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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

Expert verified
In the 4.00 L solution prepared by dissolving 2.50 moles of LiOH, the molar concentrations of OH鈦 and H鈧僌鈦 ions are 0.625 M and 1.6 脳 10鈦宦光伌 M, respectively.

Step by step solution

01

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: \[ [LiOH] = 0.625\,\text{M} \]
02

Find the concentration of OH鈦 ions

LiOH is a strong base and it dissociates completely in water: LiOH 鈫 Li鈦 + OH鈦 Since 1 mole of LiOH dissociates to produce 1 mole of OH鈦 ions, the initial concentration of OH鈦 ions ([OH鈦籡) is equal to the concentration of LiOH: \[ [OH鈦籡 = [LiOH] \] Substituting the value for [LiOH], we have: \[ [OH鈦籡 = 0.625\,\text{M} \]
03

Find the concentration of H鈧僌鈦 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掳C, the value of Kw is 1.0 脳 10鈦宦光伌. Rearranging the equation to find the concentration of H鈧僌鈦 ions ([H鈧僌鈦篯), 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 H鈧僌鈦 ions: \[ [H_{3}O^{+}] = 1.6 \times 10^{-14}\,\text{M} \] In conclusion, the molar concentrations of OH鈦 and H鈧僌鈦 ions in the solution are 0.625 M and 1.6 脳 10鈦宦光伌 M, respectively.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈦) and hydroxide anions (OH鈦). 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鈦 ions in the solution because the molar ratio of LiOH to OH鈦 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鈦 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鈦 and OH鈦, 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鈦) and hydroxide ions (OH鈦) in pure water at a certain temperature.

At 25掳C, this constant is always 1.0 脳 10鈦宦光伌M虏, which reflects the autoionization of water where water molecules dissociate into H3O鈦 and OH鈦 ions. The constancy of Kw means that in any aqueous solution at 25掳C, the product of the hydronium and hydroxide ion concentrations must always equal 1.0 脳 10鈦宦光伌M虏. This ion-product constant is indispensable in calculations involving either acid or base solutions.
Hydroxide Ion Concentration
The hydroxide ion concentration ([OH鈦籡) in a solution is a direct measure of the solution's basicity. In the context of strong bases like LiOH, the [OH鈦籡 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鈦籡 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鈦篯). 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.

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