1. Identify oxidation states and likely colors of the given complexes

We are given the low-spin complexes:

$\mathrm{K}_3[\mathrm{Co}(\mathrm{NO}_2)_6],\; \mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6],\; \mathrm{K}_3[\mathrm{Fe}(\mathrm{CN})_6],\; \mathrm{Cu}_2[\mathrm{Fe}(\mathrm{CN})_6],\; \mathrm{Zn}_2[\mathrm{Fe}(\mathrm{CN})_6]$

We need the complexes having yellow colour, then add their spin-only magnetic moments.

2. Determine the yellow-colored complexes

Known colors of these coordination compounds:

• $\mathrm{K}_3[\mathrm{Co}(\mathrm{NO}_2)_6]$ = potassium cobaltinitrite = yellow
• $\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$ = potassium ferrocyanide = pale yellow / yellow
• $\mathrm{K}_3[\mathrm{Fe}(\mathrm{CN})_6]$ = potassium ferricyanide = red
• $\mathrm{Cu}_2[\mathrm{Fe}(\mathrm{CN})_6]$ is not yellow
• $\mathrm{Zn}_2[\mathrm{Fe}(\mathrm{CN})_6]$ = zinc ferrocyanide = white

So the yellow complexes are:

$\mathrm{K}_3[\mathrm{Co}(\mathrm{NO}_2)_6] \quad \text{and} \quad \mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$

3. Find magnetic moment of $\mathrm{K}_3[\mathrm{Co}(\mathrm{NO}_2)_6]$

For $[\mathrm{Co}(\mathrm{NO}_2)_6]^{3-}$:

Let oxidation state of Co be $x$.

$x + 6(-1) = -3$ $x = +3$

So, metal ion is $\mathrm{Co}^{3+}$.

Cobalt: $Z=27$

$\mathrm{Co}: [\mathrm{Ar}]3d^7 4s^2$ $\mathrm{Co}^{3+}: 3d^6$

Given low-spin octahedral complex with strong-field ligand $\mathrm{NO}_2^-$:

$d^6 \text{ low spin} \Rightarrow t_{2g}^6 e_g^0$

Number of unpaired electrons:

$n = 0$

Spin-only magnetic moment:

$\mu = \sqrt{n(n+2)} = \sqrt{0(0+2)} = 0\;\text{B.M.}$

4. Find magnetic moment of $\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$

For $[\mathrm{Fe}(\mathrm{CN})_6]^{4-}$:

Let oxidation state of Fe be $x$.

$x + 6(-1) = -4$ $x = +2$

So, metal ion is $\mathrm{Fe}^{2+}$.

Iron: $Z=26$

$\mathrm{Fe}: [\mathrm{Ar}]3d^6 4s^2$ $\mathrm{Fe}^{2+}: 3d^6$

With strong-field ligand $\mathrm{CN}^-$ and low spin octahedral complex:

$d^6 \text{ low spin} \Rightarrow t_{2g}^6 e_g^0$

Number of unpaired electrons:

$n = 0$

Thus,

$\mu = \sqrt{0(0+2)} = 0\;\text{B.M.}$

5. Sum of magnetic moments of yellow complexes

$0 + 0 = 0\;\text{B.M.}$

Nearest integer:

$\boxed{0}$

6. Comparison with stored answer

Stored correct answer = $0$

Our derived answer also = $0$, so they agree.