Question

What are the major species present in \(0.015 M\) solutions of each of the following bases? a. \(\mathrm{KOH}\) b. \(\mathrm{Ba}(\mathrm{OH})_{2}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of each of these solutions?

Short answer

For a $0.015 \, M$ KOH solution, the major species present are K⁺ and OH⁻. The concentration of hydroxide ions [OH⁻] is 0.015 M. Calculate the pOH using the formula pOH = -log[OH⁻] and then find the pH using pH = 14 - pOH. For a $0.015 \, M$ Ba(OH)₂ solution, the major species present are Ba²⁺ and OH⁻. As Ba(OH)₂ produces 2 moles of OH⁻ ions per mole of the compound, [OH⁻] is twice the molarity of the Ba(OH)₂ solution, which is $2 \times 0.015 \, M$. Calculate the pOH using the formula pOH = -log[OH⁻] and then find the pH using pH = 14 - pOH.

Step-by-step solution

Dissociate the strong base in water

KOH is a strong base and will dissociate completely in water, producing K⁺ and OH⁻ ions: \[ \mathrm{KOH} \overset{H_{2}O}{\longrightarrow} \mathrm{K^+} + \mathrm{OH^-} \] #a. KOH solution: [OH⁻] and pH calculation#

Find the [OH⁻] for KOH

The concentration of hydroxide ions [OH⁻] is equal to the molarity of the KOH solution. In this case, [OH⁻] = 0.015 M.

Calculate the pOH

To find the pOH, use the formula pOH = -log[OH⁻]: \[ \mathrm{pOH} = -\log{(0.015)} \] Calculate the pOH value.

Calculate the pH

To find the pH, use the relationship pH = 14 - pOH. Plug in the pOH value from Step 3 to calculate the pH of the KOH solution. #b. Ba(OH)₂ solution: Major species present#

Dissociate the strong base in water

Ba(OH)₂ is a strong base and will dissociate completely in water, producing Ba²⁺ and OH⁻ ions: \[ \mathrm{Ba(OH)_{2}} \overset{H_{2}O}{\longrightarrow} \mathrm{Ba^{2+}} + 2 \mathrm{OH^{-}} \] Note that Ba(OH)₂ produces 2 moles of OH⁻ ions per mole of the compound. #b. Ba(OH)₂ solution: [OH⁻] and pH calculation#

Find the [OH⁻] for Ba(OH)₂

Since Ba(OH)₂ produces 2 moles of OH⁻ ions per mole of the compound, the concentration of hydroxide ions [OH⁻] is twice the molarity of the Ba(OH)₂ solution: \[ [\mathrm{OH^-}] = 2 \times 0.015 \, M \] Calculate the [OH⁻] for the Ba(OH)₂ solution.

Calculate the pOH

To find the pOH, use the formula pOH = -log[OH⁻]: \[ \mathrm{pOH} = -\log{[2 \times 0.015]} \] Calculate the pOH value for the Ba(OH)₂ solution.

Calculate the pH

To find the pH, use the relationship pH = 14 - pOH. Plug in the pOH value from Step 3 to calculate the pH of the Ba(OH)₂ solution.

Key concepts

Base Dissociation in Water

When strong bases like KOH and Ba(OH)₂ are dissolved in water, they undergo a process known as base dissociation. This refers to the separation of the base into its constituent ions. For KOH, this dissociation is straightforward: one molecule of KOH yields one potassium ion (K⁺) and one hydroxide ion (OH^-).

In contrast, barium hydroxide (Ba(OH)₂) dissociates to produce one barium ion (Ba²⁺) and two hydroxide ions. The difference in the number of hydroxide ions produced is significant—while KOH releases one OH^- per molecule, Ba(OH)₂ releases two, which impacts the pH calculation for these solutions.

Hydroxide Ion Concentration

The concentration of hydroxide ions, denoted as [OH^-], is a critical aspect in calculating the pH of a basic solution. For a 0.015 M KOH solution, since KOH dissociates completely, the concentration of hydroxide ions is also 0.015 M. However, Ba(OH)₂ is different due to its two hydroxide ions per formula unit, leading to a [OH^-] that is twice the molarity of the Ba(OH)₂ solution. Specifically, a 0.015 M Ba(OH)₂ solution has an [OH^-] of 0.030 M. Understanding these concentrations is necessary for accurately determining the solution's pH.

pOH and pH relationship

The concepts of pOH and pH are intrinsically linked through the equation pH + pOH = 14, which is valid at 25°C. The pOH is found by taking the negative logarithm of the hydroxide ion concentration. Once pOH is determined, it can be subtracted from 14 to find the pH. This relationship highlights a fundamental principle of aqueous solutions: as the concentration of hydroxide ions increases, resulting in a lower pOH, the pH of the solution increases, indicating higher basicity.

Strong Base Properties

Strong bases, such as KOH and Ba(OH)₂, exhibit distinct properties. They completely dissociate in water, leaving no undissociated molecules behind. This complete dissociation results in relatively high concentrations of hydroxide ions in solution as compared to weak bases which only partially dissociate. Therefore, the pH of strong base solutions will be relatively high, reflecting their strong basicity and their ability to raise the pH of the surrounding environment. Additionally, the ionic compounds of strong bases tend to be highly soluble in water, contributing to their ability to maintain high pH levels.