`HN_(3)` (hydroazic acid) is a weak acid dissociating as: `HN_(3) hArr H^(o+) + N_(3)^(Θ)`. Find the concentration of `Ag^(Θ)` ions, if excess of solid `AgN_(3)` is added to a solution maintained at `pH = 4`. The ionisation constant `K_(a)` of `HN_(3)` is `2.0 xx 10^(-5)`. The solubility of `AgN_(3)` in pure water is found to be `5.4 xx 10^(-3)` at `25^(@)C`.

Explanation

To solve the problem, we need to determine the concentration of \( \text{Ag}^+ \) ions in a solution where hydroazic acid (\( \text{HN}_3 \)) is present, and excess solid \( \text{AgN}_3 \) is added. The steps are as follows:

### Step 1: Understand the dissociation of \( \text{HN}_3 \)
The dissociation of hydroazic acid can be represented as:
\[ \text{HN}_3 \rightleftharpoons \text{H}^+ + \text{N}_3^- \]
The ionization constant (\( K_a \)) for this reaction is given as \( 2.0 \times 10^{-5} \).
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