Question

A solution is made by adding \(0.300 \mathrm{g} \mathrm{Ca}(\mathrm{OH})_{2}(s), 50.0 \mathrm{mL}\) of \(1.40 \mathrm{MNN}_{3},\) and enough water to make a final volume of 75.0 \(\mathrm{mL}\) . Assuming that all of the solid dissolves, what is the pH of the final solution?

Short answer

The pH of the final solution when 0.300 g of Ca(OH)₂, 50.0 mL of 1.40 M NH₃, and enough water to make the final volume 75.0 mL is approximately 13.034.

Step-by-step solution

Calculate the initial moles of Ca(OH)₂ and NH₃ in the solution

To do this, we will use the given information: - mass of Ca(OH)₂ = 0.300 g - volume of NH₃ solution = 50.0 mL - concentration of NH₃ = 1.40 M First, we need to convert the mass of Ca(OH)₂ to moles. We will use the molar mass of Ca(OH)₂ which is about 74.1 g/mol. Moles of Ca(OH)₂ = mass / molar mass Moles of Ca(OH)₂ = \(0.300 \mathrm{g} / 74.1 \mathrm{g/mol}\) Moles of Ca(OH)₂ ≈ 0.00405 mol Next, we will calculate the moles of NH₃ by multiplying its concentration by the volume of the solution: Moles of NH₃ = concentration × volume (in L) Moles of NH₃ = 1.40 M × 0.050 L Moles of NH₃ = 0.0700 mol

Calculate concentrations in final solution

Now that we have the initial moles of both Ca(OH)₂ and NH₃, we will find their concentrations in the final solution. The total volume of the final solution is 75.0 mL: Concentration of Ca(OH)₂ = moles / volume Concentration of Ca(OH)₂ = \(0.00405 \mathrm{mol} / 0.075 \mathrm{L}\) Concentration of Ca(OH)₂ ≈ 0.0540 M Concentration of NH₃ = moles / volume Concentration of NH₃ = \(0.0700 \mathrm{mol} / 0.075 \mathrm{L}\) Concentration of NH₃ ≈ 0.933 M

Calculate concentration of OH⁻ ions

Ca(OH)₂ dissociates in water to form 2 moles of OH⁻ ions for every 1 mole of Ca(OH)₂. Therefore, the concentration of OH⁻ ions in the solution will be: Concentration of OH⁻ = 2 × concentration of Ca(OH)₂ Concentration of OH⁻ = 2 × 0.0540 M Concentration of OH⁻ ≈ 0.108 M

Calculate the pOH of the solution

Now calculate the pOH of the solution using the concentration of OH⁻ ions: pOH = - log₁₀([OH⁻]) pOH = - log₁₀(0.108) pOH ≈ 0.966

Calculate the pH of the solution

To find the pH, we will use the relationship between pH and pOH: pH + pOH = 14 pH = 14 - pOH pH = 14 - 0.966 pH ≈ 13.034 The pH of the final solution is approximately 13.034.

Key concepts

Chemical Solution

A chemical solution is formed when a solute is dissolved in a solvent, resulting in a homogeneous mixture. In the context of the exercise, we are tasked with finding the pH of a solution comprised of multiple components, namely calcium hydroxide ( Ca(OH)_2 ) and ammonia ( NH_3 ) .

A solution's properties significantly change based on the substances mixed and their respective concentrations and volumes. Calcium hydroxide, when dissolved in water, dissociates into calcium ions ( Ca^{2+} ) and hydroxide ions ( OH^{-} ) , affecting the basicity of the solution. Meanwhile, ammonia contributes its alkalinity, thus impacting the overall pH of the solution negatively. Understanding this ability of solutes to affect a solution's characteristics is a crucial part of chemistry.

To grasp how chemical solutions are created and interact, remember:

• Both solute's known properties and the solvent's ability play critical roles in chemical behaviors of the entire solution.
• Complete dissolution assumes the solute entirely interacts and integrates with the solvent, impacting resultant solution properties like pH.

Molar Concentration

Molar concentration, also known as molarity, is a measure of the number of moles of a solute dissolved in one liter of solution. It's vital in determining how different solutes will interact with each other and the overall solution. In this problem, computing molar concentrations allows us to predict how the solution reacts, particularly concerning its pH.

Here’s how you can find the molar concentration:

• Calculate the number of moles of each substance in the solution. This typically involves dividing the mass of the solute by its molar mass.
• Divide the moles of solute by the final solution volume in liters to get molarity.

In our example, the concentration calculations for calcium hydroxide and ammonia revealed values critical to determining the solution's pH.

Remember, higher molarity can sharply steer the balance of a solution towards acidity or basicity, hence modifying the solution’s pH substantively.

Acid-Base Equilibrium

Acid-base equilibrium principles guide us in understanding how acids and bases interact in a chemical solution. This equilibrium pertains to the delicate balance between acids donating protons and bases accepting protons within a solution. The significance of equilibrium is observed in finding related measures such as pH and pOH.

In this exercise, both calcium hydroxide and ammonia are bases, contributing to the overall basic nature of the solution. Calcium hydroxide dissociates to yield hydroxide ions, making the solution more basic and leading to the calculation of pOH.

• Basic solutions typically have higher concentrations of OH^{-} ions.
• The relationship (pH + pOH = 14) is utilized to interrelate these two measures — knowing one allows the other to be calculated.

Ultimately, understanding acid-base equilibrium permits us to evaluate how various components of a solution will determine its behavior, particularly its pH.