Question

A lab technician prepared a calcium hydroxide solution by dissolving \(1.48 \mathrm{~g}\) of \(\mathrm{Ca}(\mathrm{OH})_{2}\) in water. How many milliliters of \(0.125 \mathrm{~N} \mathrm{HCI}\) solution would be required to neutralize this calcium hydroxide solution?

Short answer

The volume of $0.125 \mathrm{~N} \mathrm{HCI}$ solution needed to neutralize the calcium hydroxide solution is \( \frac{ 2 \times \frac{1.48 \mathrm{~g}}{74.096 \mathrm{~g/mol}}}{0.125 \mathrm{~N}} \times 1000\) milliliters.

Step-by-step solution

Calculate the moles of \(Ca(OH)_2\)

First, we need to find the number of moles of \(Ca(OH)_2\) in 1.48 g of the compound. To determine this, we will use the molar mass of \(Ca(OH)_2\): The molar mass of \(Ca(OH)_2 = 40.08(Ca) + 2 \times 15.999(O) + 2 \times 1.008(H) = 74.096~g/mol\) Next, use the mass and molar mass to calculate the moles of \(Ca(OH)_2\): Number of moles = mass / molar mass Number of moles = \( \frac{1.48 \mathrm{~g}}{74.096 \mathrm{~g/mol}} \)

Determine the moles of HCl needed

Now, we need to find out how many moles of \(HCl\) are needed. From a balanced chemical equation, we know that 2 moles of \(HCl\) are required to neutralize 1 mole of \(Ca(OH)_2\): \(Ca(OH)_2 + 2 HCl \rightarrow CaCl_2 + 2 H_2O\) So, the moles of \(HCl\) needed will be: Moles of \(HCl\) = 2 × moles of \(Ca(OH)_2\) = 2 × \( \frac{1.48 \mathrm{~g}}{74.096 \mathrm{~g/mol}} \)

Calculate the volume of \(0.125~N ~HCl\) solution

Finally, we have to find the volume of \(0.125~N ~HCl\) solution needed to provide the required moles of \(HCl\). Using the molar concentration (N), we can do this by dividing the moles of \(HCl\) by the concentration: Volume (in liters) = \( \frac{moles ~of~ HCl}{concentration}\) Replace moles of \(HCl\) and concentration with the values calculated in the previous steps. Volume (in liters) = \( \frac{ 2 \times \frac{1.48 \mathrm{~g}}{74.096 \mathrm{~g/mol}}}{0.125 \mathrm{~N}}\) Now, convert the volume to milliliters by multiplying by 1000: Volume (in milliliters) = Volume (in liters) × 1000 Volume (in milliliters) = \( \frac{ 2 \times \frac{1.48 \mathrm{~g}}{74.096 \mathrm{~g/mol}}}{0.125 \mathrm{~N}} \times 1000\) Calculate the final answer using the given values.

Key concepts

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. In these processes, the atoms of the reactants rearrange to form different compounds. Understanding chemical reactions is essential for solving stoichiometry problems, especially in laboratory settings.

For example, in the given exercise, the chemical reaction occurring is a neutralization reaction between calcium hydroxide \(Ca(OH)_2\) and hydrochloric acid \(HCl\). The balanced chemical equation is:

• \(Ca(OH)_2 + 2 HCl \rightarrow CaCl_2 + 2 H_2O\)

This equation tells us that one molecule of calcium hydroxide reacts with two molecules of hydrochloric acid to produce calcium chloride and water. Knowing the balanced equation helps determine the molar proportions needed for reactions to proceed to completion.

Neutralization

Neutralization is a specific type of chemical reaction where an acid and a base react to form water and a salt. It is a crucial concept in chemistry, with many practical applications, including medicine and environmental science.

In our example, calcium hydroxide \(Ca(OH)_2\), a base, neutralizes hydrochloric acid \(HCl\), an acid. The general form of a neutralization reaction is:

• \(Acid + Base \rightarrow Salt + Water\)

In the given exercise, the neutralization takes place as calcium ions \(Ca^{2+}\) and chloride ions \(Cl^-\) form calcium chloride \(CaCl_2\), while water is produced from the combination of hydrogen ions \(H^+\) and hydroxide ions \(OH^-\). By understanding neutralization, we can calculate quantities needed for complete reactions.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It serves as a bridge between the macroscopic world, where we can measure mass, and the microscopic world of atoms and molecules. This concept is integral for converting mass into moles and vice versa.

For calcium hydroxide \(Ca(OH)_2\), its molar mass is calculated by summing the atomic masses of its constituent elements:

• \(Ca = 40.08\) g/mol
• \(O = 15.999\) g/mol
• \(H = 1.008\) g/mol

Thus, \(Ca(OH)_2\) has a molar mass of:
\(40.08 + 2 \times 15.999 + 2 \times 1.008 = 74.096\) g/mol.

Using the molar mass, we can convert the given mass of calcium hydroxide to moles, which is essential for stoichiometric calculations.

Solution Preparation

Solution preparation involves creating a homogeneous mixture of solute and solvent. Concentration, such as molarity or normality, is key to determining how much solute to dissolve in a solvent to achieve desired outcomes.

In the example exercise, we're tasked with determining the volume of an \(0.125\) N \(HCl\) solution needed to neutralize \(Ca(OH)_2\). Normality (\(N\)) is a measure of solute concentration, specifically for acids and bases, related to the equivalent weight. In our case, the focus is on calculating the volume required to provide the necessary moles of \(HCl\).

• Volume (L) = \(\frac{\text{Moles of } HCl}{\text{Concentration in } N}\)
• Convert to milliliters: Multiply by 1000.

By setting up the solution and calculations properly, you can accurately prepare solutions needed for experiments and reactions.