Ascorbic acid (vitamin C, C₆H₈O₆) is a water-soluble vitamin. A solution containing 80.5 g of ascorbic acid dissolved in 210 g of water has a density of 1.22 g/mL at 55 °C. Calculate (c) the molality,

Verified step by step guidance

1. Identify the formula for molality: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).
2. Calculate the moles of ascorbic acid using its molar mass. The molar mass of C\(_6\)H\(_8\)O\(_6\) is calculated as follows: \( 6(12.01) + 8(1.01) + 6(16.00) \).
3. Convert the mass of the solvent (water) from grams to kilograms. Since the mass of water is 210 g, convert it to kilograms by dividing by 1000.
4. Use the moles of ascorbic acid and the kilograms of water to calculate the molality using the formula from step 1.
5. Ensure all units are consistent and check calculations for accuracy.

Key Concepts

Molality

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is particularly useful in situations where temperature changes may affect the volume of the solution, as it is based on mass rather than volume. The formula for calculating molality (m) is m = moles of solute / mass of solvent (in kg).

Moles of Solute

To calculate molality, one must first determine the number of moles of the solute, which in this case is ascorbic acid. The number of moles can be calculated using the formula: moles = mass (g) / molar mass (g/mol). The molar mass of ascorbic acid (C6H8O6) is approximately 176.12 g/mol, which is essential for converting grams of ascorbic acid into moles.

Density and Volume Relationship

Density is defined as mass per unit volume (g/mL), and it plays a crucial role in determining the volume of the solvent when given its mass. In this problem, the density of the solution is provided, allowing us to calculate the volume of the water used. Understanding the relationship between mass, density, and volume is essential for accurately determining the mass of the solvent in kilograms for the molality calculation.