Answer :
To determine which of the provided chemical equations is balanced, we need to compare the number of atoms of each element on both the reactant and product sides of the equation. A balanced chemical equation will have the same number of each type of atom on both sides.
Let's analyze each option step-by-step:
### Option A: [tex]\( 3 \, \text{AgNO}_3 + 2 \, \text{K}_2 \text{CrO}_4 \rightarrow 3 \, \text{KNO}_3 + 2 \, \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 3 \, \text{Ag} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 4 \, \text{K} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 3 \, \text{Ag} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex], [tex]\( 4 \, \text{K} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 3 \, \text{K} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 4 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 4 \, \text{Ag} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex], [tex]\( 3 \, \text{K} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
The counts don't match: [tex]\( 3 \, \text{Ag} \neq 4 \, \text{Ag} \)[/tex] and [tex]\( 4 \, \text{K} \neq 3 \, \text{K} \)[/tex]. This equation is not balanced.
### Option B: [tex]\( \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow 2 \, \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
The counts don't match: [tex]\( 1 \, \text{Ag} \neq 2 \, \text{Ag} \)[/tex] and [tex]\( 1 \, \text{NO}_3 \neq 2 \, \text{NO}_3 \)[/tex]. This equation is not balanced.
### Option C: [tex]\( \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 1 \, \text{K} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex], [tex]\( 1 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
The counts don't match: [tex]\( 1 \, \text{Ag} \neq 2 \, \text{Ag} \)[/tex] and [tex]\( 2 \, \text{K} \neq 1 \, \text{K} \)[/tex]. This equation is not balanced.
### Option D: [tex]\( 2 \, \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow 2 \, \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
The counts match: [tex]\( 2 \, \text{Ag} = 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 = 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} = 2 \, \text{K} \)[/tex], and [tex]\( 1 \, \text{CrO}_4 = 1 \, \text{CrO}_4 \)[/tex]. This equation is balanced.
Answer: Option D: [tex]\( 2 \, \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow 2 \, \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Let's analyze each option step-by-step:
### Option A: [tex]\( 3 \, \text{AgNO}_3 + 2 \, \text{K}_2 \text{CrO}_4 \rightarrow 3 \, \text{KNO}_3 + 2 \, \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 3 \, \text{Ag} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 4 \, \text{K} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 3 \, \text{Ag} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex], [tex]\( 4 \, \text{K} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 3 \, \text{K} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 4 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 4 \, \text{Ag} \)[/tex], [tex]\( 3 \, \text{NO}_3 \)[/tex], [tex]\( 3 \, \text{K} \)[/tex], [tex]\( 2 \, \text{CrO}_4 \)[/tex]
The counts don't match: [tex]\( 3 \, \text{Ag} \neq 4 \, \text{Ag} \)[/tex] and [tex]\( 4 \, \text{K} \neq 3 \, \text{K} \)[/tex]. This equation is not balanced.
### Option B: [tex]\( \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow 2 \, \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
The counts don't match: [tex]\( 1 \, \text{Ag} \neq 2 \, \text{Ag} \)[/tex] and [tex]\( 1 \, \text{NO}_3 \neq 2 \, \text{NO}_3 \)[/tex]. This equation is not balanced.
### Option C: [tex]\( \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 1 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 1 \, \text{K} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{NO}_3 \)[/tex], [tex]\( 1 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
The counts don't match: [tex]\( 1 \, \text{Ag} \neq 2 \, \text{Ag} \)[/tex] and [tex]\( 2 \, \text{K} \neq 1 \, \text{K} \)[/tex]. This equation is not balanced.
### Option D: [tex]\( 2 \, \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow 2 \, \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
Reactants:
- [tex]\( \text{AgNO}_3 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{K}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
Products:
- [tex]\( \text{KNO}_3 \)[/tex]: [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex]
- [tex]\( \text{Ag}_2 \text{CrO}_4 \)[/tex]: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
- Total: [tex]\( 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} \)[/tex], [tex]\( 1 \, \text{CrO}_4 \)[/tex]
The counts match: [tex]\( 2 \, \text{Ag} = 2 \, \text{Ag} \)[/tex], [tex]\( 2 \, \text{NO}_3 = 2 \, \text{NO}_3 \)[/tex], [tex]\( 2 \, \text{K} = 2 \, \text{K} \)[/tex], and [tex]\( 1 \, \text{CrO}_4 = 1 \, \text{CrO}_4 \)[/tex]. This equation is balanced.
Answer: Option D: [tex]\( 2 \, \text{AgNO}_3 + \text{K}_2 \text{CrO}_4 \rightarrow 2 \, \text{KNO}_3 + \text{Ag}_2 \text{CrO}_4 \)[/tex]
