Calcium hydroxide is an ionic compound with the chemical formula Ca(OH)2. When it is dissolved in water, it dissociates into its constituent ions, which are calcium (Ca2+) and hydroxide (OH-) ions. The pH of the resulting solution depends on the concentration of hydroxide ions.
To calculate the mass of calcium hydroxide required to prepare a 200.0 mL solution with a pH of 12.55, we first need to determine the concentration of hydroxide ions in the solution using the pH value.
The pH of 12.55 corresponds to a hydroxide ion concentration of 2.00 x 10^-3 M. This is because pH is defined as the negative logarithm of the hydrogen ion concentration, and in a basic solution, the hydroxide ion concentration is equal to the hydrogen ion concentration multiplied by the concentration of water (which is approximately 55.6 M at room temperature). So:
pH = -log[H+]
pH = 14 - log[OH-]
12.55 = 14 - log[OH-]
log[OH-] = 1.45
[OH-] = 10^-pOH
[OH-] = 10^-12.55
[OH-] = 2.00 x 10^-3 M
The molar mass of calcium hydroxide is 74.093 g/mol (40.078 g/mol for calcium + 2 x 15.999 g/mol for oxygen + 2 x 1.008 g/mol for hydrogen). The number of moles of hydroxide ions in the solution is equal to the concentration multiplied by the volume (in liters) of the solution:
moles of OH- = [OH-] x volume
moles of OH- = 2.00 x 10^-3 M x 0.200 L
moles of OH- = 4.00 x 10^-4 mol
Since each molecule of calcium hydroxide dissociates into two hydroxide ions, the number of moles of calcium hydroxide required is half of the number of moles of hydroxide ions:
moles of Ca(OH)2 = 0.5 x moles of OH-
moles of Ca(OH)2 = 0.5 x 4.00 x 10^-4 mol
moles of Ca(OH)2 = 2.00 x 10^-4 mol
Finally, we can calculate the mass of calcium hydroxide required using its molar mass:
mass of Ca(OH)2 = moles of Ca(OH)2 x molar mass
mass of Ca(OH)2 = 2.00 x 10^-4 mol x 74.093 g/mol
mass of Ca(OH)2 = 0.0148 g
Therefore, the mass of calcium hydroxide required to prepare a 200.0 mL solution with a pH of 12.55 is approximately 0.0148 g.