To balance the chemical equation [tex]\( KI + Pb(NO_3)_2 \rightarrow PbI_2 + KNO_3 \)[/tex], we need to ensure that there are equal numbers of each type of atom on both sides of the reaction. Here is a step-by-step explanation on how to balance this equation:
1. Identify each element in the equation:
- Potassium (K)
- Iodine (I)
- Lead (Pb)
- Nitrogen (N)
- Oxygen (O)
2. Write down the unbalanced equation:
[tex]\[ KI + Pb(NO_3)_2 \rightarrow PbI_2 + KNO_3 \][/tex]
3. Count the number of each atom on the reactants side and the products side:
- Reactants:
- [tex]\( KI \)[/tex]: 1 K, 1 I
- [tex]\( Pb(NO_3)_2 \)[/tex]: 1 Pb, 2 N, 6 O
- Products:
- [tex]\( PbI_2 \)[/tex]: 1 Pb, 2 I
- [tex]\( KNO_3 \)[/tex]: 1 K, 1 N, 3 O
Initial count:
- Reactants: [tex]\( K: 1, I: 1 + 2N, 6O \)[/tex]
- Products: [tex]\( 1Pb, 1K+2I, 1N+ 3O \)[/tex]
4. Balance one element at a time:
- Balance iodine (I):
The products have 2 iodines in [tex]\( PbI_2 \)[/tex] and reactants have 1 in [tex]\( KI \)[/tex]. Therefore, we need 2 [tex]\( KI \)[/tex] on the reactants side:
[tex]\[ 2 KI + Pb(NO_3)_2 \rightarrow PbI_2 + KNO_3 \][/tex]
- Balance potassium (K):
Usually adding 2 potassium Iodide to the reactant side. We need to have 2 [tex]\( KNO_3 \)[/tex] in products:
[tex]\[ 2 KI + Pb(NO_3)_2 \rightarrow PbI_2 + 2 KNO_3 \][/tex]
- Balance lead (Pb) and nitrate (NO_3):
Lead is already balanced with 1 Pb on both sides. Nitrogen and oxygen balance out with two [tex]\(KNO_3\)[/tex] on the product side which completes balance:
5. Check the final counts:
- Reactants:
- 2 [tex]\(KI\)[/tex]: 2 K, 2 I
- 1 [tex]\(Pb(NO_3)_2\)[/tex]: 1 Pb, 2 N, 6 O
- Products:
- [tex]\(PbI_2\)[/tex]: 1 Pb, 2 I
- 2 [tex]\( KNO_3 \)[/tex]: 2 K, 2 N, 6 O
Final balanced equation:
[tex]\[ 2 KI + Pb(NO_3)_2 \rightarrow PbI_2 + 2 KNO_3 \][/tex]
Thus the coefficients for [tex]\( KI \)[/tex], [tex]\( Pb(NO_3)_2 \)[/tex], [tex]\( PbI_2 \)[/tex], and [tex]\( KNO_3 \)[/tex] are 2, 1, 1, and 2 respectively.
So, the correct answer is:
[tex]\[ \boxed{2} + \boxed{1} \rightarrow \boxed{1} + \boxed{2} \][/tex]
