$x \mathrm{mg}$ of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K . The value of $x$ is ________ mg. (Nearest integer)

(Given : $\mathrm{Mg}(\mathrm{OH})_2$ is assumed to dissociate completely in $\mathrm{H}_2 \mathrm{O}$ ]

<p>To determine the mass of Mg(OH)₂ that needs to be dissolved to achieve a pH of 10.0, follow these steps:</p> <p>Given:</p> <p><p>pH = 10</p></p> <p><p>Therefore, pOH = 14 - pH = 4</p></p> <p><p>[OH⁻] = 10⁻⁴ M</p></p> <p>First, calculate the number of moles of OH⁻ ions:</p> <p>Number of moles of OH⁻ = 10⁻⁴</p> <p>Since Mg(OH)₂ dissociates completely in water, from one mole of Mg(OH)₂, you get two moles of OH⁻:</p> <p>Number of moles of Mg(OH)₂ = (10⁻⁴) / 2 = 5 × 10⁻⁵ moles</p> <p>Next, calculate the mass of Mg(OH)₂:</p> <p>Molar mass of Mg(OH)₂ = 58 g/mol</p> <p>Convert the number of moles to mass:</p> <p><p>Mass of Mg(OH)₂ = (5 × 10⁻⁵ moles) × (58 g/mol) = 2.9 × 10⁻³ g</p></p> <p><p>Convert to milligrams: 2.9 × 10⁻³ g = 2.9 mg</p></p> <p>Therefore, the calculated mass of Mg(OH)₂ required is approximately 2.9 mg.</p>