Question

A solution is prepared by dissolving \(2.50\) moles of \(\mathrm{LiOH}\) in enough water to get \(4.00 \mathrm{~L}\) of solution. What are the \(\mathrm{OH}^{-}\) and the \(\mathrm{H}_{3} \mathrm{O}^{+}\) molar concentrations?

Short answer

In the 4.00 L solution prepared by dissolving 2.50 moles of LiOH, the molar concentrations of OH⁻ and H₃O⁺ ions are 0.625 M and 1.6 × 10⁻¹⁴ M, respectively.

Step-by-step solution

Find the concentration of LiOH in the solution

The initial concentration of LiOH, which can be written as [LiOH], is determined by dividing the number of moles of LiOH (n_LiOH) by the volume of the solution (V_solution), and is given by: \[ [LiOH] = \frac{n_{LiOH}}{V_{solution}} \] Using the given values, we have: \[ [LiOH] = \frac{2.50\,\text{moles}}{4.00\,\text{L}} \] Now, we can calculate the concentration of LiOH: \[ [LiOH] = 0.625\,\text{M} \]

Find the concentration of OH⁻ ions

LiOH is a strong base and it dissociates completely in water: LiOH → Li⁺ + OH⁻ Since 1 mole of LiOH dissociates to produce 1 mole of OH⁻ ions, the initial concentration of OH⁻ ions ([OH⁻]) is equal to the concentration of LiOH: \[ [OH⁻] = [LiOH] \] Substituting the value for [LiOH], we have: \[ [OH⁻] = 0.625\,\text{M} \]

Find the concentration of H₃O⁺ ions using the ion-product constant of water, Kw

The ion-product constant of water (Kw) is given by: \[ K_w = [H_{3}O^{+}] \times [OH^-] \] At 25°C, the value of Kw is 1.0 × 10⁻¹⁴. Rearranging the equation to find the concentration of H₃O⁺ ions ([H₃O⁺]), we have: \[ [H_{3}O^{+}] = \frac{K_w}{[OH^-]} \] Substituting the known values, we get: \[ [H_{3}O^{+}] = \frac{1.0 \times 10^{-14}}{0.625} \] Now, calculate the concentration of H₃O⁺ ions: \[ [H_{3}O^{+}] = 1.6 \times 10^{-14}\,\text{M} \] In conclusion, the molar concentrations of OH⁻ and H₃O⁺ ions in the solution are 0.625 M and 1.6 × 10⁻¹⁴ M, respectively.

Key concepts

LiOH Dissolution

When lithium hydroxide (LiOH) is dissolved in water, it undergoes a process known as dissolution. This is where the solid compound separates into its component ions. For LiOH, it dissociates into lithium cations (Li⁺) and hydroxide anions (OH⁻). The key to understanding LiOH dissolution is recognizing that LiOH is a strong base, thus it dissociates completely in aqueous solution.

This implies that if we start with a certain amount of LiOH, we can expect an equivalent amount of OH⁻ ions in the solution because the molar ratio of LiOH to OH⁻ ions is 1:1. For example, dissolving 2.50 moles of LiOH in 4.00 liters of water would result in the same number of moles of OH⁻ ions in the water.

Strong Base Dissociation

Strong bases, like LiOH, are characterized by their complete dissociation in water. This means that they separate into their ions fully when dissolved. Dissociation of strong bases is a fundamental concept in understanding the behavior of these substances in solution.

It's important to clarify that when strong bases dissociate, they do not stay in equilibrium with their dissolved ions; they completely convert to the ions. Given that 1 mole of LiOH produces 1 mole of each ion,Li⁺ and OH⁻, the original concentration of the base will be equal to the concentration of hydroxide ions in the solution. This is essential information for accurately determining the pH of a solution, a common task in chemistry.

Ion-Product Constant of Water

The ion-product constant of water (Kw) is a critical concept in chemistry, particularly when dealing with acid-base chemistry and pH calculations. It defines the product of the concentrations of hydronium ions (H3O⁺) and hydroxide ions (OH⁻) in pure water at a certain temperature.

At 25°C, this constant is always 1.0 × 10⁻¹⁴M², which reflects the autoionization of water where water molecules dissociate into H3O⁺ and OH⁻ ions. The constancy of Kw means that in any aqueous solution at 25°C, the product of the hydronium and hydroxide ion concentrations must always equal 1.0 × 10⁻¹⁴M². This ion-product constant is indispensable in calculations involving either acid or base solutions.

Hydroxide Ion Concentration

The hydroxide ion concentration ([OH⁻]) in a solution is a direct measure of the solution's basicity. In the context of strong bases like LiOH, the [OH⁻] mirrors the concentration of the dissolved base because it dissociates completely.

Calculating the hydroxide ion concentration can also allow us to find the pH of a solution, since pH and [OH⁻] are inversely related through the ion-product constant of water, Kw. With the concentration of hydroxide ions known, and the value of Kw at a given temperature, we can calculate the concentration of hydronium ions ([H3O⁺]). This helps us in further understanding the acid or base nature of the solution as well as in conducting precise calculations pivotal to many fields, including biology, environmental science, and medicine.