Question

What is the molar concentration of a saturated solution of calcium hydroxide that contains \(0.185 \mathrm{~g}\) of solute in \(100.0 \mathrm{~mL}\) of solution?

Short answer

The molar concentration of the solution is 0.0250 M.

Step-by-step solution

Calculate the Molar Mass of Calcium Hydroxide

The formula for calcium hydroxide is \( \text{Ca(OH)}_2 \). The atomic weights are approximately: Calcium (Ca) = 40.08 g/mol, Oxygen (O) = 16.00 g/mol, and Hydrogen (H) = 1.01 g/mol. Calculate the molar mass: \[ \text{Molar Mass of } \text{Ca(OH)}_2 = 40.08 + 2 \times (16.00 + 1.01) = 74.10 \, \text{g/mol} \]

Convert Grams to Moles

Use the molar mass to convert the mass of solute from grams to moles.\[\text{Moles of } \text{Ca(OH)}_2 = \frac{0.185 \, \text{g}}{74.10 \, \text{g/mol}} \approx 0.00250 \, \text{mol}\]

Convert Volume from mL to L

Since molarity is expressed in terms of liters of solution, convert the volume from milliliters to liters:\[ 100.0 \, \text{mL} = 0.1000 \, \text{L} \]

Calculate the Molar Concentration

The molar concentration (molarity) is defined as the number of moles of solute per liter of solution. Use the moles calculated in Step 2 and the volume in liters from Step 3 to find the molarity:\[ \text{Molarity} = \frac{0.00250 \, \text{mol}}{0.1000 \, \text{L}} = 0.0250 \, \text{M} \]

Key concepts

Calcium Hydroxide

Calcium hydroxide, commonly known as slaked lime, is a chemical compound with the formula \( \text{Ca(OH)}_2 \). It is an inorganic white powder, often used in construction materials, and it plays a significant role in chemical industries. When dissolved in water, it helps adjust the pH levels, making it useful in water treatment and agriculture. Calcium hydroxide is alkaline in nature, and it forms a saturated solution that can be studied to find its molar concentration. Understanding its properties and being able to calculate its concentration in solutions is important for both academic studies and practical applications such as assessing its reactivity in various environments.

Molar Mass Calculation

The molar mass of a compound indicates the mass of one mole of that substance and is essential for converting grams to moles. To find the molar mass of calcium hydroxide, we sum up the atomic masses of its constituent elements:

• Calcium (Ca): 40.08 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.01 g/mol

In \( \text{Ca(OH)}_2 \), we have one calcium atom and two hydroxide groups. Each hydroxide group contains one oxygen and one hydrogen atom, making their combined mass 17.01 g/mol. Multiply this by two for the two hydroxide groups and add the mass of calcium:\[40.08 + 2 \times (16.00 + 1.01) = 74.10\, \text{g/mol}\]This precise calculation of molar mass is crucial for further steps in solving molarity problems, as it provides the bridge from mass in grams to the amount of substance in moles.

Solution Stoichiometry

Solution stoichiometry involves using balanced chemical equations to determine the relationships between concentrations and volumes of reactants and products. It is particularly useful in the calculation of molarities, which represent the concentration of a solute in a solution, expressed as moles per liter.To calculate the molar concentration of a saturated calcium hydroxide solution:

• Convert the mass of the solute (in grams) to moles using the molar mass. For example, with 0.185 grams of \( \text{Ca(OH)}_2 \), this is done by dividing the mass by the molar mass (74.10 g/mol).
• Convert the volume from milliliters to liters, as molarity is defined with liters. For 100.0 mL, this is 0.1000 L.
• Calculate molarity: divide the number of moles of solute by the volume of the solution in liters. This gives a final molarity of 0.0250 M.

This process allows us to understand and predict how solutions will behave in chemical reactions, ensuring accurate and effective application in both laboratory and real-life chemistry scenarios.