Alright, let's break down how to find the correct net ionic equation step-by-step.
### Step 1: Write Down the Total Ionic Equation
We start with the total ionic equation given:
[tex]$
Ba^{2+} + 2 NO_3^{-} + 2 Na^{+} + CO_3^{2-} \longrightarrow BaCO_3 + 2 Na^{+} + 2 NO_3^{-}
$[/tex]
### Step 2: Identify the Spectator Ions
Spectator ions are ions that do not participate in the actual chemical reaction and remain unchanged on both sides of the equation. In the given total ionic equation:
- On the reactants' side, there are [tex]\( 2 NO_3^{-} \)[/tex] and [tex]\( 2 Na^{+} \)[/tex].
- On the products' side, there are still [tex]\( 2 NO_3^{-} \)[/tex] and [tex]\( 2 Na^{+} \)[/tex].
This means that [tex]\( 2 NO_3^{-} \)[/tex] and [tex]\( 2 Na^{+} \)[/tex] are spectator ions.
### Step 3: Remove the Spectator Ions
To derive the net ionic equation, we eliminate the spectator ions from both sides of the total ionic equation, leaving us with only the ions that participate directly in the reaction.
Removing spectator ions:
[tex]$
Ba^{2+} + CO_3^{2-} \longrightarrow BaCO_3
$[/tex]
### Step 4: Write the Net Ionic Equation
After removing the spectator ions, the remaining species form the net ionic equation:
[tex]$
Ba^{2+} + CO_3^{2-} \longrightarrow BaCO_3
$[/tex]
### Step 5: Compare With the Provided Options
Next, we compare this derived net ionic equation with the provided options to identify the correct one:
1. [tex]\( Ba^{2+} + CO_3^{2-} \longrightarrow BaCO_3 \)[/tex]
2. [tex]\( 2 Na^{+} + CO_3^{2-} \longrightarrow Na_2CO_3 \)[/tex]
3. [tex]\( NO_3^{-} + Na^{+} \longrightarrow NaNO_3 \)[/tex]
4. [tex]\( Ba^{2+} + 2 NO_3^{-} \longrightarrow Ba(NO_3)_2 \)[/tex]
It is evident that the correct net ionic equation is the first option:
[tex]$
Ba^{2+} + CO_3^{2-} \longrightarrow BaCO_3
$[/tex]
Thus, the correct answer is option 1.
