Given Unbalanced Reaction:
\[
Pb(NO_3)_2 + KI \longrightarrow PbI_2 + KNO_3
\]
Step 1: Count the number of atoms on both sides
Left side:
Pb = 1
(NO₃) = 2 groups
K = 1
I = 1
Right side:
Pb = 1
I = 2
K = 1
(NO₃) = 1 group
Iodine and nitrate groups are not balanced.
Step 2: Balance Iodine (I)
Since PbI₂ contains 2 iodine atoms, we need 2 KI on the left side.
\[
Pb(NO_3)_2 + 2KI \longrightarrow PbI_2 + KNO_3
\]
Now I atoms are balanced (2 on both sides).
Step 3: Balance Potassium (K)
There are 2 potassium atoms on the left (from 2KI), so place coefficient 2 before KNO₃.
\[
Pb(NO_3)_2 + 2KI \longrightarrow PbI_2 + 2KNO_3
\]
Step 4: Check Nitrate Groups (NO₃)
Left side: 2 nitrate groups
Right side: 2 nitrate groups (from 2KNO₃)
Balanced.
Step 5: Final Check
Pb = 1 on both sides ✔
K = 2 on both sides ✔
I = 2 on both sides ✔
(NO₃) = 2 on both sides ✔
Balanced Chemical Equation:
\[
\boxed{Pb(NO_3)_2 + 2KI \longrightarrow PbI_2 + 2KNO_3}
\]