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Recently I was taught by my teacher that there is no such thing as nascent oxygen neither hydrogen. It just represents Electrons from ionic equations. Then he proceeds to give example of following partial equations. $$\ce{SO_2 + 2H_2O -> H_2SO_4 + 2H}$$ $$\ce{Cl2 + 2H -> 2HCl}$$

This equation in ionic form can be written as: $$\ce{SO2 + 2H2O ->SO4^{-2} + 4H^+ + 2e^-}$$ $$\ce{Cl2 + 2e^{-} -> 2Cl-}$$

I want some more insight on this matter and some conceptual understanding.

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$\ce{SO2}$ does react with $\ce{H2O}$ according to your second reaction (which is a half-equation) : $$\ce{SO2 + 2 H2O -> SO4^{2-} + 4 H+ + 2 e^- }$$ But $\ce{SO2}$ cannot react according to the first equation, which produces two non-combined (nascent) $\ce{H}$ atoms. Usually the electrons produced in this half-equation do not react with $\ce{H+}$ to produce free $\ce{H}$ atoms as you state. These electrons react with some stronger oxydant like $\ce{Cl2}$ or $\ce{O2}$ in equations like $$\ce{Cl2 + 2 e^- -> 2 Cl-}$$ or $$\ce{O2 + 4 e- + 4 H+ -> 2 H2O}$$ So "nascent" $\ce{H}$ atoms are not produced by $\ce{SO2}$ in water.

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