To determine which of the given chemical equations has a coefficient of 3 in front of any of the reactants when balanced, we need to balance each equation step by step.
1. Equation: [tex]\( \text{Zn} + \text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \)[/tex]
- Zinc (Zn) appears as 1 atom on each side.
- To balance chlorine (Cl), since there are 2 chlorine atoms in [tex]\( \text{ZnCl}_2 \)[/tex], we need 2 molecules of [tex]\( \text{HCl} \)[/tex]:
[tex]\[
\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2
\][/tex]
- Now, hydrogen (H) is balanced with 2 hydrogens on both sides.
- This equation is balanced with the coefficients: [tex]\(\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2\)[/tex]
- Coefficients: 1, 2, 1, 1
- No coefficient of 3 is used for any of the reactants.
2. Equation: [tex]\( \text{H}_2\text{SO}_4 + \text{B(OH)}_3 \rightarrow \text{B}_2(\text{SO}_4)_3 + \text{H}_2\text{O} \)[/tex]
- Sulfur (S) and Oxygen (O) in [tex]\( \text{H}_2\text{SO}_4 \)[/tex] and [tex]\( \text{B}_2(\text{SO}_4)_3 \)[/tex].
- Boron (B) appears as 2 atoms on the product side:
[tex]\[
\text{H}_2\text{SO}_4 + 2\text{B(OH)}_3 \rightarrow \text{B}_2(\text{SO}_4)_3 + \text{H}_2\text{O}
\][/tex]
- Now, balance hydrogens and oxygens:
[tex]\[
\text{H}_2\text{SO}_4 + 6\text{H}_2\text{O} \rightarrow 2\text{B}_2(\text{SO}_4)_3 + 6\text{H}_2\text{O}
\][/tex]
- Coefficients: 1, 2, 1, 6
- No coefficient of 3 is used for any of the reactants.
3. Equation: [tex]\( \text{Fe} + \text{AgNO}_3 \rightarrow \text{Fe(NO}_3)_2 + \text{Ag} \)[/tex]
- Iron (Fe): 1 Fe on the left and right.
- Silver (Ag): To balance Ag, we need 2 Ag on the product side:
[tex]\[
3\text{Fe} + 2\text{AgNO}_3 \rightarrow \text{Fe(NO}_3)_2 + 2\text{Ag}
\][/tex]
- Coefficients: 3, 2, 1, 2
- A coefficient of 3 is used in front of Fe.
4. Equation: \( C_2H_4O_2 + O_2 \rightarrow CO_2 + H_2O
- Balance oxygens (O):
- To balance CO2 (and H2O balance as 2):
[tex]\[
\text{C}_2\text{H}_4\text{O}_2 + 2\text{O}_2 \rightarrow 2\text{CO}_2 + 2\text{H}_2\text{O}
\][/tex]
- Coefficients: 1, 2, 2, 2
- No coefficient of 3 is used for any of the reactants.
After evaluating each equation, we find that the only equation balanced to have a coefficient of 3 in front of one of the reactants is:
[tex]\[ 3\text{Fe} + 2\text{AgNO}_3 \rightarrow \text{Fe(NO}_3)_2 + 2\text{Ag} \][/tex]
So, the answer is:
[tex]\[ \boxed{3} \][/tex]
