See the following chemical reaction:

$$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{XH}^{+}+6 \mathrm{~F}_{e}^{2+} \rightarrow \mathrm{YCr}^{3+}+6 \mathrm{~F}_{e}^{3+}+\mathrm{Z} \mathrm{H}_{2} \mathrm{O}$$

The sum of $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ is ___________

To find the sum of X, Y, and Z, we need to balance the given chemical reaction: <br/><br/> $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} + \mathrm{XH}^{+} + 6 \mathrm{Fe}^{2+} \rightarrow \mathrm{YCr}^{3+} + 6 \mathrm{Fe}^{3+} + \mathrm{ZH}_{2} \mathrm{O}$$ <br/><br/> Let's balance the reaction step by step: <br/><br/> 1. Balance the chromium atoms:<br/><br/> There are 2 chromium atoms on the left side of the equation, so we need 2 chromium atoms on the right side. Thus, Y = 2. <br/><br/> $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} + \mathrm{XH}^{+} + 6 \mathrm{Fe}^{2+} \rightarrow 2 \mathrm{Cr}^{3+} + 6 \mathrm{Fe}^{3+} + \mathrm{ZH}_{2} \mathrm{O}$$ <br/><br/> 2. Balance the oxygen atoms:<br/><br/> There are 7 oxygen atoms on the left side of the equation, so we need 7 oxygen atoms on the right side. Since each water molecule (H₂O) contains one oxygen atom, Z = 7. <br/><br/> $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} + \mathrm{XH}^{+} + 6 \mathrm{Fe}^{2+} \rightarrow 2 \mathrm{Cr}^{3+} + 6 \mathrm{Fe}^{3+} + 7 \mathrm{H}_{2} \mathrm{O}$$ <br/><br/> 3. Balance the hydrogen atoms and charges:<br/><br/> There are 14 hydrogen atoms on the right side of the equation, so we need 14 hydrogen atoms on the left side. Thus, X = 14. <br/><br/> $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} + 14 \mathrm{H}^{+} + 6 \mathrm{Fe}^{2+} \rightarrow 2 \mathrm{Cr}^{3+} + 6 \mathrm{Fe}^{3+} + 7 \mathrm{H}_{2} \mathrm{O}$$ <br/><br/> Now the chemical reaction is balanced: <br/><br/> $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} + 14 \mathrm{H}^{+} + 6 \mathrm{Fe}^{2+} \rightarrow 2 \mathrm{Cr}^{3+} + 6 \mathrm{Fe}^{3+} + 7 \mathrm{H}_{2} \mathrm{O}$$ <br/><br/> The sum of X, Y, and Z is: <br/><br/> X + Y + Z = 14 + 2 + 7 = 23 <br/><br/> So, the sum of X, Y, and Z is 23.