Question

Calculate the \(\mathrm{pH}\) of a solution made by adding 2.50 \(\mathrm{g}\) of lithium oxide \(\left(\mathrm{Li}_{2} \mathrm{O}\right)\) to enough water to make 1.500 \(\mathrm{L}\) of solution.

Short answer

The pH of the solution made by adding 2.50 g of lithium oxide (Li₂O) to 1.500 L of water is 13.048.

Step-by-step solution

Calculate the moles of Li₂O

Firstly, we need to find the number of moles of Li₂O using the given mass and molar mass. The molar mass of Li₂O is approximately the sum of twice the molar mass of Li plus the molar mass of O: \(2 \times 6.94 \, g/mol + 16.00 \, g/mol = 29.88 \, g/mol\). Now, let's calculate the number of moles: \[n = \frac{Mass}{Molar\, mass} = \frac{2.50 \, g}{29.88 \, g/mol} = 0.0837 \, mol\]

Calculate the concentration of Li₂O

With the moles of Li₂O and the volume of the solution, we can find the concentration of Li₂O: \[C_{Li_2O} = \frac{n}{V} = \frac{0.0837 \, mol}{1.5 \, L} = 0.0558 \, M\]

Write the dissociation equation for Li₂O in water

Next, we need to determine the dissociation equation for Li₂O in water: \[Li_2O_{(aq)} + H_2O_{(l)} \longrightarrow 2 Li^{+}_{(aq)} + 2 OH^{-}_{(aq)}\]

Determine the concentration of OH⁻ ions

Now, we can calculate the concentration of OH⁻ ions in the solution using the stoichiometry of the dissociation equation. Since every mole of Li₂O gives 2 moles of OH⁻ ions, the concentration of OH⁻ ions will be double the concentration of Li₂O: \[C_{OH^{-}} = 2 \times C_{Li_2O} = 2 \times 0.0558 \, M = 0.1116 \, M\]

Calculate the pH of the solution

To find the pH value, first, we need to find the pOH value using the concentration of OH⁻ ions: \[pOH = -\log_{10}(C_{OH^{-}}) = -\log_{10}(0.1116) = 0.952\] Then, using the relationship between pH and pOH (pH + pOH = 14), we can find the pH value: \[pH = 14 - pOH = 14 - 0.952 = 13.048\] Therefore, the pH of the solution is 13.048.

Key concepts

Molar Mass

Molar mass is a crucial concept in chemistry when working with substances in their various forms. It represents the mass of one mole of a substance, usually given in units of grams per mole (g/mol). To calculate the molar mass of a compound, such as lithium oxide (\(\text{Li}_2\text{O}\)), you need to sum the molar masses of all atoms in the formula.
The molar mass of lithium is approximately 6.94 g/mol. Since there are two lithium atoms in lithium oxide, you multiply this by 2. Oxygen contributes another 16.00 g/mol. Thus, by adding these, the molar mass of \(\text{Li}_2\text{O}\) is \(2 \times 6.94 \, \text{g/mol} + 16.00 \, \text{g/mol} = 29.88 \, \text{g/mol}\).

• Molar mass helps convert between the mass of a substance and the amount of substance in moles.
• It tells us how much one mole of a specific compound weighs.

Dissociation Equation

Understanding a dissociation equation is essential when dealing with salts in solutions. A dissociation equation shows how an ionic compound separates into its constituent ions in water. This is particularly important for predicting the concentrations of individual ions.
For lithium oxide (\(\text{Li}_2\text{O}\)), upon dissolving in water, it breaks down into lithium ions, \(\text{Li}^+\), and hydroxide ions, \(\text{OH}^-\). The dissociation reaction is given by:
\[\text{Li}_2\text{O}_{(aq)} + \text{H}_2\text{O}_{(l)} \longrightarrow 2 \text{Li}^+_{(aq)} + 2 \text{OH}^-_{(aq)}\]
Understanding this equation helps you see:

• Which ions are produced in the solution.
• The stoichiometry of the reaction, indicating the amount of each ion produced per molecule.

Concentration

Concentration quantifies how much of a substance is present in a given volume of solution. For chemistry problems, this is typically expressed in molarity (M), which is moles of solute per liter of solution.
After calculating the moles of \(\text{Li}_2\text{O}\), you determine the concentration by dividing the moles of solute by the volume of the solution in liters: \[C_{Li_2O} = \frac{0.0837 \, \text{mol}}{1.5 \, \text{L}} = 0.0558 \, \text{M}\]
This value indicates the concentration of \(\text{Li}_2\text{O}\) in the solution. Additionally, understanding concentration allows calculation of the required reactants or products in reactions.

• A higher concentration means more solute is present in a given volume.
• Concentration is vital when predicting how reactions will proceed in solution.

pOH

The concept of pOH is closely related to the familiar pH scale. While pH measures the concentration of hydrogen ions (\(\text{H}^+\)) in a solution, pOH measures the concentration of hydroxide ions (\(\text{OH}^-\)).
The calculation of pOH is straightforward once the concentration of \(\text{OH}^-\) ions is known: \[\text{pOH} = -\log_{10}(C_{\text{OH}^-}) = -\log_{10}(0.1116) = 0.952\]
By using pOH and knowing that the sum of pH and pOH is always 14 in any aqueous solution, you can find the pH. This relationship is powerful for determining the acidity or basicity of a solution.

• pOH is a reflection of how basic a solution is.
• pH and pOH are interconnected, allowing conversion between measurements.