Math Problem Statement

A solution is prepared by dissolving 1.928 g of KNO3 into enough water to make 651 mL. What is the molarity of the solution?

Solution

To find the molarity of the solution, we need to use the formula:

Molarity (M)=moles of solutevolume of solution in liters\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}

Step 1: Calculate the moles of KNO3\text{KNO}_3

  1. Molar mass of KNO3\text{KNO}_3:
    • Potassium (K): 39.10 g/mol
    • Nitrogen (N): 14.01 g/mol
    • Oxygen (O): 16.00 g/mol (there are 3 oxygen atoms)

Molar mass of KNO3=39.10+14.01+(3×16.00)=101.11 g/mol\text{Molar mass of } \text{KNO}_3 = 39.10 + 14.01 + (3 \times 16.00) = 101.11 \text{ g/mol}

  1. Moles of KNO3\text{KNO}_3:

Moles of KNO3=1.928 g101.11 g/mol=0.01907 moles\text{Moles of } \text{KNO}_3 = \frac{1.928 \text{ g}}{101.11 \text{ g/mol}} = 0.01907 \text{ moles}

Step 2: Convert the volume of the solution from mL to L

Volume in liters=651 mL1000=0.651 L\text{Volume in liters} = \frac{651 \text{ mL}}{1000} = 0.651 \text{ L}

Step 3: Calculate the molarity

Molarity (M)=0.01907 moles0.651 L0.02928 M\text{Molarity (M)} = \frac{0.01907 \text{ moles}}{0.651 \text{ L}} \approx 0.02928 \text{ M}

The molarity of the KNO3\text{KNO}_3 solution is approximately 0.0293 M.

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 prepare a solution with a specific molarity?
  2. What is the molarity of a solution if you have different amounts of solute?
  3. How do you convert molarity to molality?
  4. What is the difference between molarity and molality?
  5. How does temperature affect the molarity of a solution?

Tip: Always ensure that the volume of the solution is in liters when calculating molarity.

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Math Problem Analysis

Mathematical Concepts

Molarity
Molar mass calculation
Unit conversion (mL to L)

Formulas

Molarity (M) = moles of solute / volume of solution in liters

Theorems

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Suitable Grade Level

High School