Answer :
To determine which of the given equations are balanced, we'll need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's check each option step-by-step:
### Option A: [tex]\( \text{NaClO}_3 \rightarrow \text{NaCl} + 3 \text{O}_2 \)[/tex]
Reactants:
- Na: 1
- Cl: 1
- O: 3
Products:
- Na: 1
- Cl: 1
- O: 3 (because 3O[tex]\(_2\)[/tex] means 3 molecules of O[tex]\(_2\)[/tex], which equals 3x2=6 oxygen atoms)
Initially, it seems there was a confusion in counting the O atoms for reactant side correctly. Hence re-evaluating it:
- [tex]\( \text{NaClO}_3 \rightarrow Na\cdot1, Cl\cdot1, O\cdot3\cdot1 = O\cdot3\)[/tex]
Total on reactant:
- Na: 1,
- Cl:1,
- O:[tex]\(\cdot3\)[/tex]
So only by doubling checked three oxgens were on the product side too like detailed down step.
Since the number of atoms of each element is equal on both sides:
### Option A is balanced.
---
### Option B: [tex]\( 2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2 \)[/tex]
Reactants:
- Hg: 2 (from [tex]\(2 \text{HgO}\)[/tex])
- O: 2 (from [tex]\(2 \text{HgO}\)[/tex])
Products:
- Hg: 2 (from [tex]\(2 \text{Hg}\)[/tex])
- O: 2 (from [tex]\(\text{O}_2\)[/tex] which has 2 oxygen atoms)
The number of atoms of each element is equal on both sides:
### Option B is balanced.
---
### Option C: [tex]\( 2 \text{ZnS} + \text{O}_2 \rightarrow 2 \text{ZnO} + 2 \text{SO}_2 \)[/tex]
Reactants:
- Zn: 2 (from [tex]\(2 \text{ZnS}\)[/tex])
- S: 2 (from [tex]\(2 \text{ZnS}\)[/tex])
- O: 2 (from [tex]\(\text{O}_2\)[/tex])
Products:
- Zn: 2 (from [tex]\(2 \text{ZnO}\)[/tex])
- S: 2 (from [tex]\(2 \text{SO}_2\)[/tex])
- O: 2 (from [tex]\(2 \text{ZnO}\)[/tex] and 4 from [tex]\(2 \text{SO}_2\)[/tex] where each molecule of [tex]\(\text{SO}_2\)[/tex] contains 2 oxygen atoms, total 2x2=4)
Comparing both side, Oxygen 2 in reactants not matched right-hand total =2+4= 6.
The number of atoms of Oxygen is not equal both sides:
### Option C is NOT balanced.
---
### Option D: [tex]\( 4 \text{CO} + \text{Fe}_3\text{O}_4 \rightarrow 4 \text{CO}_2 + \text{Fe} \)[/tex]
Reactants:
- C: 4 (from [tex]\(4 \text{CO}\)[/tex])
- O: 4 (from [tex]\(4 \text{CO}\)[/tex]) + 4(from [tex]\(\text{Fe}_3\text{O}_4 goes here\)[/tex])
- Fe: 3 (from [tex]\(\text{Fe}_3\text{O}_4 \)[/tex])
Products:
- C: 4 (from [tex]\(4 \text{CO}_2\)[/tex])
- O: 4 * 2 =8 (total from 4 [tex]\(\text{CO}_2\)[/tex])
- Fe: varied - n_particle has been missed analyhs per balance idea maybe cross looked no =3.
The number of atoms is not equal Fe essentially got dropped check:
### Option D is NOT balanced.
---
### Option E: [tex]\( 2 \text{Fe} + 2 \text{Cl}_2 \rightarrow 2 \text{FeCl}_3 \)[/tex]
Reactants:
- Fe: 2 (from [tex]\(2 \text{Fe}\)[/tex])
- Cl: 4 (from [tex]\(2 \text{Cl}_2\)[/tex] )
Products:
- Fe: 2 (from [tex]\(2 \text{FeCl}_3\)[/tex])
- Cl: 6 (from [tex]\(2 \text{FeCl}_3)\)[/tex] where each molecule FeCl3 cotains 3 and side multiplied !.
( \(chlorine are 6 check while say specific-4 react)
The number of atoms of chlorine is mismatched simply 2FeCl3 seek 3fe total maybe not checked:
### Option E is NOT balanced.
---
So summarizing:
- Option A and B are correctly balanced equations.
