How many grams of water should you add to 32.5 g of sucrose, C12H22O11, to get a 0.850 m solution?

Verified step by step guidance

Step 1: Understand the definition of molality (m), which is the number of moles of solute per kilogram of solvent. The formula is: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).

Step 2: Calculate the moles of sucrose. First, find the molar mass of sucrose (C_{12}H_{22}O_{11}) by adding the atomic masses of all the atoms in the formula: \( 12 \times 12.01 + 22 \times 1.01 + 11 \times 16.00 \). Then, use the formula: \( \text{moles of sucrose} = \frac{\text{mass of sucrose}}{\text{molar mass of sucrose}} \).

Step 3: Rearrange the molality formula to solve for the mass of the solvent (water in this case): \( \text{kilograms of solvent} = \frac{\text{moles of solute}}{m} \).

Step 4: Convert the mass of the solvent from kilograms to grams by multiplying by 1000, since 1 kg = 1000 g.

Step 5: Calculate the total mass of water needed by subtracting the initial mass of sucrose from the mass of the solvent calculated in Step 4.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity and Molality

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution, while molality (m) is defined as the number of moles of solute per kilogram of solvent. In this question, we are dealing with molality, which is particularly useful when the temperature may affect the volume of the solution.

Calculating Moles

To find the number of moles of a substance, you can use the formula: moles = mass (g) / molar mass (g/mol). For sucrose, you need to calculate its molar mass by summing the atomic masses of its constituent elements, which is essential for determining how many moles are present in the given mass of sucrose.

Solution Preparation

When preparing a solution, it is important to understand the relationship between the solute, solvent, and the desired concentration. In this case, to achieve a specific molality, you must calculate the mass of water needed based on the moles of sucrose and the definition of molality, which requires knowing the mass of the solvent (water) in kilograms.

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