Calculate the number of moles and the mass of the solute in each of the following solutions: (a) \(325 \mathrm{mL}\) of \(8.23 \times 10^{-5} \mathrm{M} \mathrm{KI}\), a source of iodine in the diet. (b) 75.0 mL of 2.2 \(\times 10^{-5} \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\), a sample of acid rain. (c) 0.2500 L of 0.1135 \(M\) K \(_{2}\) CrO \(_{4}\), an analytical reagent used in iron assays. (d) \(10.5 \mathrm{L}\) of \(3.716 M\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4},\) a liquid fertilizer.

Understanding the relationship between molarity and volume is crucial for solving many chemistry problems involving solutions. Molarity, denoted as M, is a measure of concentration that represents the number of moles of a solute contained in one liter of solution. It tells us how 'concentrated' or 'dilute' a solution is.

To find the number of moles of a solute in a given volume of solution, you simply multiply the molarity by the volume in liters. This process is often summarized with the formula: \[ \text{moles} = \text{Molarity} \times \text{Volume in liters} \].

When working with volumes that are not in liters, like milliliters (mL), one must convert them to liters by dividing by 1000, because molarity is based on liters of solution. This step is essential to ensure that units are consistent, allowing for accurate calculations. It's the starting point for determining the amount of any solute needed for a reaction or present in a sample.

Once the number of moles of a solute in a solution is known from the molarity and volume, the next step often requires finding the solute's mass. This process is essential in various fields, from cooking to pharmaceuticals, and of course, in chemical laboratories.

The mass of a solute is found by multiplying the number of moles by the solute's molar mass. The molar mass (in grams per mole, g/mol) is a constant value that represents the mass of one mole of substance. Thus, the formula used is: \[ \text{Mass of solute} = \text{Number of moles} \times \text{Molar mass} \].

By understanding the concept of molar mass and its role in this calculation, you can determine the specific mass of any solute required to make a solution of a desired concentration or to react entirely with another substance. The accurate determination of solute mass is a fundamental step in preparing solutions for lab experiments and industrial processes alike.

The molar mass of a compound is a critical value in chemistry that serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. It is the mass of one mole of that compound and is expressed in grams per mole (g/mol).

To find the molar mass of a compound, one must sum the molar masses of all the individual elements within the chemical formula, taking into account their respective amounts. For instance, the molar mass of water (\(\mathrm{H_2O}\)) would be calculated by adding together the molar masses of hydrogen (\(2 \times 1.008 \text{g/mol}\)) and oxygen (\(1 \times 16.00 \text{g/mol}\)).

Thus, the ability to calculate molar mass is fundamental to many aspects of chemistry, whether you're interested in the mass of a reactant needed for a reaction or determining the mass of a product. In the exercises provided, knowing the molar mass of KI, H2SO4, K2CrO4, and (NH4)2SO4 is vital for converting moles into grams to find the mass of each solute. Remember, while the numbers may vary, the method of determining molar mass remains constant.