Textbook Question
A 0.944 M solution of glucose, C6H12O6, in water has a density of 1.0624 g/mL at 20 °C. What is the concentration of this solution in the following units? (a) Mole fraction
Ch.13 - Solutions & Their Properties
Chapter 13, Problem 79
Lactose, C12H22O11, is a naturally occurring sugar found in mammalian milk. A 0.335 M solution of lactose in water has a density of 1.0432 g/L at 20 °C. What is the concentra- tion of this solution in the following units?(b) Mass percent
Verified step by step guidance1
Calculate the mass of lactose in 1 liter of solution. Use the molarity of the solution (0.335 M) which means there are 0.335 moles of lactose per liter. Multiply the number of moles by the molar mass of lactose (C12H22O11), which is approximately 342 g/mol.
Calculate the total mass of the solution. Since the density of the solution is 1.0432 g/mL, and there are 1000 mL in a liter, multiply the density by 1000 to find the mass of 1 liter of solution.
Determine the mass of lactose in grams per liter from step 1 and add this to the mass of water to confirm it matches the total mass calculated in step 2. This step serves as a check.
Calculate the mass percent of lactose in the solution. The mass percent is given by the formula: (mass of solute / mass of solution) x 100%. Use the mass of lactose from step 1 and the total mass of the solution from step 2.
Express the final result as a percentage to find the mass percent concentration of lactose in the solution.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molarity
Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this case, a 0.335 M solution of lactose indicates that there are 0.335 moles of lactose in every liter of the solution. Understanding molarity is essential for converting between different concentration units, such as mass percent.
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Molarity
Density
Density is the mass of a substance per unit volume, typically expressed in grams per liter (g/L) or grams per cubic centimeter (g/cm³). The density of the lactose solution at 1.0432 g/L is crucial for calculating the mass of the solution, which is necessary for determining mass percent. It allows us to relate the volume of the solution to its total mass.
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Mass Percent
Mass percent is a way of expressing the concentration of a component in a mixture, calculated as the mass of the solute divided by the total mass of the solution, multiplied by 100. To find the mass percent of lactose in the solution, one must first determine the mass of lactose and the total mass of the solution using the molarity and density values provided.
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Related Practice
Textbook Question
A 0.944 M solution of glucose, C6H12O6, in water has a density of 1.0624 g/mL at 20 °C. What is the concentration of this solution in the following units? (b) Mass percent
Textbook Question
A 0.944 M solution of glucose, C6H12O6, in water has a density of 1.0624 g/mL at 20 °C. What is the concentration of this solution in the following units? (c) Molality
Textbook Question
Look at the solubility graph in Figure 13.7, and estimate which member of each of the following pairs has the higher molar solubility at the given temperature.(b) CH3CO2Na or glucose at 20 °C