Question

Determine \(\left[\mathrm{OH}^{-}\right]\)in each base solution. If the acid is weak, indicate the value that \(\left[\mathrm{OH}^{-}\right]\)is less than. (a) \(0.25 \mathrm{M} \mathrm{NaOH}\) (b) \(0.25 \mathrm{MNH}_{3}\) (c) \(0.25 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}\) (d) \(1.25 \mathrm{M} \mathrm{KOH}\)

Short answer

\)\left[\mathrm{OH}^{-}\right]\) values: (a) 0.25 M, (b) less than 0.25 M, (c) 0.50 M, (d) 1.25 M

Step-by-step solution

Determine \)\left[\mathrm{OH}^{-}\right]\) for 0.25 M NaOH

Sodium hydroxide (NaOH) is a strong base, which completely dissociates in water. For every mole of NaOH dissolved, one mole of OH- ions is produced. Therefore, the concentration of OH- will be equal to the concentration of NaOH, which is 0.25 M.

Calculate \)\left[\mathrm{OH}^{-}\right]\) for 0.25 M NH3

Ammonia (NH3) is a weak base and does not completely dissociate in water. The concentration of OH- will be less than the concentration of NH3. The exact value of \[\mathrm{OH}^{-}\] can be found using the Kb value for NH3 and the base dissociation equation. However, without the Kb value, we can only state that \[\mathrm{OH}^{-}\] is less than 0.25 M.

Determine \)\left[\mathrm{OH}^{-}\right]\) for 0.25 M Sr(OH)2

Strontium hydroxide (Sr(OH)2) is a strong base, which completely dissociates in water. However, each Sr(OH)2 unit produces two OH- ions upon dissociation. Therefore, the OH- concentration will be twice the concentration of Sr(OH)2, which means the OH- concentration will be 0.50 M.

Calculate \)\left[\mathrm{OH}^{-}\right]\) for 1.25 M KOH

Potassium hydroxide (KOH) is a strong base that completely dissociates in water. Thus, the concentration of OH- will be equal to the concentration of KOH, which is 1.25 M.

Key concepts

Strong Base Dissociation

When encountering a strong base like sodium hydroxide (NaOH) or potassium hydroxide (KOH), it's crucial to understand that these substances completely dissociate in water. What does this mean? Simply put, for every one unit of a strong base added to water, it will completely separate into its constituent ions without any remaining undissociated molecules. For instance, NaOH will dissociate into Na+ and OH- ions.

Due to this full dissociation, the concentration of hydroxide ions \(\left[\mathrm{OH}^-\right]\) in the solution will be directly equal to the initial concentration of the strong base. If you dissolve 1.25 moles of KOH in a liter of water, you will end up with a \(\left[\mathrm{OH}^-\right]\) of 1.25 M as well, because each KOH provides one OH- ion. It's a one-to-one correspondence, making the calculation straightforward.

Weak Base Equilibrium

In contrast to strong bases, weak bases like ammonia (NH3) do not completely dissociate in water. They reach a state of dynamic equilibrium where the forward and reverse reactions occur at the same rate, resulting in both undissociated base and its ions being present in the solution.

A key point to remember is that the concentration \(\left[\mathrm{OH}^-\right]\) produced by a weak base will always be less than the initial concentration of the base due to partial dissociation. The actual concentration of \(\left[\mathrm{OH}^-\right]\) in a solution of NH3, for example, would require knowledge of the base dissociation constant (Kb), as the complete dissociation cannot be assumed.

Base Dissociation Constant (Kb)

The base dissociation constant, Kb, is a value that tells us about the degree to which a weak base dissociates in water. It is a specific type of equilibrium constant that applies to the dissociation of bases. A higher Kb value indicates a stronger tendency for a base to dissociate and hence, a higher concentration of hydroxide ions in solution.

Using the expression for Kb, one can calculate the hydroxide ion concentration from a given initial concentration of a weak base. While strong bases have a straightforward calculation for hydroxide ion concentration, with weak bases you use the expression \( Kb = \frac{\left[\mathrm{B}^+\right]\left[\mathrm{OH}^-\right]}{\left[\mathrm{B}\right]} \) where \(\left[\mathrm{B}\right]\) is the concentration of the undissociated base. The process involves setting up an ICE (Initial, Change, Equilibrium) table and solving for the unknown \(\left[\mathrm{OH}^-\right]\) to find the equilibrium concentrations.

Chemical Equilibrium

Chemical equilibrium refers to the state in which the rate of the forward reaction equals the rate of the reverse reaction, leading to no net change in the concentrations of reactants and products over time. It is a key concept in understanding how weak bases dissociate in aqueous solutions.

At equilibrium, the concentrations of all reactants and products remain constant. For weak bases like NH3, this means that at equilibrium, a certain amount of the base remains as NH3 while the remainder exists as NH4+ and OH- ions. This balance is described by the equilibrium constant (Kb for bases), which is crucial for calculating concentrations at equilibrium. A thorough understanding of chemical equilibrium is essential for solving problems relating to weak base dissociation and hydroxide ion concentration in such systems.