Consider the following molecules: Br₃O₈, F₂O, H₂S₄O₆, H₂S₅O₆, and C₃O₂. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is:

The correct answer is 6.

To determine the total number of atoms having a zero oxidation state across the given molecules, let us analyze the structure and oxidation state of each individual atom in every molecule step-by-step.

1. Tribromine octoxide (${\mathrm{Br}}_3{O}_8$):
The structure of ${\mathrm{Br}}_3{O}_8$ consists of a chain of three bromine atoms: $O_3\mathrm{Br}-{\mathrm{BrO}}_2-{\mathrm{BrO}}_3$.
- The two terminal bromine atoms are each attached to three oxygen atoms ($-{\mathrm{BrO}}_3$), giving them an oxidation state of +6 each.
- The central bromine atom is attached to two oxygen atoms and two bromine atoms ($-{\mathrm{BrO}}_2-$), giving it an oxidation state of +4.
- All oxygen atoms have an oxidation state of -2.
Thus, 0 atoms are in the zero oxidation state in ${\mathrm{Br}}_3{O}_8$.

2. Oxygen difluoride ($F_{2}O$):
In $F_{2}O$, fluorine is more electronegative than oxygen.
- Fluorine has an oxidation state of -1.
- Oxygen has an oxidation state of +2.
Thus, 0 atoms are in the zero oxidation state in $F_{2}O$.

3. Tetrathionic acid ($H_2{S}_4{O}_6$):
The structure is $\mathrm{HO}-{\mathrm{SO}}_2-S-S-{\mathrm{SO}}_2-\mathrm{OH}$.
- The two terminal sulfur atoms are bonded to oxygen atoms and have an oxidation state of +5.
- The two central sulfur atoms are bonded only to other sulfur atoms ($-S-S-$), so there is no electronegativity difference.
Therefore, the 2 central sulfur atoms each have an oxidation state of 0.
Number of zero oxidation state atoms in $H_2{S}_4{O}_6$ = 2 (the 2 central S atoms).

4. Pentathionic acid ($H_2{S}_5{O}_6$):
The structure is $\mathrm{HO}-{\mathrm{SO}}_2-S-S-S-{\mathrm{SO}}_2-\mathrm{OH}$.
- The two terminal sulfur atoms bonded to oxygen have an oxidation state of +5.
- The three middle sulfur atoms are bonded only to adjacent sulfur atoms ($-S-S-S-$), so they experience no net loss or gain of electron density.
Therefore, all 3 central sulfur atoms have an oxidation state of 0.
Number of zero oxidation state atoms in $H_2{S}_5{O}_6$ = 3 (the 3 central S atoms).

5. Carbon suboxide ($C_3{O}_2$):
The structure is linear: $O=C=C=C=O$.
- The two terminal carbon atoms are double-bonded to oxygen atoms, giving them an oxidation state of +2 each.
- The central carbon atom is double-bonded to two carbon atoms ($=C=$), meaning it shares electrons equally with adjacent identical carbon atoms.
Therefore, the central carbon atom has an oxidation state of 0.
Number of zero oxidation state atoms in $C_3{O}_2$ = 1 (the central C atom).

Total Sum Calculation:
Summing up the number of atoms in the zero oxidation state from each molecule:

$\text{Total}=0+0+2+3+1=6$