. In \(25 \mathrm{~g}\) of a \(7.5 \%\) by mass solution of \(\mathrm{CaSO}_{4}\) (a) how many grams of solute are present? (b) how many grams of solvent are present?

Understanding the relationship between solute and solvent is crucial in the study of solutions. In a solution, the solute is the substance that gets dissolved, while the solvent is the substance that does the dissolving. The mass of both components can tell us a lot about the solution's concentration. For instance, if you have a 25 g sample of a solution and you know that the solute makes up 7.5% of the total mass, a simple calculation will reveal the actual mass of the solute present.

To determine the solute mass, you would use the formula:
\[ \text{Mass of solute} = \left(\frac{\text{Percentage of solute}}{100}\right) \times \text{Total mass of solution} \].
Applying this to our problem gives us \(1.875\text{ g}\) of solute. Knowing the mass of the solute allows us to figure out how much of the sample is made up of the solvent. By subtracting the solute mass from the total mass of the solution, we get the mass of the solvent. In our problem, this means the solvent mass would be \(25\text{ g}\) - \(1.875\text{ g}\) = \(23.125\text{ g}\). This relationship is fundamental when it comes to preparing and understanding chemical solutions.

The concentration of a solution provides information on the proportion of solute in the solvent. It can be expressed in various ways, but one common method is the percent by mass, which compares the mass of the solute to the total mass of the solution. To calculate the percent by mass, you can use the formula:
\[ \text{Percent by mass} = \left(\frac{\text{Mass of solute}}{\text{Total mass of solution}}\right) \times 100 \% \].

Concentration calculations are vital when you're considering the potency or strength of a solution. In our example with \(25\text{ g}\) of a \(7.5\%\) by mass \(\text{CaSO}_4\) solution, we already know the percentage of solute, which allows us to work backward to find the actual mass of the solute and solvent in the solution.

The preparation of chemical solutions requires precise calculations and an understanding of the components involved—the solute and the solvent. Accuracy during this process is paramount, as it ensures the desired concentration of the resulting solution is achieved.

Essentially, when preparing a solution, you first decide on the desired concentration. Then, you calculate the amount of solute needed using the formula above. After weighing the accurate amount of solute, you dissolve it in an appropriate amount of solvent until the solute is completely dispersed, forming a homogeneous mixture.

For example, if you're asked to prepare a \(7.5\%\) solution of a substance like \(\text{CaSO}_4\), and you know the total mass of the solution you need, you can calculate and weigh out the exact amount of \(\text{CaSO}_4\) and then add enough solvent to obtain the final desired mass of the solution. Close attention and accurate measurement will ensure a successful preparation of the chemical solution.