How many grams of CaO should be dissolved in sufficient water to make 1.00 L of a solution with a pH of 10.50?

검증된 단계별 안내

Determine the concentration of hydroxide ions, [OH^-], in the solution using the pH value. Use the relationship: \( \text{pH} + \text{pOH} = 14 \) to find pOH, then calculate [OH^-] using \( \text{pOH} = -\log[\text{OH}^-] \).

Write the balanced chemical equation for the dissolution of CaO in water: \( \text{CaO} + \text{H}_2\text{O} \rightarrow \text{Ca}^{2+} + 2\text{OH}^- \).

Use the stoichiometry of the reaction to relate the moles of CaO to the moles of OH^- produced. From the balanced equation, 1 mole of CaO produces 2 moles of OH^-.

Calculate the moles of CaO needed to produce the required moles of OH^- using the stoichiometric relationship from the balanced equation.

Convert the moles of CaO to grams using the molar mass of CaO (\( \text{CaO} = 40.08 + 16.00 = 56.08 \text{ g/mol} \)).

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주요 개념

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pH and pOH

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. A pH of 10.50 indicates a basic solution, where the concentration of hydroxide ions can be calculated using the formula pOH = 14 - pH. Understanding pH and pOH is essential for determining the concentration of hydroxide ions in the solution.

Dissociation of CaO

Calcium oxide (CaO) is a strong base that dissociates completely in water to form calcium ions (Ca²⁺) and hydroxide ions (OH⁻). The reaction can be represented as CaO + H₂O → Ca²⁺ + 2OH⁻. Knowing the stoichiometry of this dissociation is crucial for calculating how much CaO is needed to achieve the desired hydroxide ion concentration for a specific pH.

Molarity and Mass Calculation

Molarity (M) is defined as the number of moles of solute per liter of solution. To find the mass of CaO required, one must first calculate the moles of hydroxide ions needed based on the desired pH, then use the molar mass of CaO to convert moles to grams. This process involves applying the formula: mass = moles × molar mass, which is fundamental in solution preparation.