See the following chemical reaction:
Cr$$_2$$O$$_7^{2-}$$ + XH$$^+$$ + 6Fe$$^{2+}$$ $$\to$$ YCr$$^{3+}$$ + 6Fe$$^{3+}$$ + ZH$$_2$$O
The sum of X, Y and Z is _____.

Balancing the equation:

$$Cr_2O_7^{2-} + XH^+ + 6Fe^{2+} \to YCr^{3+} + 6Fe^{3+} + ZH_2O$$

Balancing Cr: 2 Cr on left → Y = 2

Balancing Fe: Already balanced (6 on each side).

Balancing charge:

Left: $$-2 + X(+1) + 6(+2) = X + 10$$

Right: $$2(+3) + 6(+3) + 0 = 24$$

$$X + 10 = 24 \implies X = 14$$

Balancing O: 7 O on left → Z = 7

Balancing H: $$14H$$ on left = $$2 \times 7 = 14H$$ on right ✓

$$X + Y + Z = 14 + 2 + 7 = 23$$

This matches the answer key value of $$\mathbf{23}$$.