Determine the volume of \(0.150 \mathrm{M} \mathrm{NaOH}\) solution required to neutralize each sample of hydrochloric acid. The neutralization reaction is: $$ \mathrm{NaOH}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q) $$ (a) \(25 \mathrm{~mL}\) of a \(0.150 \mathrm{M} \mathrm{HCl}\) solution (b) \(55 \mathrm{~mL}\) of a \(0.055 \mathrm{M} \mathrm{HCl}\) solution (c) \(175 \mathrm{~mL}\) of a \(0.885 \mathrm{M} \mathrm{HCl}\) solution

The concept of molarity is fundamental in understanding neutralization reactions, as it measures the concentration of a solution in terms of moles of solute per liter of solution. It's denoted by the letter 'M' and is calculated by dividing the number of moles of the solute by the volume of the solution in liters. In a chemical context, it tells us how 'strong' or 'concentrated' a solution is.

For example, if we have a 1-liter solution of hydrochloric acid (HCl) with a molarity of 0.150 M, this means there are 0.150 moles of HCl in that solution. To convert milliliters to liters (since molarity deals with liters), you divide by 1000. Therefore, for a 25 mL solution, the volume in liters is 0.025 L (since 25 mL = 0.025 L).

Understanding molarity is crucial when you need to calculate how much of one solution is needed to react completely with a given amount of another solution, as in a neutralization reaction. By using the molarity of each reactant, you can calculate the moles of each substance, thus quantifying the exact volumes needed to achieve neutralization.

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants converting to products with their respective formulas and states (solid, liquid, gas, or aqueous). For the neutralization reaction given in the exercise, \[\mathrm{NaOH}(aq) + \mathrm{HCl}(aq) \rightarrow \mathrm{H}_{2}O(l) + \mathrm{NaCl}(aq)\], each reactant and product is followed by an abbreviation representing its physical state. The reactants are sodium hydroxide (NaOH) and hydrochloric acid (HCl), both in aqueous solutions, while the products are water (H2O) in the liquid state and sodium chloride (NaCl), also in an aqueous solution.

It's vital to recognize that a balanced equation adheres to the law of conservation of mass, meaning the number of atoms for each element must be the same on both sides. In this example, the reaction shows a one-to-one ratio between NaOH and HCl. This ratio is essential for stoichiometry and calculations because it allows us to directly relate the volume and concentration of one reactant to the required volume and concentration of the other.

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the substances involved in chemical reactions. The one-to-one molar ratio in our NaOH and HCl reaction simplifies stoichiometry calculations and lets us directly equate moles of NaOH needed to moles of HCl present.

Using the molarity and volume of HCl, we can find the moles with the formula \( \text{Moles of HCl} = \text{Molarity of HCl} (M) \times \text{Volume of HCl} (L) \). Since the reaction is a one-to-one ratio, the moles of HCl are equal to the moles of NaOH needed. Consequently, you can then use the molarity of the NaOH solution to find the required volume using \( \text{Volume of NaOH} = \text{Moles of HCl} / \text{Molarity of NaOH} \).

For instance, with a 0.150 M HCl solution, if you have 25 mL or 0.025 L, the moles of HCl are \( 0.150 M \times 0.025 L \). Since both solutions are of the same molarity (0.150 M), you need an equal volume of NaOH, which in this case is 25 mL or 0.025 L.

When working through such calculations, always ensure to convert volumes into liters, calculate moles accurately, and use the molarity effectively to find the required volume.