Question

Calculate the mass/volume percent \((\mathrm{m} / \mathrm{v})\) for the solute in each of the following solutions: a. \(2.50 \mathrm{~g}\) of \(\mathrm{LiCl}\) in \(40.0 \mathrm{~mL}\) of \(\mathrm{LiCl}\) solution b. \(7.5 \mathrm{~g}\) of casein in \(120 \mathrm{~mL}\) of low-fat milk

Short answer

For both solutions, the mass/volume percent \((\mathrm{m} / \mathrm{v})\) is 6.25 \%.

Step-by-step solution

- Understand the Formula for Mass/Volume Percent

The formula for calculating mass/volume percent \((\mathrm{m} / \mathrm{v})\) is given by: \[ \text{mass/volume percent} = \left( \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \right) \times 100 \% \] This formula will be used to find the answer for each part of the problem.

- Calculate \( \mathrm{m} / \mathrm{v} \) for Part (a)

Given: Mass of \(\text{LiCl}\) = 2.50 g; Volume of solution = 40.0 mL. Using the formula: \[ \text{mass/volume percent} = \left( \frac{2.50 \text{~g}}{40.0 \text{~mL}} \right) \times 100 \% = 6.25 \% \] Thus, the mass/volume percent for part (a) is 6.25 \%.

- Calculate \(\textrm{m} / \mathrm{v} \) for Part (b)

Given: Mass of casein = 7.5 g; Volume of solution = 120 mL. Using the formula: \[ \text{mass/volume percent} = \left( \frac{7.5 \text{~g}}{120 \text{~mL}} \right) \times 100 \% = 6.25 \% \] Therefore, the mass/volume percent for part (b) is 6.25 \%.

Key concepts

solute concentration

Solute concentration refers to the amount of solute present in a given quantity of solution. In the case of mass/volume percent, it measures how many grams of solite are present in 100 mL of solution. This is an essential concept in chemistry because it helps in understanding and preparing solutions with desired properties. For example, in our problem, the solute is either LiCl or casein, and the solvent is water or low-fat milk. To calculate the concentration, use the formula: mass of solute divided by the total volume of the solution, then multiply by 100 to get a percentage. This easily shows how concentrated the solution is.

mass-volume relationship

The mass-volume relationship is crucial for calculating solution concentrations. It links the weight of the solute (given in grams) with the total volume of the solution (usually given in milliliters). For the given exercise, you need to know two things: the mass of the solute, such as 2.50 grams of LiCl or 7.5 grams of casein, and the volume of the solution, like 40.0 mL of LiCl solution or 120 mL of low-fat milk. By applying the formula, you can find out the mass/volume percent effectively. This relationship makes it easier to prepare solutions by measuring the right amount of solute needed for a specific volume of solvent.

solution preparation

To prepare a solution accurately, you must consider both the solute and the solvent. The exercise illustrates how to calculate the mass/volume percent for this purpose. Here’s how you can do it step by step:
First, measure the exact mass of the solute you’ll be using. For instance, taking 2.50 grams of LiCl or 7.5 grams of casein.
Next, measure the volume of the solvent with precision. In this case, 40.0 mL of water or 120 mL of low-fat milk.
Finally, mix the solute thoroughly into the solvent until completely dissolved. This ensures the final solution has a uniform concentration throughout. By using the formula for mass/volume percent, you can easily verify if you have prepared the solution correctly. This method helps in creating solutions with precise concentrations, which is essential for experiments and various applications in chemistry.