Math Problem Statement

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

Solution

To find the mass of NH3\text{NH}_3 required to make a 0.250 molal (mm) solution in 475 g of methanol, we can use the definition of molality:

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

Step 1: Rearrange the formula to solve for moles of NH3\text{NH}_3

Moles of NH3=Molality (m)×Mass of solvent in kg\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

Mass of solvent in kg=475 g1000=0.475 kg\text{Mass of solvent in kg} = \frac{475 \text{ g}}{1000} = 0.475 \text{ kg}

Step 3: Calculate the moles of NH3\text{NH}_3

Moles of NH3=0.250m×0.475kg=0.11875moles\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 NH3\text{NH}_3

  • Nitrogen (N): 14.01 g/mol
  • Hydrogen (H): 1.008 g/mol (there are 3 hydrogen atoms)

Molar mass of NH3=14.01+(3×1.008)=17.034 g/mol\text{Molar mass of } \text{NH}_3 = 14.01 + (3 \times 1.008) = 17.034 \text{ g/mol}

Step 5: Calculate the mass of NH3\text{NH}_3

Mass of NH3=Moles of NH3×Molar mass of NH3\text{Mass of } \text{NH}_3 = \text{Moles of } \text{NH}_3 \times \text{Molar mass of } \text{NH}_3

Mass of NH3=0.11875moles×17.034g/mol2.022g\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 NH3\text{NH}_3 that must be dissolved in 475 g of methanol to make a 0.250 mm 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.

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Math Problem Analysis

Mathematical Concepts

Molality
Molar mass calculation
Unit conversion

Formulas

Molality (m) = moles of solute / mass of solvent in kg
Molar mass of NH3 = 14.01 + (3 * 1.008)

Theorems

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Suitable Grade Level

High School