Question

A student plans to divide the molarity of his solution by its volume to determine the number of moles of solvent in it. He is making two mistakes here. Identify the mistakes and correct both of them.

Short answer

The student's mistakes are: (1) confusing solute with solvent, as they are using molarity which measures the concentration of the solute, and (2) dividing molarity by volume, which would give the reciprocal of the volume, not the moles of solvent. To correct these, we should (1) use molality instead of molarity, which relates to solvent mass, and (2) use the relationship: molality = moles of solute / mass of solvent (in kg), to find the moles of solvent using its molar mass.

Step-by-step solution

Mistake 1: Confusing solute with solvent

The student wants to find the number of moles of solvent, but instead, they are using the molarity of the solution, which is actually a measure of the concentration of the solute in the solution. The relationship between molarity and moles of solute is given by M = moles of solute / volume of solution (in liters). It is important to distinguish between solute and solvent.

Correction 1: Use molality instead of molarity

To find the number of moles of solvent, we need to use the concept of molality (m), which is the ratio of moles of solute to the mass of the solvent (in kilograms). Given the molality of the solution, we can find the mass of the solvent and then use that information to find the number of moles of solvent.

Mistake 2: Dividing molarity by volume

The student plans to divide the molarity of the solution by its volume to find the number of moles of solvent. However, this calculation would actually give a value that represents the reciprocal of the volume, not the number of moles of solvent.

Correction 2: Use the proper relationship to find moles

To find the number of moles of solvent, we should use the relationship between molality, moles of solute, and mass of solvent: molality (m) = moles of solute / mass of solvent (in kg) If we know the molality of the solution and the moles of solute present, we can solve for the mass of the solvent (in kilograms) and then find the number of moles of solvent using its molar mass. This will give us the correct value for the moles of solvent in the solution.

Key concepts

Solute and Solvent Distinction

Understanding the difference between solute and solvent is fundamental in solution chemistry. A solution typically comprises two parts: the solute and the solvent. The solute is the substance that is dissolved. For instance, in a saltwater solution, salt is the solute.
On the other hand, the solvent is the substance in which the solute dissolves. In our saltwater example, water acts as the solvent.

Key points to remember about solutes and solvents:

• The solute is usually present in a smaller amount compared to the solvent.
• The solvent determines the state (solid, liquid, gas) of the overall solution.
• In most cases, changes to the solute concentration can influence the properties of the solvent, including boiling and freezing points.

With this clear distinction, we avoid common mistakes, such as confusing which component is in greater quantity or forgetting their specific roles in forming a solution.

Moles and Molar Concepts

Moles and molarity are essential concepts in chemistry that allow us to quantify substances. The concept of a mole is a fundamental unit in chemistry, equivalent to Avogadro's number, which is approximately 6.022 × 10²³ particles (atoms or molecules).

Molarity (M) is one way to express the concentration of a solution, defined as the number of moles of solute per liter of solution. The formula for molarity is given by:\[M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}.\]However, in this exercise, the student was correct in calculating the amount of solute, but mistakenly tried to apply molarity to find the moles of solvent. To accurately find moles of solvent, one must shift to molality or other methods.- **Molality ( m)** is a concentration measure expressed in moles of solute per kilogram of solvent:\[m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}.\]This distinction is crucial because using the wrong method can lead to inaccurate conclusions about the solution's composition.

Solution Chemistry Concepts

Understanding solution chemistry concepts is essential for analyzing and creating solutions effectively. A solution is a homogeneous mixture, which means it has a uniform composition throughout. Key properties of solutions include concentration, saturation, and the interactions of solute and solvent molecules.

Concentration describes the amount of solute dissolved in a solvent and is commonly expressed in terms of molarity, molality, or mass percent. Each measurement provides different insights and is used based on the solution's requirements, including its temperature stability or required concentration. - **Saturation**: A solution becomes saturated when it cannot dissolve any more solute. Upon reaching this point, any additional solute will remain undissolved unless there's a change in temperature. - **Intermolecular interactions**: The way solute molecules interact with solvent molecules affects properties like solubility, boiling point, and vapor pressure. These interactions are key in predicting how different substances will behave when mixed. Accurate understanding of these properties ensures you form solutions with desired characteristics. It also helps in troubleshooting any miscalculations or errors in formulation, like the ones highlighted in the exercise.