Textbook Question
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 (a) the mass percentage,
Ch.13 - Properties of Solutions
Chapter 13, Problem 48d
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 (d) the molarity of ascorbic acid in this solution.
Verified step by step guidance1
First, calculate the number of moles of ascorbic acid (C6H8O6) using its molar mass. The molar mass of C6H8O6 is calculated by adding the atomic masses of all the atoms in the formula: (6 * 12.01 g/mol for carbon) + (8 * 1.01 g/mol for hydrogen) + (6 * 16.00 g/mol for oxygen).
Next, use the formula for moles: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Substitute the mass of ascorbic acid (80.5 g) and the molar mass calculated in the previous step to find the number of moles of ascorbic acid.
Calculate the total volume of the solution in liters. Use the density of the solution (1.22 g/mL) to find the volume: \( \text{volume} = \frac{\text{mass of solution}}{\text{density}} \). The mass of the solution is the sum of the mass of ascorbic acid and the mass of water (80.5 g + 210 g). Convert the volume from mL to L by dividing by 1000.
Finally, calculate the molarity of the ascorbic acid solution using the formula: \( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \). Substitute the number of moles of ascorbic acid and the volume of the solution in liters to find the molarity.
Review the calculations to ensure all units are consistent and the steps are followed correctly to determine the molarity of the ascorbic acid solution.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molarity
Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). To calculate molarity, you need to know the amount of solute in moles and the total volume of the solution in liters. This concept is essential for understanding how concentrated a solution is and is commonly used in chemistry for preparing solutions.
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Molarity
Density
Density is defined as mass per unit volume and is typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). In this context, the density of the solution helps to convert the mass of the solution into volume, which is necessary for calculating molarity. Understanding density is crucial for determining how much space a given mass of solution occupies.
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Moles and Molar Mass
A mole is a unit in chemistry that represents 6.022 x 10²³ entities, such as atoms or molecules. The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). For ascorbic acid, knowing its molar mass allows you to convert grams of the substance into moles, which is a critical step in calculating molarity.
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Related Practice
Textbook Question
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,
Textbook Question
The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH3OH in 98.7 mL of CH3CN. (a) What is the mole fraction of methanol in the solution?
Textbook Question
The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH3OH in 98.7 mL of CH3CN. (b) What is the molality of the solution?
Textbook Question
The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH3OH in 98.7 mL of CH3CN. (c) Assuming that the volumes are additive, what is the molarity of CH3OH in the solution?