Question

Calculate the \(\mathrm{pOH}\) and \(\mathrm{pH}\) of the following aqueous solutions at \(25^{\circ} \mathrm{C}:\) (a) \(1.24 \mathrm{M} \mathrm{LiOH},\) (b) \(0.22 \mathrm{M}\) \(\mathrm{Ba}(\mathrm{OH})_{2}\) (c) \(0.085 \mathrm{M} \mathrm{NaOH}\).

Short answer

(a) pH = 13.1, (b) pH = 13.7, (c) pH = 12.9.

Step-by-step solution

Understanding the Relationship

For any base M(OH)_n, if we know the concentration 'c' of the base, the hydroxide ion concentration, [OH^-], is given by n × c.

Calculating [OH^-]

(a) For 1.24 M LiOH, which dissociates completely into Li^+ and OH^-, [OH^-] = 1.24 M. (b) For 0.22 M Ba(OH)_2, which provides two OH^- ions per formula unit, [OH^-] = 2 × 0.22 = 0.44 M. (c) For 0.085 M NaOH, [OH^-] = 0.085 M since it dissociates completely into Na^+ and OH^-.

Calculating pOH

Use the formula pOH = -log[OH^-]. (a) pOH for 1.24 M LiOH: pOH = -log(1.24). (b) pOH for 0.44 M Ba(OH)_2: pOH = -log(0.44). (c) pOH for 0.085 M NaOH: pOH = -log(0.085).

Calculating pH

Use the relationship pH + pOH = 14 at 25°C. (a) pH = 14 - pOH for 1.24 M LiOH. (b) pH = 14 - pOH for 0.44 M Ba(OH)_2. (c) pH = 14 - pOH for 0.085 M NaOH.

Key concepts

Strong Bases

Strong bases are compounds that can completely dissociate in water. This means they separate into their component ions when dissolved. For example, some common strong bases include lithium hydroxide (LiOH), sodium hydroxide (NaOH), and barium hydroxide (Ba(OH)_2).

Strong bases play a crucial role in chemistry because of their ability to increase the concentration of hydroxide ions in a solution. This makes them excellent for neutralizing acids. In practice, when strong bases are added to water, they will fully break apart, unlike weak bases, which only partially dissociate.

In summary, when dealing with strong bases, you can expect them to completely dissociate, making calculations more straightforward. For instance, 1 mole of LiOH will give 1 mole of hydroxide ions.

Hydroxide Ion Concentration

The concentration of hydroxide ions, \([OH^-]\), in a solution is an essential factor in understanding the basicity of that solution. When a base like Ba(OH)₂ dissociates, it breaks apart to release hydroxide ions. For every molecule of \( ext{Ba(OH)₂}\), there are two hydroxide ions released.

Calculating the \([OH^-]\) is straightforward with strong bases. For a solution of \(0.22 \, ext{M} \, ext{Ba(OH)₂}\), since it releases two hydroxide ions per formula unit, the concentration would be \(2 \times 0.22 = 0.44 \, ext{M}\).

This measurement not only tells us how basic a solution is but also helps in determining the pH and pOH values.

Dissociation of Bases

The dissociation process is when a compound breaks into simpler constituents or fragments. In the context of strong bases like NaOH, dissociation refers to the complete separation of its ions in an aqueous solution.

When NaOH dissociates, it yields sodium ions \(\text{(Na}^+\text{)}\) and hydroxide ions \(\text{(OH}^-\text{)}\). This complete dissociation distinguishes strong bases from weak bases, which only partially separate in water.

Understanding this process is key in chemistry, as it explains why some solutions exhibit greater basicity. The complete dissociation into ions allows those ions to interact in further reactions, significantly influencing the pH of the solution.

pH and pOH Relationship

The relationship between pH and pOH is fundamental in chemistry, especially when dealing with acid-base reactions. At room temperature (25°C), this relationship is expressed through the equation:\[\text{pH} + \text{pOH} = 14\]

This important formula allows us to interconvert between pH and pOH values. For instance, if the pOH of a solution is calculated and found to be 1.5, the pH can be determined by subtracting 1.5 from 14, yielding a pH of 12.5.

It's crucial to grasp this link, as it provides insight into the acidity or basicity of a solution. When dealing with basic solutions, the pOH is often more direct to calculate, helping to quickly analyze the properties of the solution.