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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 (Li₂O) to 1.500 L of water is 13.048.

Step by step solution

01

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: \[n = \frac{Mass}{Molar\, mass} = \frac{2.50 \, g}{29.88 \, g/mol} = 0.0837 \, mol\]
02

Calculate the concentration of Li₂O

With the moles of Li₂O and the volume of the solution, we can find the concentration of Li₂O: \[C_{Li_2O} = \frac{n}{V} = \frac{0.0837 \, mol}{1.5 \, L} = 0.0558 \, M\]
03

Write the dissociation equation for Li₂O in water

Next, we need to determine the dissociation equation for Li₂O in water: \[Li_2O_{(aq)} + H_2O_{(l)} \longrightarrow 2 Li^{+}_{(aq)} + 2 OH^{-}_{(aq)}\]
04

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: \[C_{OH^{-}} = 2 \times C_{Li_2O} = 2 \times 0.0558 \, M = 0.1116 \, M\]
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⁻ 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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Most popular questions from this chapter

Which of the following statements is false? (a) An Arrhenius base increases the concentration of OH \(^{-}\) in water. (b) A Bronsted-Lowry base is a proton acceptor. (c) Water can act as a Bronsted-Lowry acid. (d) Water can act as a Bronsted-Lowry base. (e) Any compound that contains an \(-\)OH group acts as a Bronsted-Lowry base.

What is the boiling point of a 0.10\(M\) solution of \(\mathrm{NaHSO}_{4}\) if the solution has a density of 1.002 \(\mathrm{g} / \mathrm{mL} ?\)

Is each of the following statements true or false? (a) All strong acids contain one or more H atoms. (b) A strong acid is a strong electrolyte. (c) A \(1.0-M\) solution of a strong acid will have \(\mathrm{pH}=1.0 .\)

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: (a) \(0.0167 M \mathrm{HNO}_{3},(\mathbf{b}) 0.225 \mathrm{g}\) of \(\mathrm{HClO}_{3}\) in 2.00 \(\mathrm{L}\) of solution, \((\mathbf{c}) 15.00 \mathrm{mL}\) of 1.00 \(\mathrm{M} \mathrm{HCl}\) diluted to \(0.500 \mathrm{L},\) (d) a mixture formed by adding 50.0 \(\mathrm{mL}\) of 0.020 \(\mathrm{MHCl}\) to 125 \(\mathrm{mL}\) of 0.010 \(\mathrm{M} \mathrm{HI} .\)

Carbon dioxide in the atmosphere dissolves in raindrops to produce carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right),\) causing the pH of clean, unpolluted rain to range from about 5.2 to 5.6. What are the ranges of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in the raindrops?
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