Question

Calculate the concentration of an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) that has a \(\mathrm{pH}\) of \(12.05 .\)

Short answer

The concentration of the aqueous solution of Ca(OH)₂ with a pH of 12.05 is 0.0056 M.

Step-by-step solution

Calculate pOH

Since pH and pOH are related by the equation: pH + pOH = 14, we can calculate the pOH of the solution: pOH = 14 - 12.05 = 1.95

Calculate the concentration of OH⁻ ions

The pOH is the negative logarithm of the hydroxide ion concentration. Therefore, to find the concentration of OH⁻ ions, we can use the formula: [OH⁻] = 10^(-pOH) [OH⁻] = 10^(-1.95) [OH⁻] = 0.0112 M

Calculate the concentration of Ca(OH)₂

Recall that for every Ca(OH)₂ molecule that dissociates, 2 OH⁻ ions are produced. Therefore, the concentration of Ca(OH)₂ in the solution can be determined by dividing the concentration of OH⁻ ions by 2: [Ca(OH)₂] = [OH⁻]/2 [Ca(OH)₂] = 0.0112 M / 2 [Ca(OH)₂] = 0.0056 M The concentration of the aqueous solution of Ca(OH)₂ with a pH of 12.05 is 0.0056 M.

Key concepts

Aqueous Solution Concentration

Understanding the concentration of substances in an aqueous solution is crucial for many areas of chemistry, especially when dealing with reactions and solution properties. Concentration is a measure of the amount of solute that is dissolved in a solvent. In the context of an aqueous solution, the solvent is water. Concentrations are generally expressed in terms of molarity, denoted as M, which is moles of solute per liter of solution.

When a compound like calcium hydroxide ewline, ewlineCa(OH)_2), is dissolved in water, it dissociates into ions. For Ca(OH)_2, this dissociation releases one calcium ion (Ca^2+) and two hydroxide ions (OH^-) for each formula unit that dissolves. This ion release is the basis of calculating how much Ca(OH)_2 we initially had in the solution. Since every mole of Ca(OH)_2 produces two moles of OH^-, to find the original concentration of Ca(OH)_2, you divide the concentration of OH^- by 2. Hence, the concentration of the aqueous solution of Ca(OH)_2 in our exercise was determined to be 0.0056 M.

pOH and pH Relationship

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with 0 being the most acidic, 7 neutral, and 14 the most basic. The relationship between pH and pOH is an essential concept in acid-base chemistry and is defined by the equation:

ewline pH + pOH = 14 ewline

This equation is a consequence of the water ion product, which states that at 25°C, the concentration of hydrogen ions ewline (H^+) ewline and hydroxide ions ewline (OH^-) ewline in pure water multiply to a constant, 1 x 10^-14 M^2. The pOH is similar to pH but reflects the concentration of hydroxide ions instead. If you know the pH of a solution, you can easily find its pOH, and vice versa, which is invaluable when dealing with alkaline solutions, where pOH is more directly related to the properties of the solution.

Hydroxide Ion Concentration

The hydroxide ion concentration in a solution is a direct measure of its basicity. The more hydroxide ions present, the more basic the solution. In acid-base chemistry, hydroxide ion concentration is often expressed in terms of pOH, which is the negative logarithm (base 10) of the hydroxide ion concentration:

ewline pOH = -log[OH^-] ewline

This relationship is pivotal because it allows us to easily convert between the pOH value of a solution and its hydroxide ion concentration using the formula:

ewline [OH^-] = 10^(-pOH) ewline

This enables chemists to determine the hydroxide ion concentration from a more intuitive pOH value. In our exercise, using the pOH value of 1.95, we calculated the hydroxide ion concentration to be 0.0112 M, which tells us the solution is quite basic, as expected from a pH of 12.05.