Problem 66 - Chemistry The Science in Context

Question

How many moles of solute are there in the following solutions? a. \(0.750 \mathrm{m}\) glucose solution made by dissolving the glucose in \(10.0 \mathrm{kg}\) of water b. \(0.183 \mathrm{m} \mathrm{Na}_{2} \mathrm{CrO}_{4}\) solution made by dissolving the \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) in \(900.0 \mathrm{g}\) of water c. \(1.425 \mathrm{m}\) urea solution made by dissolving the urea in \(750.0 \mathrm{g}\) of water

Step-by-Step Solution

Answer

Question: Calculate the moles of solute in the given solutions: a. A glucose solution with a molality of 0.750 m and a solvent mass of 10.0 kg. b. A sodium chromate (\(\mathrm{Na}_{2} \mathrm{CrO}_{4}\)) solution with a molality of 0.183 m and a solvent mass of 900.0 g. c. A urea solution with a molality of 1.425 m and a solvent mass of 750.0 g. Answer: a. 7.50 moles of glucose b. 0.1647 moles of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) c. 1.06875 moles of urea

Step 1: Identify the molality and mass of solvent for each solution.

For each solution, molality and mass of the solvent are given. We have the following information: a. Molality of glucose solution: 0.750 m; mass of solvent (water): 10.0 kg b. Molality of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) solution: 0.183 m; mass of solvent (water): 900.0 g (0.9 kg) c. Molality of urea solution: 1.425 m; mass of solvent (water): 750.0 g (0.75 kg)

Step 2: Calculate the moles of solute using the formula.

Next, we will use the formula Moles of solute = molality (m) × mass of solvent (kg) for each solution: a. Glucose solution: Moles of glucose = 0.750 m × 10 kg = 7.50 moles b. \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) solution: Moles of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) = 0.183 m × 0.9 kg = 0.1647 moles c. Urea solution: Moles of urea = 1.425 m × 0.75 kg = 1.06875 moles

Step 3: Present the final answer.

The moles of solute for each solution are as follows: a. Glucose solution: 7.50 moles of glucose b. \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) solution: 0.1647 moles of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) c. Urea solution: 1.06875 moles of urea

Key Concepts

Moles of Solute

When we talk about the "moles of solute," we are referring to the amount of the dissolved component, also known as the solute, present in a solution. The concept of moles allows us to quantify the number of molecules or atoms in a given sample. They are a fundamental unit in chemistry, providing a bridge between the atomic scale and the macroscopic world.

Molality ( \[m\]), a key parameter, is critical to finding the moles of solute in a solution. It is defined as the number of moles of solute per kilogram of solvent. This value helps us calculate the moles using the simple formula:

• Moles of solute = molality (\[m\]) \times mass of solvent (in kg)

In practical terms, knowing the moles of solute helps us understand how much of a substance is present in a particular volume of solution. It is also crucial for predicting the outcomes of chemical reactions involving the solution.

Mass of Solvent

The "mass of solvent" plays a crucial role in calculating molality and describing the concentration of a solution. The solvent is typically the component of a solution that is present in the greatest amount, and it serves as the medium in which the solute is dissolved.

In calculations involving molality, the mass of the solvent is expressed in kilograms. This uniformity ensures consistency and precision across various chemical calculations.

• When the solvent's mass is given in grams, as often is the case, it must be converted to kilograms (e.g., 900 g becomes 0.9 kg).
• This conversion is important because molality uses mass measured in kilograms, not grams.

To determine the moles of solute using molality, calculating the correct mass of solvent is essential. Without it, the relationship between the solvent's mass and the amount of solute in molality calculations would not accurately reflect the concentration of the solution.

Chemical Solutions

Chemical solutions are homogeneous mixtures comprising two or more substances. A solution is made of a solute and a solvent. The solute is the substance that gets dissolved, and the solvent is the substance it dissolves into.

Understanding solutions is fundamental as they play a vital role in nearly all chemical processes, from industrial production to biological functions.

• Solutions can be solid, liquid, or gas, but in most chemistry contexts like those involving aqueous solutions, they are liquids.
• Concentration metrics like molality, which depend on the moles of solute and mass of solvent, are crucial for describing solutions accurately.

This knowledge applies from everyday experiences, such as saltwater or sugar solutions, to complex laboratory and industrial applications. By mastering the concept of solutions, one gains the ability to predict how substances will behave in various environments.