Calculate Sum of Zero Oxidation State Atoms Across Molecules

To determine the sum of the number of atoms in their zero oxidation state across the given molecules, we analyze the structure and oxidation states of the constituent atoms in each molecule:

1. $\text{Br}_3\text{O}_8$ (Tribromooctaoxide):

   • Structure: $\text{O}_3\text{Br}-\text{Br}(\text{O}_2)-\text{BrO}_3$
   • The two terminal bromine ($\text{Br}$) atoms are each bonded to three oxygen ($\text{O}$) atoms, giving them an oxidation state of $+6$.
   • The central bromine ($\text{Br}$) atom is bonded to two oxygen ($\text{O}$) atoms and two bromine ($\text{Br}$) atoms, giving it an oxidation state of $+4$.
   • All oxygen ($\text{O}$) atoms have an oxidation state of $-2$.
   • Number of atoms with zero oxidation state in $\text{Br}_3\text{O}_8$: $0$

2. $\text{F}_2\text{O}$ (Oxygen difluoride):

   • Structure: $\text{F}-\text{O}-\text{F}$
   • Since fluorine ($\text{F}$) is more electronegative than oxygen ($\text{O}$), each $\text{F}$ atom has an oxidation state of $-1$, and the $\text{O}$ atom has an oxidation state of $+2$.
   • Number of atoms with zero oxidation state in $\text{F}_2\text{O}$: $0$

3. $\text{H}_2\text{S}_4\text{O}_6$ (Tetrathionic acid):

   • Structure: $\text{HO}-\text{S}(=\text{O})_2-\text{S}-\text{S}-\text{S}(=\text{O})_2-\text{OH}$
   • The two terminal sulfur ($\text{S}$) atoms are bonded to oxygen atoms and have an oxidation state of $+5$.
   • The two central sulfur ($\text{S}$) atoms form homonuclear $\text{S}-\text{S}$ bonds and are not attached to any other element, so each has an oxidation state of $0$.
   • Number of atoms with zero oxidation state in $\text{H}_2\text{S}_4\text{O}_6$: $2$

4. $\text{H}_2\text{S}_5\text{O}_6$ (Pentathionic acid):

   • Structure: $\text{HO}-\text{S}(=\text{O})_2-\text{S}-\text{S}-\text{S}-\text{S}(=\text{O})_2-\text{OH}$
   • The two terminal sulfur ($\text{S}$) atoms have an oxidation state of $+5$.
   • The three central sulfur ($\text{S}$) atoms are bonded only to adjacent sulfur atoms, so each has an oxidation state of $0$.
   • Number of atoms with zero oxidation state in $\text{H}_2\text{S}_5\text{O}_6$: $3$

5. $\text{C}_3\text{O}_2$ (Carbon suboxide):

   • Structure: $\text{O}=\text{C}=\text{C}=\text{C}=\text{O}$
   • The two terminal carbon ($\text{C}$) atoms are double-bonded to oxygen atoms, giving them an oxidation state of $+2$.
   • The central carbon ($\text{C}$) atom is double-bonded to two other carbon atoms, giving it an oxidation state of $0$.
   • The oxygen ($\text{O}$) atoms have an oxidation state of $-2$.
   • Number of atoms with zero oxidation state in $\text{C}_3\text{O}_2$: $1$

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Sum Calculation:

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