# Consider the following equations:

Question:

Consider the following equations:

$2 \mathrm{Fe}^{2+}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \times \mathrm{A}+\mathrm{y} \mathrm{B}$

(in basic medium)

$2 \mathrm{MnO}_{4}^{-}+6 \mathrm{H}^{+}+5 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{x}^{\prime} \mathrm{C}+\mathrm{y}^{\prime} \mathrm{D}+\mathrm{z}^{\prime} \mathrm{E}$

(in acidic medium)

The sum of the stoichiometric coefficients

$x, y, x^{\prime}, y^{\prime}$ and $z^{\prime}$ for products $A, B, C, D$ and $\mathrm{E}$, respectively, is__________.

Solution:

$\left[\mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{3+}+\mathrm{e}^{-}\right] \times 2$

$\frac{\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{HO}^{\odot}}{2 \mathrm{Fe}^{2+}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{Fe}^{3+}+2 \mathrm{HO}_{(q \omega)}^{\ominus}}$

$x=2 \quad y=2$

$\left[8 \mathrm{H}^{+}+\mathrm{MnO}_{4}^{-}+5 \mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+}+4 \mathrm{H}_{2} \mathrm{O}\right] \times 2$

$\left[\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{O}_{2(\mathrm{~g})}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-}\right] \times 5$

$\Rightarrow 16 \mathrm{H}^{+}+2 \mathrm{MnO}_{4}^{-}+5 \mathrm{H}_{2} \mathrm{O}_{2}$

$\rightarrow 2 \mathrm{Mn}^{2+}+8 \mathrm{H}_{2} \mathrm{O}+5 \mathrm{O}_{2(\mathrm{~g})}+10 \mathrm{H}^{+}$

$\Rightarrow 6 \mathrm{H}^{+}+2 \mathrm{MnO}_{4}^{-}+5 \mathrm{H}_{2} \mathrm{O}_{2}$

$\rightarrow 2 \mathrm{Mn}^{2+}+8 \mathrm{H}_{2} \mathrm{O}+5 \mathrm{O}_{2(\mathrm{~g})}$

So $\quad x^{\prime}=2 \quad y^{\prime}=8 \quad z^{\prime}=5$

so $\quad x+y+x^{\prime}+y^{\prime}+z^{\prime}$

$\Rightarrow \quad 2+2+2+8+5$

$\Rightarrow \quad 19$