Calculate the mass (in g) of solid potassium hydroxide required to prepare:
a) 1.75 litres of a solution with pH 11.5
pOH = 14 - pH = 2.5
[OH⁻] = 1.0E-2.5 = .0032 M
1.75 * .0032 = .0056 moles of KOH
multiply by the molar mass to find the quantity required
To calculate the mass of solid potassium hydroxide (KOH) required, we need to determine the concentration of the KOH solution. The pH alone is not sufficient to calculate the concentration, as it only provides information about the acidity or alkalinity of the solution.
Once we have the concentration, we can use the formula:
mass (in g) = volume (in L) × concentration (in mol/L) × molar mass (in g/mol)
Molar mass of KOH = 39.1 g/mol (for potassium) + 16.0 g/mol (for oxygen) + 1.0 g/mol (for hydrogen) = 56.1 g/mol
To determine the concentration of the KOH solution from the given pH, we need to calculate the hydroxide ion concentration ([OH-]). The pH can be used to find the concentration of hydrogen ions ([H+]) by using the formula:
[H+] = 10^(-pH)
In a neutral solution, the concentration of [H+] is equal to [OH-]. However, in basic solutions like KOH, the concentration of [OH-] is higher than [H+].
The concentration of hydroxide ions ([OH-]) can be calculated by using the formula:
[OH-] = Kw / [H+]
where Kw is the equilibrium constant for water and its value at room temperature is 1.0 x 10^-14.
Therefore, [OH-] = (1.0 x 10^-14) / [H+]
Let's calculate the concentration of hydroxide ions ([OH-]) using the formula above.
[H+] = 10^(-11.5) = 3.16 x 10^(-12) M
[OH-] = (1.0 x 10^-14) / (3.16 x 10^(-12)) ≈ 3.16 x 10^(-3) M
Now that we have the concentration of KOH, we can plug it into the mass calculation formula:
mass (in g) = 1.75 L × 3.16 x 10^(-3) M × 56.1 g/mol ≈ 0.102 g
Therefore, approximately 0.102 grams of solid potassium hydroxide (KOH) is required to prepare 1.75 liters of a solution with pH 11.5.