What is the molality of a solution that has 3 mol of glucose in 6 kg of water?
A. $\frac{6 kg}{3 mol}$
B. $\frac{3 mol}{6 L}$
C. $\frac{3 kg}{6 L}$
D. $\frac{3 mol}{6 kg}$
Answer (2)
Define molality as moles of solute per kilogram of solvent.
Use the formula: Molality = Kilograms of solvent Moles of solute .
Substitute the given values: Molality = 6 kg 3 mol .
Calculate the molality: Molality = 0.5 kg mol . The answer is 6 k g 3 m o l .
Explanation
Understanding the Problem We are given a solution of glucose in water, and we need to find the molality of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. In this case, glucose is the solute and water is the solvent.
Stating the Formula We are given that there are 3 moles of glucose and 6 kg of water. To find the molality, we will use the formula:
Molality = Kilograms of solvent Moles of solute
Substituting the Values Now, we substitute the given values into the formula:
Molality = 6 kg 3 mol
Calculating the Molality Next, we simplify the expression:
Molality = 6 3 kg mol = 0.5 kg mol
So, the molality of the solution is 0.5 mol/kg.
Final Answer The molality of the solution is 0.5 mol/kg, which corresponds to option D: 6 k g 3 m o l .
Examples
Molality is used in various applications, such as calculating the freezing point depression or boiling point elevation of solutions. For example, if you want to determine how much salt to add to water to prevent it from freezing at a certain temperature, you would use the molality of the salt solution in your calculations. This concept is also crucial in understanding colligative properties of solutions, which are properties that depend on the concentration of solute particles rather than the nature of the solute itself.
The molality of the solution, calculated as moles of solute per kilogram of solvent, is 0.5 mol/kg. This corresponds to option D: 6 k g 3 m o l .
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