Question

What volume of 0.225 M \(\mathrm{Ca}(\mathrm{OH}) 2\) solution is needed to deliver \(100.0 \mathrm{~g}\) of \(\mathrm{Ca}(\mathrm{OH})_{2}\) ?

Short answer

Approximately 6.00 L of the solution is needed.

Step-by-step solution

Calculate Moles of Ca(OH)₂

First, use the molar mass to find how many moles are in 100.0 g of \( \mathrm{Ca(OH)_2} \). The molar mass of \( \mathrm{Ca(OH)_2} \) is \( 40.08 + 2(15.999 + 1.008) = 74.092 \, \text{g/mol} \). Therefore, the number of moles in 100.0 g is \[\text{moles of } \mathrm{Ca(OH)_2} = \frac{100.0 \, \text{g}}{74.092 \, \text{g/mol}} \approx 1.349 \, \text{mol}.\]

Use Molarity for Volume Calculation

Molarity \( M \) is defined as moles of solute per liter of solution. Rearrange the equation to solve for volume: \[V = \frac{\text{moles}}{M}.\]Substitute the known values into the equation: \[V = \frac{1.349 \, \text{mol}}{0.225 \, \text{M}} \approx 5.996 \, \text{L}.\]

Provide Final Answer

The volume needed is approximately \( 6.00 \, \text{L} \) after rounding to three significant figures, which matches the precision given in the original problem data.

Key concepts

Moles to Volume Conversion

Understanding how to convert moles to volume is a fundamental concept in chemistry, especially when working with solutions. This concept involves connecting the number of moles of a substance to the volume of the solution it occupies.
- Moles are a measurement of the substance's quantity at the atomic or molecular level.- Volume is the space that this quantity occupies when dissolved in a solution.
For a solution with a known molarity, the volume can be determined using the formula:
\[ V = \frac{\text{moles}}{M} \]
Where:- \( V \) is the volume of the solution in liters.- Moles refers to the quantity of the solute.- \( M \) is the molarity of the solution.
By understanding this relationship, you can easily figure out the amount of solution needed to achieve a desired number of moles, thereby solving many practical chemistry problems.

Ca(OH)₂

Calcium Hydroxide, known chemically as \( \mathrm{Ca(OH)_2} \), is a compound frequently encountered in various chemical reactions and solutions.
- Its molar mass is important for calculations related to solution preparation and reaction stoichiometry.- It's crucial to accurately calculate its molar mass, which for \( \mathrm{Ca(OH)_2} \) is \( 74.092 \, \text{g/mol} \).
This compound is used in diverse applications such as:

• Neutralizing acids
• As a pH regulator
• In construction as lime

Understanding the properties and behavior of \( \mathrm{Ca(OH)_2} \) helps in predicting its reactions and concentrations in various scenarios, making it an essential compound in chemistry problem solving.

Solution Concentration

Solution concentration is a term that describes how much solute is present in a given volume of solvent or solution. This is often expressed in terms of molarity, which is one of the most common measures.
Molarity (\( M \)) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
This unit is critical because it provides a direct measurement of the solution's strength.- A higher molarity means a greater concentration of solute.- It affects the solution's properties such as boiling point, freezing point, and reaction rate.
Knowing how to calculate and adjust the concentration is vital for tasks ranging from titrations in labs to industrial-scale reactions, emphasizing the importance of mastering this concept.

Chemistry Problem Solving

Solving chemistry problems can often involve a structured approach, allowing us to tackle complex calculations step-by-step. Key features include:

• Understanding the problem requirements
• Breaking down the problem into clear steps
• Using known values and formulas
• Checking units for consistency

In the given exercise, applying the molarity concept enabled us to connect moles with volume to find the desired solution volume. Each step provides a piece of the puzzle:
1. Calculate moles from given mass and molar mass. 2. Use molarity to determine volume from moles.
This structured methodology not only provides the correct answer but also reinforces understanding by illustrating how concepts interlink, making chemistry problem-solving clearer and more logical.