Let's analyze each of the given reactions to determine which one displays an example of an Arrhenius base.
The Arrhenius theory defines a base as a substance that increases the concentration of hydroxide ions (OH⁻) when dissolved in water.
### Reaction Analysis:
1. Reaction 1:
[tex]\[
\text{NaOH (s)} \rightarrow \text{Na}^{+} (\text{aq}) + \text{OH}^{-} (\text{aq})
\][/tex]
- Sodium hydroxide ([tex]\(\text{NaOH}\)[/tex]) dissociates in water to produce sodium ions ([tex]\(\text{Na}^{+}\)[/tex]) and hydroxide ions ([tex]\(\text{OH}^{-}\)[/tex]).
- This increases the concentration of [tex]\(\text{OH}^{-}\)[/tex] ions in the solution.
- According to the Arrhenius definition, this indicates that [tex]\(\text{NaOH}\)[/tex] is an Arrhenius base.
2. Reaction 2:
[tex]\[
\text{HCl (g)} + \text{H}_2\text{O (l)} \rightarrow \text{H}_3\text{O}^{+} (\text{aq}) + \text{Cl}^{-} (\text{aq})
\][/tex]
- Hydrochloric acid ([tex]\(\text{HCl}\)[/tex]) reacts with water to produce hydronium ions ([tex]\(\text{H}_3\text{O}^{+}\)[/tex]) and chloride ions ([tex]\(\text{Cl}^{-}\)[/tex]).
- This increases the concentration of [tex]\(\text{H}_3\text{O}^{+}\)[/tex] (or [tex]\(\text{H}^{+}\)[/tex]) ions, indicating that HCl is an Arrhenius acid rather than a base.
3. Reaction 3:
[tex]\[
\text{CH}_3\text{COOH (aq)} + \text{H}_2\text{O (l)} \rightarrow \text{H}_3\text{O}^{+} (\text{aq}) + \text{CH}_3\text{COO}^{-} (\text{aq})
\][/tex]
- Acetic acid ([tex]\(\text{CH}_3\text{COOH}\)[/tex]) reacts with water to produce hydronium ions ([tex]\(\text{H}_3\text{O}^{+}\)[/tex]) and acetate ions ([tex]\(\text{CH}_3\text{COO}^{-}\)[/tex]).
- Like the second reaction, this increases the concentration of [tex]\(\text{H}_3\text{O}^{+}\)[/tex] (or [tex]\(\text{H}^{+}\)[/tex]) ions, indicating it is an Arrhenius acid, not a base.
4. Reaction 4:
[tex]\[
\text{NH}_3 (\text{aq}) + \text{HC}_2\text{H}_3\text{O}_2 (\text{aq}) \rightarrow \text{NH}_4^{+} (\text{aq}) + \text{C}_2\text{H}_3\text{O}_2^{-} (\text{aq})
\][/tex]
- Ammonia ([tex]\(\text{NH}_3\)[/tex]) reacts with acetic acid ([tex]\(\text{HC}_2\text{H}_3\text{O}_2\)[/tex]) to produce ammonium ions ([tex]\(\text{NH}_4^{+}\)[/tex]) and acetate ions ([tex]\(\text{C}_2\text{H}_3\text{O}_2^{-}\)[/tex]).
- However, this does not involve the production of [tex]\(\text{OH}^{-}\)[/tex] ions. Instead, it is indicative of a neutralization reaction involving a weak base (ammonia) and a weak acid (acetic acid), but it does not adhere strictly to the Arrhenius definition of a base.
### Conclusion:
- Based on the definition of an Arrhenius base, the reaction that involves the increase of [tex]\(\text{OH}^{-}\)[/tex] ions concentration is Reaction 1:
[tex]\[
\text{NaOH (s)} \rightarrow \text{Na}^{+} (\text{aq}) + \text{OH}^{-} (\text{aq})
\][/tex]
- Therefore, the reaction that displays an example of an Arrhenius base is Reaction 1.
