Question

In water, \(\mathrm{O}^{2-}\) is a strong base. If \(50.0 \mathrm{mg}\) of \(\mathrm{Li}_{2} \mathrm{O}\) is dissolved in \(750.0 \mathrm{mL}\) of aqueous solution, what will be the pH of the solution?

Short answer

The pH of the solution is approximately 11.65.

Step-by-step solution

Calculating moles of lithium oxide

To calculate the number of moles of lithium oxide \(Li_2O\), the given mass \(50.0mg = 0.050g\) is divided by the molar mass of \(Li_2O\) which is approximately \(30g/mol\). Therefore, the moles of \(Li_2O\) is \(\frac{0.050g}{30g/mol}=0.00167mol\).

Calculating concentration of hydroxide ions

When Li2O dissolves in water, it forms 2OH- ions per formula unit, so the 0.00167 mol of Li2O will produce 2*0.00167=0.00333 mol of OH-. To calculate the concentration of OH- ions, the number of moles of OH- divide by the volume of the solution in liters which is 0.750L. Therefore, the concentration of OH- is \(\frac{0.00333mol}{0.75L}= 0.00444 M\).

Calculating the pH of the solution

To calculate the pH, we first need to find the concentration of hydronium ions \([H_3O^+]\) from the hydroxide concentration using the ion product of water, which is \( KW = [H_3O^+][OH^-] \). At 25°C, KW is \(1.00 x 10^-14 \). Therefore, \( [H_3O^+] = \frac{KW}{{OH^-}} = \frac{1.00 x 10^-14}{0.00444}= 2.25 x 10^-12 \). The pH is calculated using the formula \( pH = -log[H_3O^+] \). When the values are substituted, the pH of the solution is calculated to be about 11.65.

Key concepts

Acid-Base Equilibrium

In the world of chemistry, the concept of acid-base equilibrium forms the backbone of many reactions. In simple terms, acid-base equilibrium refers to the balance between acidic and basic components in a solution, typically characterized by the pH scale. Understanding this balance is crucial as it helps us predict and explain how substances behave when dissolved in water.
For example, when a strong base like lithium oxide (\(\text{Li}_2\text{O}\)) is dissolved in water, it readily reacts with water to produce OH⁻ ions. These hydroxide ions increase the basicity of the solution, pushing the equilibrium towards the basic side of the pH scale (above pH 7). The interplay between acids and bases in a solution is pivotal for calculating important properties like pH, \([\text{H}_3\text{O}^+]\) concentration, and more.
It’s important to remember:

• A strong base will significantly raise the pH of a solution.
• The pH scale typically ranges from 0 to 14, with 7 being neutral.
• Bases contribute to the increase of OH⁻ ions in solution.

This equilibrium concept is essential for understanding how different substances influence acidity or basicity in a solution.

Molarity

Molarity is a convenient way to express the concentration of a solute in a solution. Defined as the number of moles of solute per liter of solution (mol/L or M), molarity allows chemists to determine how substances interact on a molecular level.
Molarity is crucial for balancing chemical equations, participating in stoichiometric calculations, and evaluating solution reactions. In our exercise, the molarity of the OH⁻ ions was calculated by dividing the amount of substance (moles of OH⁻) by the volume of the solution。

• Calculation: The moles of \(\text{Li}_2\text{O}\) lead to 0.00333 moles of OH⁻ when fully dissolved.
• Volume: The total volume of the solution is 0.750 liters.
• Molarity of OH⁻ ions: \(\frac{0.00333 \text{ mol}}{0.75 \text{ L}} = 0.00444 \text{ M}\)

Understanding molarity aids in predicting how a solution will behave, especially when linked with other calculations like pH determination.

Ion Product of Water

The ion product of water, denoted as \(K_w\), is a fundamental concept in chemistry that springs from the self-ionization of water. This means that in pure water, water molecules dissociate into equal amounts of hydrogen ions \([\text{H}^+]\) and hydroxide ions \([\text{OH}^-]\).
At 25°C, \(K_w\) is 1.00 x 10⁻¹⁴, a constant value that helps us connect \([\text{H}_3\text{O}^+]\) and \([\text{OH}^-]\) concentrations in a solution, providing a way to calculate one if the other is known. In our scenario, knowing the hydroxide concentration allowed us to find the hydronium concentration as:

• \([\text{H}_3\text{O}^+] = \frac{1.00 \times 10^{-14}}{\left[\text{OH}^-\right]}\)
• Knowing \([\text{H}_3\text{O}^+]\), the pH can be easily calculated as \(pH = -\log[\text{H}_3\text{O}^+]\).

The ion product of water establishes the neutral point on the pH scale and can help interpret how an acidic or basic an environment is through these ion calculations.

Hydroxide Ion Concentration

The hydroxide ion concentration, frequently overlooked, plays a major role in determining the pH of basic solutions. When a basic compound like lithium oxide (\(\text{Li}_2\text{O}\)) dissolves in water, it releases hydroxide ions \((\text{OH}^-)\), which decrease the acidity and increase the basic nature of the solution.
To calculate the hydroxide ion concentration, knowing the chemical reaction or compounds involved allows us to use stoichiometry.
Specifically:

• Each mole of \(\text{Li}_2\text{O}\) yields two moles of \(\text{OH}^-\).
• The molarity calculated from \(0.00167 \text{ mol of } \text{Li}_2\text{O}\) results in a \(0.00444 \text{ M }\text{OH}^- \) concentration.

Once this concentration is known, it can be used alongside \(K_w\) to evaluate the hydronium ion concentration and subsequently the pH. Thus, working with hydroxide ion concentration is essential for complete pH calculation for basic solutions.