Question

$Cr_2O_7^{2-} \longrightarrow Cr^{+3}$

[eq". was given] Eq. mass of $Cr = ?$

Answer 1

M/3

Answer 2

To determine the equivalent mass of Cr in the given reaction $Cr_2O_7^{2-} \longrightarrow Cr^{+3}$, we need to find the change in the oxidation state of Chromium.

1. Determine the oxidation state of Cr in $Cr_2O_7^{2-}$:

Let the oxidation state of Cr be $x$. The oxidation state of oxygen is -2.

For the $Cr_2O_7^{2-}$ ion, the sum of oxidation states must equal the charge of the ion (-2).

$2(x) + 7(-2) = -2$

$2x - 14 = -2$

$2x = 14 - 2$

$2x = 12$

$x = +6$

So, the oxidation state of Cr in $Cr_2O_7^{2-}$ is +6.

2. Determine the oxidation state of Cr in $Cr^{+3}$:

The oxidation state of Cr in $Cr^{+3}$ is directly given as +3.

3. Calculate the change in oxidation state per Cr atom:

The change in oxidation state for one Cr atom is the absolute difference between its initial and final oxidation states:

Change = $|(+6) - (+3)| = 3$

This change represents the number of electrons gained by one Cr atom. In a redox reaction, this value corresponds to the n-factor (or valency factor) for the element.

4. Calculate the equivalent mass of Cr:

The equivalent mass of an element in a redox reaction is given by its atomic mass divided by the number of electrons gained or lost per atom (which is the change in oxidation state per atom).

Let 'M' be the atomic mass of Cr.

Equivalent mass of Cr = $\frac{\text{Atomic Mass of Cr}}{\text{Change in oxidation state per Cr atom}}$

Equivalent mass of Cr = $\frac{M}{3}$

The equivalent mass of Cr is M/3, where M is the atomic mass of Chromium.