What is the molality of ammonia in a solution containing 0.85 g of `NH^3` in 100 cm of a liquid of density `0.85 g cm^(-3)`?

Answer

To find the molality of ammonia in the solution, we will follow these steps:

### Step 1: Calculate the number of moles of ammonia (NH₃)
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of NH₃ = 0.85 g
- Molar mass of NH₃ = 14 (N) + 1*3 (H) = 17 g/mol

Calculating the moles:
\[ \text{Number of moles of NH₃} = \frac{0.85 \text{ g}}{17 \text{ g/mol}} = 0.05 \text{ moles} \]

### Step 2: Calculate the mass of the solution
We know the volume of the solution and its density. The mass of the solution can be calculated using the formula:
\[ \text{Mass of solution} = \text{Volume} \times \text{Density} \]
Given:
- Volume of solution = 100 cm³ = 100 mL
- Density = 0.85 g/cm³

Calculating the mass of the solution:
\[ \text{Mass of solution} = 100 \text{ cm}^3 \times 0.85 \text{ g/cm}^3 = 85 \text{ g} \]

### Step 3: Calculate the mass of the solvent
The mass of the solvent can be calculated by subtracting the mass of ammonia from the mass of the solution:
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of NH₃} \]
Calculating the mass of the solvent:
\[ \text{Mass of solvent} = 85 \text{ g} - 0.85 \text{ g} = 84.15 \text{ g} \]

### Step 4: Convert the mass of the solvent to kilograms
To convert grams to kilograms, we divide by 1000:
\[ \text{Mass of solvent in kg} = \frac{84.15 \text{ g}}{1000} = 0.08415 \text{ kg} \]

### Step 5: Calculate the molality of ammonia
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[ \text{Molality} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]
Calculating the molality:
\[ \text{Molality} = \frac{0.05 \text{ moles}}{0.08415 \text{ kg}} \approx 0.59 \text{ mol/kg} \]

### Final Answer:
The molality of ammonia in the solution is approximately **0.59 mol/kg**.

---