Question

What volume of \(0.175 M \mathrm{HCl}\) solution is needed to neutralize \(24.9 \mathrm{mL}\) of \(0.451 \mathrm{M}\) NaOH solution?

Short answer

The volume of a \(0.175 M\) HCl solution needed to neutralize \(24.9 mL\) of \(0.451 M\) NaOH solution is \(64 mL\).

Step-by-step solution

Calculate the moles of NaOH in the given solution

We have the volume (24.9 mL) and molarity (0.451 M) of the NaOH solution. We can calculate the moles of NaOH using the formula: moles = molarity × volume Since the volume should be in liters, we will first convert the volume from mL to L: volume (in L) = 24.9 mL × (1 L / 1000 mL) = 0.0249 L Now, we can calculate the moles of NaOH: moles of NaOH = 0.451 M × 0.0249 L = 0.0112 mol

Calculate the moles of HCl required for neutralization

According to the balanced chemical equation, one mole of HCl reacts with one mole of NaOH. Thus, the moles of HCl needed to neutralize the given NaOH solution are the same as the moles of NaOH. moles of HCl = moles of NaOH = 0.0112 mol

Calculate the volume of the 0.175 M HCl solution needed

We have the molarity (0.175 M) and moles (0.0112 mol) of the HCl solution. We can calculate the volume of the HCl solution using the formula: volume = moles / molarity volume of HCl solution = 0.0112 mol / 0.175 M = 0.064 L Now, convert the volume from L to mL: volume of HCl solution = 0.064 L × (1000 mL / 1 L) = 64 mL The volume of a 0.175 M HCl solution needed to neutralize the 24.9 mL of 0.451 M NaOH solution is 64 mL.

Key concepts

Neutralization Reaction

A neutralization reaction is a chemical process where an acid and a base react with each other to form water and a salt. This reaction forms the basis of titration calculations in which the goal is to determine the concentration of one solution using a solution with a known concentration. For instance, in our exercise, hydrochloric acid (HCl) is the acid, and sodium hydroxide (NaOH) is the base.

The reaction between them can be written as:
\(\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}\).

To achieve neutralization, the number of moles of HCl must equal the number of moles of NaOH because they react in a 1:1 ratio according to the balanced chemical equation. Understanding this concept is crucial, as it's the first step in performing a correct titration calculation.

Molarity and Concentration

Understanding Molarity

Molarity, often designated by the capital letter 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 formula for calculating molarity is:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \].

If we use the provided exercise as an example, to find the volume of hydrochloric acid needed, one must first understand the concentration of the given sodium hydroxide solution.

Application in Calculations

As seen in the step-by-step solution, the concept of molarity is applied to find the amount of substance in moles before one can proceed to any further calculations. This understanding is pivotal for correctly solving titration problems.

Stoichiometry

Stoichiometry is a section of chemistry that involves using relationships between reactants and/or products in a chemical reaction to determine the desired quantitative data. It is the mathematical backbone of chemistry, ensuring the precise measurement of substances. Stoichiometry uses the concept of the mole ratio derived from the balanced chemical equation to understand how different amounts of substances will react.

In our exercise example, the stoichiometry of the neutralization reaction tells us there is a 1:1 mole ratio between hydrochloric acid and sodium hydroxide. The stoichiometry allows us to predict that 0.0112 moles of HCl will neutralize 0.0112 moles of NaOH, leading to the final calculation of the required volume of the HCl solution. Grasping stoichiometry is fundamental to successfully performing titration calculations, as it relates the quantities of the reactants involved in the reaction.