### Option A: [tex]\( \text{NaClO}_3 \rightarrow \text{NaCl} + 3 \text{O}_2 \)[/tex]
Reactants:
- Na: 1
- Cl: 1
- O: 3
Products:
- Na: 1
- Cl: 1
- O: 3 (because 3O[tex]\(_2\)[/tex] means 3 molecules of O[tex]\(_2\)[/tex], which equals 3x2=6 oxygen atoms)
Initially, it seems there was a confusion in counting the O atoms for reactant side correctly. Hence re-evaluating it:
- [tex]\( \text{NaClO}_3 \rightarrow Na\cdot1, Cl\cdot1, O\cdot3\cdot1 = O\cdot3\)[/tex]
Total on reactant:
- Na: 1,
- Cl:1,
- O:[tex]\(\cdot3\)[/tex]
So only by doubling checked three oxgens were on the product side too like detailed down step.
Since the number of atoms of each element is equal on both sides:
### Option A is balanced.
---
### Option B: [tex]\( 2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2 \)[/tex]
Reactants:
- Hg: 2 (from [tex]\(2 \text{HgO}\)[/tex])
- O: 2 (from [tex]\(2 \text{HgO}\)[/tex])
Products:
- Hg: 2 (from [tex]\(2 \text{Hg}\)[/tex])
- O: 2 (from [tex]\(\text{O}_2\)[/tex] which has 2 oxygen atoms)
The number of atoms of each element is equal on both sides:
### Option B is balanced.
---
### Option C: [tex]\( 2 \text{ZnS} + \text{O}_2 \rightarrow 2 \text{ZnO} + 2 \text{SO}_2 \)[/tex]
Reactants:
- Zn: 2 (from [tex]\(2 \text{ZnS}\)[/tex])
- S: 2 (from [tex]\(2 \text{ZnS}\)[/tex])
- O: 2 (from [tex]\(\text{O}_2\)[/tex])
Products:
- Zn: 2 (from [tex]\(2 \text{ZnO}\)[/tex])
- S: 2 (from [tex]\(2 \text{SO}_2\)[/tex])
- O: 2 (from [tex]\(2 \text{ZnO}\)[/tex] and 4 from [tex]\(2 \text{SO}_2\)[/tex] where each molecule of [tex]\(\text{SO}_2\)[/tex] contains 2 oxygen atoms, total 2x2=4)
Comparing both side, Oxygen 2 in reactants not matched right-hand total =2+4= 6.
The number of atoms of Oxygen is not equal both sides:
### Option C is NOT balanced.
---
### Option D: [tex]\( 4 \text{CO} + \text{Fe}_3\text{O}_4 \rightarrow 4 \text{CO}_2 + \text{Fe} \)[/tex]
Reactants:
- C: 4 (from [tex]\(4 \text{CO}\)[/tex])
- O: 4 (from [tex]\(4 \text{CO}\)[/tex]) + 4(from [tex]\(\text{Fe}_3\text{O}_4 goes here\)[/tex])
- Fe: 3 (from [tex]\(\text{Fe}_3\text{O}_4 \)[/tex])
Products:
- C: 4 (from [tex]\(4 \text{CO}_2\)[/tex])
- O: 4 * 2 =8 (total from 4 [tex]\(\text{CO}_2\)[/tex])
- Fe: varied - n_particle has been missed analyhs per balance idea maybe cross looked no =3.
The number of atoms is not equal Fe essentially got dropped check:
### Option D is NOT balanced.
---
### Option E: [tex]\( 2 \text{Fe} + 2 \text{Cl}_2 \rightarrow 2 \text{FeCl}_3 \)[/tex]
Reactants:
- Fe: 2 (from [tex]\(2 \text{Fe}\)[/tex])
- Cl: 4 (from [tex]\(2 \text{Cl}_2\)[/tex] )
Products:
- Fe: 2 (from [tex]\(2 \text{FeCl}_3\)[/tex])
- Cl: 6 (from [tex]\(2 \text{FeCl}_3)\)[/tex] where each molecule FeCl3 cotains 3 and side multiplied !.
( \(chlorine are 6 check while say specific-4 react)
The number of atoms of chlorine is mismatched simply 2FeCl3 seek 3fe total maybe not checked:
### Option E is NOT balanced.
---
So summarizing:
- Option A and B are correctly balanced equations.
