Cr2O7^-2 (aq) -> Cr3+ (aq)
The chemical equation you provided represents a redox reaction involving the conversion of dichromate ion (Cr2O7^-2) in solution to chromium(III) ion (Cr^3+). To understand how this reaction occurs, we need to analyze the oxidation numbers of the elements involved in the equation.
In dichromate ion (Cr2O7^-2), the overall charge of the ion is -2. The oxygen atoms in most compounds have an oxidation state of -2, so the total oxidation number contributed by the oxygen atoms is -14 (7 × -2). Therefore, the oxidation number of chromium (Cr) must be +12 (-14 + (-2)) to balance out the overall charge of -2.
On the other hand, chromium(III) ion (Cr^3+) has an oxidation number of +3 because each oxygen atom contributes an oxidation state of -2, so a total of three -2 charges will give +6 in total. To balance out the charge, chromium must have an oxidation number of +3.
Now, let's look at the reaction:
Cr2O7^-2 (aq) -> Cr^3+ (aq)
In this reaction, each dichromate ion (Cr2O7^-2) loses three electrons, leading to the formation of two chromium(III) ions (Cr^3+). The electrons being lost are balanced by gaining oxygen atoms from water, creating hydroxide ions (OH^-). So, the complete reaction can be written as:
Cr2O7^-2 (aq) + 14H+ (aq) + 6e^- -> 2Cr^3+ (aq) + 7H2O (l)
To balance the equation, 14 hydrogen ions (H^+) are added on the left side to account for the charge difference. The water molecule (H2O) is added on the product side to balance the oxygen atoms.
In summary, the given chemical equation represents the conversion of dichromate ion (Cr2O7^-2) to chromium(III) ion (Cr^3+) through the loss of three electrons per dichromate ion.