How many grams of `NH_(4)NO_(3)` should be dissolved per litre of solution to have a ph of 5.13 ? `K_(b)` for `NH_(3)` iss `1.8 xx10^(3)`

Explanation

To solve the problem of how many grams of \( NH_4NO_3 \) (ammonium nitrate) should be dissolved per liter of solution to achieve a pH of 5.13, we can follow these steps:

### Step 1: Understand the Hydrolysis of the Salt
Ammonium nitrate (\( NH_4NO_3 \)) dissociates in water to form \( NH_4^+ \) (ammonium ion) and \( NO_3^- \) (nitrate ion). The ammonium ion can undergo hydrolysis to form \( NH_4OH \) (ammonium hydroxide) and \( H^+ \) ions, which will affect the pH of the solution.

### Step 2: Determine the pH and pKa
Given that the pH of the solution is 5.13, we can find the \( pK_a \) of the ammonium ion. Since \( pK_w = 14 \) at 25°C, we can calculate \( pK_a \) using the relationship:
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