Question

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

Short answer

The pH of the solution is 11.775.

Step-by-step solution

Calculate the moles of CaO

To calculate the moles of CaO, we can use its molar mass and the given mass: Molar mass of CaO = \(40.08 (Ca) + 16.00 (O) = 56.08 \,\mathrm{g/mol}\) mass of CaO = 0.25 g moles of CaO = mass / molar mass = \(0.25 \,\mathrm{g} / 56.08 \,\mathrm{g/mol} = 4.46 \times 10^{-3} \,\mathrm{mol}\)

Reaction and ionization of CaO in water

CaO reacts with water and ionizes as follows: \(CaO + H_2O \rightarrow Ca(OH)_2\) For each mole of CaO reacted, one mole of Ca(OH)2 is formed. The ionization of Ca(OH)2 in water is: \(Ca(OH)_2 \rightarrow Ca^{2+} + 2OH^-\) For each mole of Ca(OH)2, two moles of OH- are released.

Calculate the concentration of OH- ions

Since one mole of CaO produces two moles of OH-, converting the moles of CaO into moles of OH-: moles of OH- = 2 * moles of CaO = 2 * \(4.46 \times 10^{-3}\,\mathrm{mol}\) = \(8.92 \times 10^{-3}\,\mathrm{mol}\) Now, we need to consider the volume of the solution, which is 1500 mL or 1.5L. OH- concentration = moles of OH- / volume OH- concentration = \(8.92 \times 10^{-3}\,\mathrm{mol} / 1.5 \,\mathrm{L} = 5.95 \times 10^{-3} \,\mathrm{M}\)

Calculate the pOH and pH of the solution

Since we have the concentration of OH- ions in the solution, we can find the pOH using the formula: pOH = - log10 (OH- concentration) = - log10(5.95 × 10^{-3}) = 2.225 Now, we can find the pH using the relationship between pH and pOH: pH + pOH = 14 pH = 14 - pOH pH = 14 - 2.225 = 11.775 So, the pH of the solution is 11.775.

Key concepts

pH

The pH is a scale used to specify how acidic or basic (alkaline) a water-based solution is. The pH scale ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are basic. pH is a logarithmic measure of the hydrogen ion concentration and is calculated as \(\text{{pH}} = -\log_{10}[H^+]\). In the given exercise, the pH calculation is particularly interesting because it involves a basic solution. Starting with the hydroxide ion concentration, and knowing that the sum of pH and pOH equals 14, we can easily switch between the two. This is a critical component of understanding acid-base equilibria, which is essential for students of chemistry at all levels.

In daily practice, pH measurement is relevant in a variety of fields, such as medicine, biology, chemistry, and environmental science. For instance, maintaining the correct pH levels is vital in blood chemistry, pharmaceutical product formulation, or for ensuring the health of aquatic ecosystems.

molar mass

Molar mass is the weight of one mole (or 6.022 x 10^23 particles) of a substance expressed in grams per mole (g/mol). It is directly related to the atomic or molecular weight of a substance, as listed on the periodic table for elements or calculated by summing the atomic weights for compounds. In the exercise solution, we use the molar mass of calcium oxide (CaO) to determine how many moles of the substance are in a 0.25 g sample. Calculating molar mass is a fundamental task in chemistry which allows the conversion from mass to moles, a critical step in stoichiometry and in the determination of reactant and product quantities in chemical reactions.

Understanding this concept is essential for students because it is the bridge between the macroscopic world we can measure and the microscopic world of atoms and molecules. Calculating molar mass accurately is crucial for preparing solutions of desired molarity and for understanding material properties.

Ionization

Ionization in chemistry refers to the process where an atom or a molecule either gains or loses electrons to form ions. Specifically for acids and bases, ionization is the process by which an acid or base releases hydrogen (H+) or hydroxide (OH-) ions, respectively, when dissolved in water. In our exercise, calcium oxide (CaO) reacts with water and ionizes to produce calcium ions (Ca2+) and hydroxide ions (OH-). Each mole of CaO produces two moles of OH- ions upon dissolution and ionization, an important nuance that affects the pH of the solution.

Ionization is essential for understanding electrical conductivity, reactivity, solubility, and pH in solutions. In acid-base reactions, ionization is responsible for the formation of the acidic or basic nature of the solution. Hence, a thorough grasp of ionization is indispensable for students tackling problems in acid-base chemistry.

Acid-base chemistry

Acid-base chemistry is the study of the properties of acids and bases, their reactions, and their role in chemical equilibria. Acids are substances that release hydrogen ions (H+) in solution, while bases release hydroxide ions (OH-). The interaction between acids and bases can result in neutralization, producing water and a salt. Moreover, the concept of acid and base extends to include acid-base pairs and buffers, crucial for maintaining stability in biological systems and industrial processes.

In the context of our exercise, we demonstrate an acid-base reaction where lime, a base, ionizes in water leading to the release of hydroxide ions, increasing the solution's pH. For students, mastering acid-base chemistry is important not only for understanding the properties of substances but also for predicting the outcomes of chemical reactions and solving problems involving pH and titration.