To determine which of the given substances is an Arrhenius acid, we need to recall the definition of an Arrhenius acid. An Arrhenius acid is a substance that increases the concentration of [tex]\( \text{H}^+ \)[/tex] ions when dissolved in water.
Let's analyze each of the given substances:
1. [tex]\( \text{BF}_3 \)[/tex]: Boron trifluoride is not an Arrhenius acid. It is known to act as a Lewis acid because it can accept a pair of electrons, but it does not release [tex]\( \text{H}^+ \)[/tex] ions in solution.
2. HCN (Hydrogen cyanide): When hydrogen cyanide dissolves in water, it partially ionizes to produce [tex]\( \text{H}^+ \)[/tex] ions:
[tex]\[
\text{HCN} \rightarrow \text{H}^+ + \text{CN}^-
\][/tex]
Therefore, HCN is an Arrhenius acid as it increases the concentration of [tex]\( \text{H}^+ \)[/tex] ions in aqueous solution.
3. [tex]\( \text{NH}_3 \)[/tex]: Ammonia (NH₃) is not an Arrhenius acid. Instead, it acts as a base in water by accepting [tex]\( \text{H}^+ \)[/tex] ions to form [tex]\( \text{NH}_4^+ \)[/tex]:
[tex]\[
\text{NH}_3 + \text{H}_2\text{O} \rightarrow \text{NH}_4^+ + \text{OH}^-
\][/tex]
4. [tex]\( \text{Mg(OH)}_2 \)[/tex]: Magnesium hydroxide is a base, not an acid. It dissociates in water to produce [tex]\( \text{OH}^- \)[/tex] ions:
[tex]\[
\text{Mg(OH)}_2 \rightarrow \text{Mg}^{2+} + 2\text{OH}^-
\][/tex]
Based on this analysis, the correct substance among the given choices that functions as an Arrhenius acid is HCN (Hydrogen cyanide).
Thus, the answer is:
[tex]\[
\boxed{2}
\][/tex]
