The dissolution of ammonia gas in water does not obey Henry's law. On dissolving. a major portion of ammonia molecules unite with `H_(2),O` to form `NH_(4),OH` molecules. A portion of the latter again dissociates into `NH_(4)^(+)`, and `OH^(-)` ions. In solution thercfore, we have `NH_(3)`, molecules, `NH_(4),OH` molecules and `NH_(4)^(+)`, ions and the following equilibrium exist:
`NH_(3(g))` (pressure P and concentration c) `rarr NH_(3(l)) + H_(2),Orarr NH_(4),OH rarr NH_(4)^(+) rarr,+OH^(-)`
Let `c_(1)`,mol/L of `NH_(3)`, pass in liquid state which on dissolution in water forms `c_(2)` mol/ L of `NH_(4),OH.` The solution contains `c_(3)`mol/L of `NH_(4)^(+)`, ions.
Total concentration of undissociated ammonium hydroxide is

Options

A. `C_(1)`
B. `C_(1)+C_(2)+C_(3)`
C. `C_(1)+C_(3)`
D. `C_(2)-C_(3)`

Answer

To solve the problem, we need to analyze the dissolution of ammonia in water and the resulting equilibrium. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding the Dissolution Process
When ammonia gas (NH₃) dissolves in water, it forms ammonium hydroxide (NH₄OH). This process can be represented as:
\[ \text{NH}_3(g) \rightleftharpoons \text{NH}_3(l) + \text{H}_2O \rightleftharpoons \text{NH}_4OH \rightleftharpoons \text{NH}_4^+ + \text{OH}^- \]

### Step 2: Defining Concentrations
Let:
- \( c_1 \) = concentration of NH₃ in liquid state (mol/L)
- \( c_2 \) = concentration of NH₄OH formed (mol/L)
- \( c_3 \) = concentration of NH₄⁺ ions in solution (mol/L)

### Step 3: Establishing Relationships
From the equilibrium established, we know that:
- A portion of NH₄OH dissociates into NH₄⁺ and OH⁻ ions.
- The concentration of undissociated NH₄OH can be calculated using the relationship between these concentrations.

### Step 4: Calculating Undissociated NH₄OH
The total concentration of undissociated ammonium hydroxide (NH₄OH) can be expressed as:
\[ \text{Undissociated NH}_4OH = c_2 - c_3 \]

This equation indicates that the total concentration of NH₄OH formed (\( c_2 \)) minus the concentration of NH₄⁺ ions (\( c_3 \)) gives us the concentration of undissociated NH₄OH.

### Final Expression
Thus, the total concentration of undissociated ammonium hydroxide is:
\[ \text{Total concentration of undissociated NH}_4OH = c_2 - c_3 \]

### Summary
The final answer for the total concentration of undissociated ammonium hydroxide is \( c_2 - c_3 \).

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