Question

Calculate the concentration (in molarity) of an $\mathrm{NaOH}$ solution if $25.0\mathrm{mL}$ of the solution is needed to neutralize $17.4\mathrm{mL}$ of a $0.312\mathrm{M}\mathrm{HCl}$ solution.

Short answer

The molarity of the NaOH solution is approximately 0.217 M.

Step-by-step solution

Understanding the Neutralization Reaction

First, recognize that the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) is a neutralization reaction, which can be represented by the equation: $$\mathrm{NaOH}+\mathrm{HCl}\to \mathrm{NaCl}+{\mathrm{H}}_2\mathrm{O}$$. This means that one mole of NaOH reacts with one mole of HCl.

Calculate Moles of HCl

Since the molarity of the HCl solution is given, use the formula for moles: $\text{moles}=\text{molarity}\times \text{volume in liters}$. The volume of HCl is 17.4 mL, which is 0.0174 L. Therefore, the moles of HCl are: $$\text{moles of HCl}=0.312\text{M}\times 0.0174\text{L}=0.0054288\text{moles}$$.

Determine Moles of NaOH Required

Since the reaction is a 1:1 ratio according to the balanced equation, the moles of NaOH needed will be equal to the moles of HCl. Therefore, $\text{moles of NaOH}=0.0054288\text{moles}$.

Calculate the Molarity of NaOH

Now, use the definition of molarity, which is: $\text{molarity}=\frac{\text{moles of solute}}{\text{volume of solution in liters}}$. The volume of the NaOH solution is 25.0 mL, or 0.025 L. Therefore, the molarity $M$ of the NaOH solution is: $$M=\frac{0.0054288\text{moles}}{0.025\text{L}}=0.217152\text{M}$$.

Key concepts

Neutralization Reaction

Neutralization reactions are vital in chemistry, especially in acid-base chemistry. It involves combining an acid and a base to form water and a salt. This type of reaction is important as it helps us understand how different solutions react. Understanding neutralization helps us calculate changes in concentrations during reactions. In a typical neutralization, acids donate protons (H+) while bases provide hydroxide ions (OH-). They react to form water

• Acids + Bases → Water + Salt

In our example, NaOH (a base) and HCl (an acid) form water and NaCl (salt). The balanced equation $$\mathrm{NaOH}+\mathrm{HCl}\to \mathrm{NaCl}+{\mathrm{H}}_2\mathrm{O}$$ shows the 1:1 ratio for the reaction. Understanding this reaction is key to solving such exercises. It allows us to predict the amounts of each substance needed to fully react. Grasping neutralization reactions is essential for mastering stoichiometric calculations in acid-base chemistry.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It plays a crucial role, especially in reactions like neutralization occurring in defined ratios. Knowing how to calculate the moles of reactants and products is a core skill in stoichiometry. It’s like the math of chemistry. Here's why stoichiometry is so important:

• It helps us determine the proportional amounts of reactants needed.
• It allows us to calculate unknown quantities such as molarity or volume.

In our problem, stoichiometry assists in recognizing that NaOH and HCl react in a 1:1 mole ratio. Hence, the moles of NaOH required equals the moles of HCl used. This reflection through stoichiometry makes computations manageable and accurate, particularly in laboratory settings. Mastery of stoichiometry is foundational for students to succeed in various chemical calculations.

Mole Concept

The mole concept is central to chemistry and is essential in calculating amounts in chemical reactions. A mole is a unit used to express amounts of a chemical substance. Understanding moles allows us to calculate how much of a substance is involved in a given reaction.

• 1 mole = 6.022 x 10^23 particles (Avogadro's number).
• Moles relate mass to the number of particles and vice versa.

In the exercise, moles are derived from the given molarity and volume using the formula:$$\text{moles}=\text{molarity}\times \text{volume in liters}$$With this formula, the moles of HCl and subsequently NaOH were calculated. The mole concept thus translates volumes and molarities into quantitative terms, helping us connect theoretical concepts with practical measures.

Acid-Base Reaction

Acid-base reactions are fundamental in both chemistry and everyday life. They form a core part of numerous processes we observe around us. An acid-base reaction involves an acid donating a proton to a base, which leads to a neutralization process.

• Acids release H+ ions in solutions.
• Bases release OH- ions.

In our case, the acid (HCl) reacts with the base (NaOH) resulting in the formation of water and salt. Such reactions are also important in titration methods, where concentrations of solutions are determined. Acid-base reactions are often marked by a change in pH, signifying the extent of the reaction. This understanding allows us to intervene or predict changes in various systems, be it biological, industrial, or environmental. Embracing the mechanisms of acid-base reactions enriches our grasp of both simple and complex chemical interactions.