Problem 210 - Introductory Chemistry Atoms First

Question

When \(5.00 \mathrm{~g}\) of a solute is dissolved in sufficient solvent to produce \(100.0 \mathrm{~mL}\) of solution, (a) What is the percent by mass/volume concentration of the solute? (b) What additional information do you need to calculate the percent by mass concentration of the solute, and how would you calculate that concentration once you had the missing information?

Step-by-Step Solution

Answer

The percent by mass/volume concentration of the solute in the solution is 5.00%. To calculate the percent by mass concentration, we would need to know the mass of the solvent or the total mass of the solution. With this information, we can use the formula \( \frac{Mass\: of\: solute}{Total\: mass\: of\: solution}\times 100\% \) or \( \frac{Mass\: of\: solute}{Mass\: of\: solute + Mass\: of\: solvent}\times 100\% \) to find the percent by mass concentration of the solute.

Step 1: Determine the mass and volume of the solution

We are given the mass of the solute (5.00 g) and the volume of the solution (100.0 mL).

Step 2: Calculate the percent by mass/volume concentration

To find the percent by mass/volume concentration, we will use the formula: \[ Percent\: by\: mass/volume\: concentration\ = \frac{Mass\: of\: solute}{Volume\: of\: solution}\times 100\%\] Now, substitute the given values and solve for the percent by mass/volume concentration: \[\frac{5.00 \mathrm{~g}}{100.0 \mathrm{~mL}} \times 100\% = 5.00 \% \] Therefore, the percent by mass/volume concentration of the solute in the solution is 5.00%. #b) Additional information required to calculate percent by mass concentration#

Step 1: Identify the missing information

To calculate the percent by mass concentration of the solute, we need to know the mass of the solvent or the total mass of the solution.

Step 2: Calculate the percent by mass concentration

If we have the missing information (mass of solvent or total mass of the solution), we can calculate the percent by mass concentration using the formula. Percent by mass concentration: \[ \frac{Mass\: of\: solute}{Total\: mass\: of\: solution}\times 100\% \] If we are given the mass of solvent, the formula becomes: \[ \frac{Mass\: of\: solute}{Mass\: of\: solute + Mass\: of\: solvent}\times 100\% \] Once we have the missing information, we can substitute the values and calculate the percent by mass concentration of the solute in the solution.

Key Concepts

Understanding Percent by Mass/Volume

Percent by mass/volume is a useful way of expressing the concentration of a solution, especially when dealing with a solid solute and a liquid solvent. This measure indicates how many grams of solute are present in 100 milliliters of the solution. It is calculated as follows:

• Mass of solute: The weight of the dissolved substance, often given in grams.
• Volume of solution: The total volume of the solution after the solute is dissolved, usually measured in milliliters.

To find the percent by mass/volume, use the formula: \[ \text{Percent by mass/volume} = \frac{\text{Mass of solute}}{\text{Volume of solution}} \times 100\% \]In the given exercise, with a solute mass of 5.00 g and a solution volume of 100.0 mL, the calculation is: \[ \frac{5.00 \text{ g}}{100.0 \text{ mL}} \times 100\% = 5.00\% \]This tells us that in every 100 mL of the solution, there are 5 grams of the solute.

Exploring Solute and Solvent

Understanding the roles of solute and solvent in a solution is fundamental in chemistry. Here is what differentiates them:

• Solute: This is the substance that is dissolved in a solution. In the context of our exercise, the solute is the material that weighs 5.00 g.
• Solvent: This is the substance that dissolves the solute, and often exists in a greater quantity. In most cases involving solutions with a liquid phase, the solvent is usually a liquid such as water or alcohol.

The interaction between solute and solvent dictates the properties of the solution. The concentration of the solution depends on how much solute is being dissolved by the solvent. If you wanted to determine the percent by mass concentration, knowledge about the total mass of these components would be necessary as well.

Solution Preparation Guidelines

Preparing a solution requires careful measurement and mixing to achieve the desired concentration. Here’s a simple guideline to follow:

• Measure the Solute: Use an accurate scale to measure the exact mass of the solute. This precision is crucial for correct concentration calculations.
• Prepare the Solvent: Before adding the solute, ensure that the volume of the solvent is ready. For instance, in our case, you would ensure to have the solvent volume that will, combined with the solute, give the final desired solution volume.
• Mix until Homogeneous: Add the solute into the solvent and stir thoroughly. Ensure that the solute fully dissolves to create a uniform solution.

Problem-solving often involves adjusting the solution parameters based on the concentration you obtain. For example, if additional solute or solvent is added, it would affect the final concentration. Understanding how to manipulate these aspects is key in laboratory settings.