Calculate the molarity of the solutions made by mixing \(175 \mathrm{~mL}\) of \(3.0 \mathrm{M} \mathrm{HCl}\) with the following: (a) \(250 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}\) (b) \(115 \mathrm{~mL}\) of \(6.0 \mathrm{M} \mathrm{HCl}\)

Understanding the concentration of solutions is fundamental when working with chemicals in a lab setting or studying chemistry. The concentration tells us how much of a solute is dissolved within a given volume of solvent, and is a measure of the strength of the solution. Molarity, represented by the symbol M, is one of the most common units for expressing concentration. It is defined as the number of moles of solute per liter of solution.

To calculate molarity, use the formula: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]. This requires knowing both the quantity of the solute in moles and the total volume of the solution in liters. For instance, if you dissolve 1 mole of a substance in exactly 1 liter of water, the solution is 1 Molar (1 M). However, if you dissolve the same amount in 2 liters of water, the concentration drops to 0.5 M. The reason for this is because the solute has more space to spread out, effectively reducing its concentration.

The process of dilution involves adding more solvent to a solution without adding more solute, thereby decreasing the solution's concentration. Dilution is a critical concept in practical chemistry where precise concentrations are necessary for reactions or analyses. The key to calculating dilutions is the conservation of moles of solute—as the solvent volume increases, the number of moles remains unchanged, but the molarity decreases.

The dilution equation, which is derived from the definition of molarity, can be expressed as: \[ M_{1}V_{1} = M_{2}V_{2} \]. Here, \(M_1\) and \(V_1\) are the molarity and volume of the initial solution, and \(M_2\) and \(V_2\) are the molarity and volume of the final diluted solution. This formula indicates that the product of the initial concentration and volume is equal to the product of the final concentration and volume. Therefore, if you know any three of these values, you can calculate the fourth.

Example of Dilution

Imagine you have a solution of 3 M HCl and you add water to it, making the final volume larger. Since the number of moles of HCl remains constant, the final molarity will be lower than the initial 3 M, depending on the final volume of the solution.

Stoichiometry is a branch of chemistry that involves calculating the relative quantities of reactants and products involved in chemical reactions. It is based on the conservation of mass and the concept of moles, allowing chemists to predict the amounts of substances consumed and produced in a given reaction. For reactions in solution, stoichiometry often requires an understanding of molarity to quantify the reactants.

When solving stoichiometry problems, it's essential to balance the chemical equation to ensure that the number of atoms for each element is the same on the reactants side as on the products side. The balanced equation then provides the mole ratios needed to convert between quantities of different substances.

Using Stoichiometry in Solutions

When mixing solutions of reactants, you use stoichiometry to find out how much product can form from given quantities of reactants. This involves molarity calculations to ensure reactants are in the correct proportions as dictated by the balanced equation. If solutions of different molarities are mixed, the resulting molarity can be found through stoichiometry, considering the volumes and molarities of the mixed solutions.