaction where lead(II) nitrate decomposes to yield lead(II) oxide, nitrogen dioxide, and oxygen gas. There is no displacement of a metal here.
After considering all the options, clearly, the reaction in option 2 ($Cr_2O_3 + 2Al \xrightarrow{\Delta} Al_2O_3 + 2Cr$) is the correct example of a metal displacement reaction. Aluminum, being more reactive, displaces chromium from its compound to form aluminum oxide and free chromium.