ppm of sucrose in aqueous solution of sucrose is 341.88. Find the molality of solution.

To find the molality of a sucrose solution when you know the parts per million (ppm), you can follow a systematic approach. In this case, you have a sucrose concentration of 341.88 ppm. Let's break down the steps to calculate the molality of the solution.

Understanding ppm and its Relation to Molality

Parts per million (ppm) is a way of expressing very dilute concentrations. Specifically, 341.88 ppm means that there are 341.88 grams of sucrose in one million grams of solution. To convert this into molality, we need to understand the relationship between mass, moles, and the solvent's mass.

Step-by-Step Calculation

• Convert ppm to grams of solute: Since 341.88 ppm indicates 341.88 grams of sucrose in 1,000,000 grams of solution, we can express this as:
• Mass of sucrose (solute): 341.88 g
• Mass of solution: 1,000,000 g

Next, we need to find the mass of the solvent (water) in the solution. The mass of the solvent can be calculated by subtracting the mass of the solute from the total mass of the solution:

• Mass of solvent (water): 1,000,000 g - 341.88 g = 999,658.12 g

Calculating Moles of Sucrose

To find the molality, we need to convert the mass of sucrose into moles. The molar mass of sucrose (C₁₂H₂₂O₁₁) is approximately 342.30 g/mol. Using this, we can calculate the number of moles of sucrose:

• Moles of sucrose: Number of moles = Mass (g) / Molar mass (g/mol) Number of moles = 341.88 g / 342.30 g/mol ≈ 0.999 moles

Finding Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. Since we have the number of moles of sucrose and the mass of the solvent in grams, we can convert the mass of the solvent to kilograms:

• Mass of solvent in kg: 999,658.12 g = 999.658 kg

Now we can calculate the molality:

• Molality (m): Molality = Moles of solute / Mass of solvent (kg) Molality = 0.999 moles / 999.658 kg ≈ 0.001 m

Final Result

The molality of the sucrose solution with a concentration of 341.88 ppm is approximately 0.001 m. This means there is about 0.001 moles of sucrose per kilogram of water in the solution. Understanding these calculations can help you grasp how concentrations are related in different contexts, whether in chemistry labs or real-world applications.