Alright, let's work through the solution step-by-step.
### Step 1: Understanding the Reaction
The reaction between hydroiodic acid (HI) and aqueous lithium sulfide (Li₂S) can be represented in a molecular form:
[tex]\[ 2 \text{HI}(aq) + \text{Li}_2\text{S}(aq) \rightarrow \text{H}_2\text{S}(g) + 2 \text{LiI}(aq) \][/tex]
### Step 2: Breaking Down into Ions
To write the complete ionic equation, we need to break down the compounds that are in aqueous state into their respective ions:
1. Hydroiodic acid (HI) dissociates in water:
[tex]\[ \text{HI}(aq) \rightarrow \text{H}^{+}(aq) + \text{I}^{-}(aq) \][/tex]
Since we have 2 HI:
[tex]\[ 2 \text{HI}(aq) \rightarrow 2 \text{H}^{+}(aq) + 2 \text{I}^{-}(aq) \][/tex]
2. Lithium sulfide (Li₂S) dissociates in water:
[tex]\[ \text{Li}_2\text{S}(aq) \rightarrow 2 \text{Li}^{+}(aq) + \text{S}^{2-}(aq) \][/tex]
### Step 3: Writing the Ionic Reactants and Products
Now, we combine these ions on the reactant side:
[tex]\[ 2 \text{H}^{+}(aq) + 2 \text{I}^{-}(aq) + 2 \text{Li}^{+}(aq) + \text{S}^{2-}(aq) \][/tex]
Likewise, on the product side, lithium iodide will remain dissociated in its ionic form, while hydrogen sulfide (H₂S) will be a gas and remain in its molecular form.
[tex]\[ \text{H}_2\text{S}(g) + 2 \text{Li}^{+}(aq) + 2 \text{I}^{-}(aq) \][/tex]
### Step 4: Assembling the Complete Ionic Equation
The ions on both sides should now match:
[tex]\[ 2 \text{H}^{+}(aq) + 2 \text{I}^{-}(aq) + 2 \text{Li}^{+}(aq) + \text{S}^{2-}(aq) \rightarrow \text{H}_2\text{S}(g) + 2 \text{Li}^{+}(aq) + 2 \text{I}^{-}(aq) \][/tex]
### Step 5: Identifying the Equation From the Options
Evaluating the given options, the complete ionic equation is:
[tex]\[ 2 \text{H}^{+}(aq) + 2 \text{I}^{-}(aq) + 2 \text{Li}^{+}(aq) + \text{S}^{2-}(aq) \rightarrow \text{H}_2\text{S}(g) + 2 \text{Li}^{+}(aq) + 2 \text{I}^{-}(aq) \][/tex]
### Conclusion
From the given options, option d matches exactly with our complete ionic equation:
d. [tex]\( 2 \text{H} ^{+}( \text{aq} ) + 2 \text{I} ^{-}( \text{aq} ) + 2 \text{Li} ^{+}( \text{aq} ) + \text{S} ^{2-}( \text{aq} ) \rightarrow \text{H}_2 \text{S}( \text{g} ) + 2 \text{Li} ^{+}( \text{aq} ) + 2 \text{I} ^{-}( \text{aq} ) \)[/tex]
Thus, the correct choice is 4, which corresponds to option d.
