What mass (in g) of NH3 must be dissolved in 475 g of methanol to make a 0.250 *m* solution?


To find the mass of \( \text{NH}_3 \) required to make a 0.250 molal (\( m \)) solution in 475 g of methanol, we can use the definition of molality:

\[
\text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}
\]

### Step 1: Rearrange the formula to solve for moles of \( \text{NH}_3 \)
\[
\text{Moles of } \text{NH}_3 = \text{Molality (m)} \times \text{Mass of solvent in kg}
\]

### Step 2: Convert the mass of methanol from grams to kilograms
\[
\text{Mass of solvent in kg} = \frac{475 \text{ g}}{1000} = 0.475 \text{ kg}
\]

### Step 3: Calculate the moles of \( \text{NH}_3 \)
\[
\text{Moles of } \text{NH}_3 = 0.250 \, m \times 0.475 \, \text{kg} = 0.11875 \, \text{moles}
\]

### Step 4: Calculate the molar mass of \( \text{NH}_3 \)
- Nitrogen (N): 14.01 g/mol
- Hydrogen (H): 1.008 g/mol (there are 3 hydrogen atoms)

\[
\text{Molar mass of } \text{NH}_3 = 14.01 + (3 \times 1.008) = 17.034 \text{ g/mol}
\]

### Step 5: Calculate the mass of \( \text{NH}_3 \)
\[
\text{Mass of } \text{NH}_3 = \text{Moles of } \text{NH}_3 \times \text{Molar mass of } \text{NH}_3
\]

\[
\text{Mass of } \text{NH}_3 = 0.11875 \, \text{moles} \times 17.034 \, \text{g/mol} \approx 2.022 \, \text{g}
\]

So, the mass of \( \text{NH}_3 \) that must be dissolved in 475 g of methanol to make a 0.250 \( m \) solution is approximately **2.022 g**.

Would you like more details or have any questions about this calculation?

Here are five related questions you might find helpful:
1. How do you calculate the molality of a solution given the mass of solute and solvent?
2. How does the density of a solvent affect the preparation of solutions?
3. What is the difference between molality and molarity?
4. How would you prepare a solution with a specific molality using a different solute?
5. What is the effect of temperature on the molality of a solution?

**Tip:** Molality is independent of temperature, making it particularly useful in situations where temperature varies.

Learn how to calculate the mass of NH3 required to prepare a 0.250 molal (m) solution in 475 g of methanol. Follow step-by-step instructions with detailed explanations on molality, molar mass calculation of NH3, and unit conversion. Suitable for high school students studying chemistry.

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