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Chapter 16: Problem 104

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

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

Step by step solution

01

Calculate the moles of Li鈧侽

Firstly, we need to find the number of moles of Li鈧侽 using the given mass and molar mass. The molar mass of Li鈧侽 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: \[n = \frac{Mass}{Molar\, mass} = \frac{2.50 \, g}{29.88 \, g/mol} = 0.0837 \, mol\]
02

Calculate the concentration of Li鈧侽

With the moles of Li鈧侽 and the volume of the solution, we can find the concentration of Li鈧侽: \[C_{Li_2O} = \frac{n}{V} = \frac{0.0837 \, mol}{1.5 \, L} = 0.0558 \, M\]
03

Write the dissociation equation for Li鈧侽 in water

Next, we need to determine the dissociation equation for Li鈧侽 in water: \[Li_2O_{(aq)} + H_2O_{(l)} \longrightarrow 2 Li^{+}_{(aq)} + 2 OH^{-}_{(aq)}\]
04

Determine the concentration of OH鈦� ions

Now, we can calculate the concentration of OH鈦� ions in the solution using the stoichiometry of the dissociation equation. Since every mole of Li鈧侽 gives 2 moles of OH鈦� ions, the concentration of OH鈦� ions will be double the concentration of Li鈧侽: \[C_{OH^{-}} = 2 \times C_{Li_2O} = 2 \times 0.0558 \, M = 0.1116 \, M\]
05

Calculate the pH of the solution

To find the pH value, first, we need to find the pOH value using the concentration of OH鈦� 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.

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Key Concepts

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

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.

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Most popular questions from this chapter

Calculate the molar concentration of \(\mathrm{OH}^{-}\) in a 0.075 \(\mathrm{M}\) solution of ethylamine \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} ; K_{b}=6.4 \times 10^{-4}\right) .\) Calculate the pH of this solution.

Calculate \(\left[\mathrm{OH}^{-}\right]\) and \(\mathrm{pH}\) for (a) \(1.5 \times 10^{-3} \mathrm{MSr}(\mathrm{OH})_{2}\) (b) 2.250 \(\mathrm{g}\) of LiOH in 250.0 \(\mathrm{mL}\) of solution, \((\mathbf{c}) 1.00\) mL of 0.175 M NaOH diluted to \(2.00 \mathrm{L},\) (d) a solution formed by adding 5.00 \(\mathrm{mL}\) of 0.105 \(\mathrm{M} \mathrm{KOH}\) to 15.0 \(\mathrm{mL}\) of \(9.5 \times 10^{-2} \mathrm{MCa}(\mathrm{OH})_{2}.\)

The hypochlorite ion, \(\mathrm{ClO}^{-},\) acts as a weak base. (a) Is \(\mathrm{ClO}^{-},\) a stronger or weaker base than hydroxylamine? (b) When \(\mathrm{ClO}^{-}\) acts as a base, which atom, Cl or \(\mathrm{O},\) acts as the proton acceptor? (c) Can you use formal charges to rationalize your answer to part (b) ?

Label each of the following as being a strong base, a weak base, or a species with negligible basicity. In each case write the formula of its conjugate acid, and indicate whether the conjugate acid is a strong acid, a weak acid, or a species with negligible acidity: \((\mathbf{a})\mathrm{CH}_{3} \mathrm{COO}^{-},(\mathbf{b}) \mathrm{HCO}_{3}^{-},(\mathbf{c}) \mathrm{O}^{2-},(\mathbf{d}) \mathrm{Cl}^{-},(\mathbf{e}) \mathrm{NH}_{3}\)

Phenylacetic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\right)\) is one of the substances that accumulates in the blood of people with phenylketonuria, an inherited disorder that can cause mental retardation or even death. A 0.085\(M\) solution of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\) has a pH of \(2.68 .\) Calculate the \(K_{a}\) value for this acid.
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