Quels sont les coefficients stœchiométriques a, b, c, d, e, f de la réaction suivante: aFe^{2+}(aq) + bCr_2O_7^{2-}(aq) + cH^+(aq) \rightleftharpoons dFe^{3+}(aq) + eCr^{3+}(aq) +... Quels sont les coefficients stœchiométriques a, b, c, d, e, f de la réaction suivante: aFe^{2+}(aq) + bCr_2O_7^{2-}(aq) + cH^+(aq) \rightleftharpoons dFe^{3+}(aq) + eCr^{3+}(aq) + fH_2O? Read more

Steps to Solve

1. Balance Cr (Chrome) Since there are 2 Cr atoms in $Cr_2O_7^{2-}$, we need 2 $Cr^{3+}$ on the product side. So, $e = 2b$.

2. Balance Fe (Fer) The number of Fe atoms must be the same on both sides. Thus, $a = d$.

3. Balance O (Oxygène) There are $7b$ oxygen atoms on the reactant side (from $Cr_2O_7^{2-}$), so we need $f = 7b$ on the product side.

4. Balance H (Hydrogène) The number of H atoms must also be the same on both sides. Thus, $c = 2f$. Since $f = 7b$, then $c = 14b$.

5. Balance Charge The total charge on the reactant side must equal the total charge on the product side: $2a - 2b + c = 3d + 3e$ Substitute $a = d$ and $e = 2b$: $2a - 2b + c = 3a + 6b$ $c = a + 8b$ Substitute $c=14b$: $14b = a + 8b$ $a = 6b$

6. Determine the coefficients Let $b = 1$. Then $a = 6$, $d = 6$, $e = 2$, $f = 7$, and $c = 14$.

The balanced equation is: $6Fe^{2+}(aq) + Cr_2O_7^{2-}(aq) + 14H^+(aq) \rightleftharpoons 6Fe^{3+}(aq) + 2Cr^{3+}(aq) + 7H_2O$. Therefore, $a = 6$, $b = 1$, $c = 14$, $d = 6$, $e = 2$, and $f = 7$.