To solve the problem, we need to address each of the requested calculations step by step. The problem involves the preparation of a solution where 10.00 g of KNO₃ (Potassium Nitrate) is dissolved in water to obtain a solution with a mass percentage of 10.00%.

Let's break down the problem:

1. Mass Percentage (Given)

• Mass of KNO₃ (solute) = 10.00 g
• Mass % of KNO₃ = 10.00%

2. Mass of Solution Calculation

The mass percentage is given by the formula:

\text{Mass %} = \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \times 100

Rearranging to find the mass of the solution:

\text{Mass of Solution} = \frac{\text{Mass of Solute} \times 100}{\text{Mass %}} = \frac{10.00 \times 100}{10.00} = 100.00 \, \text{g}

So, the total mass of the solution is 100.00 g.

3. Molality Calculation

Molality is defined as:

$\text{Molality} = \frac{\text{Moles of Solute}}{\text{Mass of Solvent (in kg)}}$

• Molar mass of KNO₃ = 101.1 g/mol

Moles of KNO₃:

$\text{Moles of KNO₃} = \frac{10.00 \, \text{g}}{101.1 \, \text{g/mol}} = 0.0989 \, \text{mol}$

Mass of solvent (water) = Mass of solution - Mass of solute = 100.00 g - 10.00 g = 90.00 g = 0.0900 kg

Molality:

$\text{Molality} = \frac{0.0989 \, \text{mol}}{0.0900 \, \text{kg}} = 1.10 \, \text{mol/kg}$

4. Parts per Million (ppm) Calculation

PPM is defined as:

$\text{ppm} = \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \times 10^6$

$\text{ppm} = \frac{10.00 \, \text{g}}{100.00 \, \text{g}} \times 10^6 = 100,000 \, \text{ppm}$

5. Parts per Billion (ppb) Calculation

PPB is defined as:

$\text{ppb} = \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \times 10^9$

$\text{ppb} = \frac{10.00 \, \text{g}}{100.00 \, \text{g}} \times 10^9 = 100,000,000 \, \text{ppb}$

6. Molarity Calculation

Molarity is defined as:

$\text{Molarity} = \frac{\text{Moles of Solute}}{\text{Volume of Solution (in L)}}$

To find the volume of the solution, we use the specific gravity (sp.gr.):

$\text{Volume of Solution} = \frac{\text{Mass of Solution}}{\text{Specific Gravity}} = \frac{100.00 \, \text{g}}{1.0650 \, \text{g/mL}} = 93.90 \, \text{mL} = 0.0939 \, \text{L}$

Molarity:

$\text{Molarity} = \frac{0.0989 \, \text{mol}}{0.0939 \, \text{L}} = 1.05 \, \text{M}$

Final Answers:

• Molality: 1.10 mol/kg
• PPM: 100,000 ppm
• PPB: 100,000,000 ppb
• Molarity: 1.05 M

Would you like any details or have any questions about these calculations?

Related Questions:

1. How would the molality change if the mass percentage of the solute were 20% instead of 10%?
2. What effect would changing the solvent from water to ethanol have on the molality of the solution?
3. How does specific gravity influence the calculation of molarity?
4. Can you explain the difference between molality and molarity in terms of practical applications?
5. If more KNO₃ were added to the solution, how would ppm and ppb values change?

Tip:

When preparing solutions, always remember that molality is temperature-independent, while molarity can vary with temperature due to the change in volume of the solvent.