The conductivity of a saturated solution of Ca(OH)2 is 3.06*10^-6 ohm cm and its equivalent conductance is 1.53 ohm cm2 eq. Its solubility is

To determine the solubility of calcium hydroxide, Ca(OH)₂, from the given conductivity and equivalent conductance, we can use the relationship between these values and the solubility product. Let's break this down step by step.

Understanding the Concepts

Conductivity (κ) is a measure of a solution's ability to conduct electricity, which depends on the concentration of ions in the solution. Equivalent conductance (Λ) is a measure of how well one equivalent of an electrolyte conducts electricity in a solution. The relationship between conductivity and equivalent conductance can be expressed as:

Λ = κ / c

Where:

• Λ = equivalent conductance (ohm cm²/eq)
• κ = conductivity (ohm cm)
• c = concentration of the solution (eq/cm³)

Calculating the Concentration

From the information provided:

• Conductivity, κ = 3.06 × 10^-6 ohm cm
• Equivalent conductance, Λ = 1.53 ohm cm²/eq

We can rearrange the formula to find the concentration (c):

c = κ / Λ

Substituting the values:

c = (3.06 × 10^-6 ohm cm) / (1.53 ohm cm²/eq)

Calculating this gives:

c ≈ 2.00 × 10^-6 eq/cm³

Relating Concentration to Solubility

Now that we have the concentration in equivalents per cubic centimeter, we need to convert this to solubility in grams per liter. The solubility of Ca(OH)₂ can be calculated using its molar mass and the fact that one mole of Ca(OH)₂ produces two equivalents of hydroxide ions (OH^-).

The molar mass of Ca(OH)₂ is approximately 74.09 g/mol. Since one mole of Ca(OH)₂ yields two equivalents, we can relate the concentration of the solution to its solubility:

Solubility (g/L) = c (eq/cm³) × 1000 (cm³/L) × (molar mass / number of equivalents)

Here, the number of equivalents for Ca(OH)₂ is 2 (because it dissociates into one Ca²⁺ and two OH^- ions). Thus:

Solubility = (2.00 × 10^-6 eq/cm³) × 1000 cm³/L × (74.09 g/mol / 2)

Calculating this gives:

Solubility ≈ 0.07409 g/L

Final Thoughts

In summary, the solubility of a saturated solution of Ca(OH)₂ is approximately 0.07409 g/L. This process illustrates how conductivity and equivalent conductance can be used to derive solubility, showcasing the interconnectedness of these concepts in physical chemistry.