Problem 19 - Chemistry Matter and Change

Question

Challenge How much calcium hydroxide \(\left(\mathrm{Ca}(\mathrm{OH})_{2}\right),\) in grams, is needed to produce 1.5 \(\mathrm{L}\) of a 0.25 \(\mathrm{M}\) solution?

Step-by-Step Solution

Answer

27.79 grams of \(\text{Ca(OH)}_2\) is needed.

Step 1: Understanding the Problem

We need to prepare a solution of calcium hydroxide, \(\text{Ca(OH)}_2\), with a given molarity and volume. The challenge is to calculate how many grams of \(\text{Ca(OH)}_2\) are required to make 1.5 L of a 0.25 M solution.

Step 2: Expressing Solution Formula

The formula to calculate the amount of solute (\(\text{mass in grams}\)) needed for a given molarity (\(M\)) and volume (\(V\)) of solution in liters is:\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{Volume in liters}} \]Therefore, moles of solute = \( M \times V \).

Step 3: Calculating Moles

Given: \( M = 0.25 \text{ M} \) and \( V = 1.5 \text{ L} \). Use the formula for moles:\[ \text{moles of \(\text{Ca(OH)}_2\)} = 0.25 \times 1.5 = 0.375 \text{ moles} \]

Step 4: Finding the Molar Mass of Calcium Hydroxide

Calculate the molar mass of \(\text{Ca(OH)}_2\):- Calcium (Ca) = 40.08 g/mol- Oxygen (O) = 16.00 g/mol- Hydrogen (H) = 1.01 g/molMolar mass of \(\text{Ca(OH)}_2\) = 40.08 + 2(16.00 + 1.01) = 74.10 \text{ g/mol}.

Step 5: Calculating the Mass Required

Use the relationship between moles and mass:\[ \text{mass = moles} \times \text{molar mass} \]= \(0.375 \times 74.10 = 27.7875 \text{ grams} \).

Step 6: Final Answer

Therefore, approximately 27.79 grams (rounded to two decimal places) of \(\text{Ca(OH)}_2\) is needed to prepare 1.5 L of a 0.25 M solution.

Key Concepts

Calcium Hydroxide

Calcium hydroxide, known chemically as \( \text{Ca(OH)}_2 \), is a white powder often used in chemistry labs. It's derived from limestone or calcium carbonate. This compound is widely applied in water treatment, as a pH regulator, and in the construction industry for making mortar and plaster. Understanding its properties is key to handling it safely and effectively in solution preparation.
When preparing solutions involving calcium hydroxide, it's important to note that it's sparingly soluble in water. This means only a certain limit of it can dissolve in water, but it's enough for many practical applications. The balanced chemical formula shows each calcium atom bonded to two hydroxide groups. It's the ability of these hydroxide ions to increase pH that makes calcium hydroxide useful in adjusting acidity.

Molarity Calculation

Molarity, often denoted by \( M \), is a measure of the concentration of a solute in a solution. It's defined as the number of moles of a solute dissolved in a liter of solution. Calculating molarity is essential for preparing chemical solutions with desired concentrations.
To find molarity, use the formula:

\[ M = \frac{\text{moles of solute}}{\text{Volume in liters}} \]
This formula reflects the relation between the amount of material and the volume it occupies. Knowing how to calculate molarity helps in adjusting solutions for various applications, whether it’s for experiments or industrial purposes.

• To determine the number of moles, multiply molarity by volume.
• This direct relationship allows you to adjust concentration levels by changing one of the variables, either adding more solute or adjusting the solution volume.

Molar Mass

Molar mass is an essential concept in chemistry, indicating the mass of one mole of a substance, typically expressed in g/mol. It's calculated by summing the atomic masses of all atoms in a molecule.

For calcium hydroxide, \( \text{Ca(OH)}_2 \), we calculate its molar mass by adding:

• Calcium (Ca) with a molar mass of 40.08 g/mol
• Two oxygen atoms (O) at 16.00 g/mol each
• Two hydrogen atoms (H) at 1.01 g/mol each

So, the molar mass is:

\[ \text{Molar Mass of \( \text{Ca(OH)}_2 \)} = 40.08 + 2(16.00 + 1.01) = 74.10 \text{ g/mol} \]
Knowing molar mass allows chemists to convert between the mass of a chemical and the number of moles it contains easily, which is critical in stoichiometry calculations.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It's based on the conservation of mass, where the total mass of reactants equals the total mass of products.

In solution preparation, stoichiometry allows us to determine the exact amounts needed to achieve specific chemical reactions or concentrations. When calculating how much calcium hydroxide is required to produce a solution, this concept helps ensure accurate measurements. Here’s a simple breakdown of how it’s applied:

• First, identify all the chemicals involved and their chemical formulas.
• Next, use the balanced chemical equation to find the mole ratio of reactants to products.
• Finally, apply this ratio to determine the mass of reactants needed for a desired concentration of products.

By mastering stoichiometry, students can predict the outcomes of reactions and prepare solutions with precision, an essential skill in both laboratory and industrial chemistry.