A bottle contains \(1.00 \mathrm{~L}\) of a stock solution of \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) of unknown concentration. A lab technician dilutes \(5.00 \mathrm{~mL}\) of the stock solution to \(100.0 \mathrm{~mL}\) with water. He then determines the \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) concentration of this solution to be \(0.0478 \mathrm{M}\). What is the \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) concentration of the stock solution?

Understanding the dilution formula is essential in determining the concentration of a solution after it has been diluted. It's represented by the equation:
\[ C_1 \times V_1 = C_2 \times V_2 \]
Here, \( C_1 \) is the concentration of the original solution, and \( V_1 \) is its volume, while \( C_2 \) is the concentration of the diluted solution, and \( V_2 \) is the final volume after dilution. The principle behind the formula is based on the conservation of moles; the number of moles of solute before dilution (\( C_1 \times V_1 \)) is equal to the number of moles after dilution (\( C_2 \times V_2 \)). When a solution is diluted with a solvent, the quantity of solute remains the same, but the volume increases, leading to a decrease in concentration.
In terms of practical application, when you know three of these variables, you can easily calculate the fourth one. This is particularly useful in laboratories when preparing solutions with precise concentrations for experiments.

Molarity, often symbolized as \( M \), is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The unit for molarity is moles per liter (mol/L). Mathematically, molarity can be expressed as:
\[ M = \frac{n}{V} \]
where \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. Molarity is a critical concept in stoichiometry because it directly relates the volume of a solution to the amount of substance in moles, making it possible to determine the quantity of a reactant or product in a chemical reaction. When calculating molarity, ensure that you use correct units for volume (liters) and account for the purity and molecular weight of the substance to find the number of moles accurately.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the substances as they participate in various chemical reactions. It is grounded in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction, leading to predictable relationships between reactants and products.
Core Concepts in Stoichiometry:

• Atomic and molecular mass, which are used to calculate the number of moles in a given mass of a substance.
• The mole concept, which allows chemists to convert between mass, particle number, and gas volume at standard temperature and pressure (STP).
• Reaction coefficients, which indicate the proportional amount of reactants and products in a balanced chemical equation.
• The limiting reactant, which restricts the amount of product formed in a reaction.

This branch of chemistry helps in calculating the amount of reactants needed to produce a certain amount of product or the quantity of products that can be synthesized from given reactants. Proper application of stoichiometric principles is critical when it comes to chemical solution preparation to avoid excesses and deficiencies of reactants.

Preparing a chemical solution of a desired molarity is a fundamental laboratory skill in chemistry. It involves dissolving a specified amount of solute, typically in the form of a solid, into a solvent to reach a specific volume. The steps include:
Steps to Prepare a Chemical Solution:

• Determining the desired molarity and volume of the solution needed.
• Calculating the amount of solute required using stoichiometry and the molar mass of the solute.
• Accurately weighing the solute and dissolving it in a portion of the solvent.
• Transferring the solution to a volumetric flask and adding solvent up to the desired volume mark.

It's crucial to mix the solution thoroughly to ensure homogeneity. Factors such as temperature and purity of the reagents can affect the final concentration, so it's recommended to adjust conditions and calculate concentrations with precision. This meticulous process ensures that the chemical reactions performed will have predictable and reproducible results.