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Chapter 14: Problem 150

A 0.25 -g sample of lime (CaO) is dissolved in enough water to make 1500 \(\mathrm{mL}\) of solution. Calculate the pH of the solution.

Short Answer

Expert verified
The pH of the lime (CaO) solution is approximately 11.77.

Step by step solution

01

Calculate moles of CaO

First, we need to calculate the number of moles of CaO present in the 0.25-g sample. To do this, we can use the molar mass of CaO (Ca = 40.08 g/mol and O = 16.00 g/mol): Molar mass of CaO = 40.08 + 16.00 = 56.08 g/mol Now, we can calculate the number of moles of CaO in the sample using its mass and molar mass: Moles of CaO = (Mass of CaO) / (Molar mass of CaO) = \( \frac{0.25 \text{ g}}{56.08 \text{ g/mol}} \) Moles of CaO = 0.00446 mol
02

Calculate the concentration of CaO in the solution

Now that we have the moles of CaO, we can calculate its concentration in the 1500 mL solution: Concentration of CaO = (Moles of CaO) / (Volume of solution in L) Concentration of CaO = \( \frac{0.00446 \text{ mol}}{1.5 \text{ L}} \) Concentration of CaO = 0.00297 mol/L
03

Calculate the concentration of hydroxide ions (OH⁻)

When CaO dissolves in water, it reacts to form calcium hydroxide (Ca(OH)₂) as follows: CaO + H₂O → Ca(OH)₂ Since each mole of CaO reacts to produce one mole of Ca(OH)₂, and each mole of Ca(OH)₂ produces two moles of OH⁻ ions, the concentration of OH⁻ ions would be double the concentration of CaO. Concentration of OH⁻ = 2 × Concentration of CaO = 2 × 0.00297 mol/L Concentration of OH⁻ = 0.00594 mol/L
04

Calculate the pH of the solution

To calculate the pH of the solution, first, we'll calculate the pOH using the concentration of OH⁻ ions: pOH = -log₁₀[OH⁻] = -log₁₀(0.00594) pOH ≈ 2.23 Since the relationship between pH and pOH is given by: pH + pOH = 14 We can find the pH of the solution: pH = 14 - pOH = 14 - 2.23 pH ≈ 11.77 The pH of the lime (CaO) solution is approximately 11.77.

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Most popular questions from this chapter

What mass of \(\mathrm{NaOH}(s)\) must be added to 1.0 \(\mathrm{L}\) of 0.050 \(\mathrm{M}\) \(\mathrm{NH}_{3}\) to ensure that the percent ionization of \(\mathrm{NH}_{3}\) is no greater than 0.0010\(\% ?\) Assume no volume change on addition of \(\mathrm{NaOH} .\)

Will the following oxides give acidic, basic, or neutral solutions when dissolved in water? Write reactions to justify your answers. a. \(\mathrm{Li}_{2} \mathrm{O}\) b. \(\mathrm{CO}_{2}\) c. \(\mathrm{SrO}\)

A typical sample of vinegar has a pH of \(3.0 .\) Assuming that vinegar is only an aqueous solution of acetic acid \(\left(K_{\mathrm{a}}=1.8 \times\right.\) \(10^{-5}\) ), calculate the concentration of acetic acid in vinegar.

Arrange the following 0.10\(M\) solutions in order from most acidic to most basic. See Appendix 5 for \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) values. $$ \mathrm{CaBr}_{2}, \mathrm{KNO}_{2}, \mathrm{HClO}_{4}, \quad \mathrm{HNO}_{2}, \quad \mathrm{HONH}_{3} \mathrm{ClO}_{4} $$

For solutions of the same concentration, as acid strength increases, indicate what happens to each of the following (increases, decreases, or doesn't change). $$ \begin{array}{ll}{\text { a. }\left[\mathrm{H}^{+}\right]} & {\text { d. pOH }} \\ {\text { b. pH }} & {\text { e. } K_{\mathrm{a}}} \\ {\text { c. }\left[\mathrm{OH}^{-}\right]}\end{array} $$
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