A \(0.4324 \mathrm{g}\) sample of a potassium hydroxide-lithium hydroxide mixture requires \(28.28 \mathrm{mL}\) of \(0.3520 \mathrm{M} \mathrm{HCl}\) for its titration to the equivalence point. What is the mass percent lithium hydroxide in this mixture?

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Step by step solution

01

Calculate moles of HCl

Molarity is defined as the number of moles of solute per litre of solution. So, the amount of moles of HCl can be calculated by multiplying the molarity by the volume (in litres). Moles of \(HCl = 0.3520 \, M \times 0.02828 \, L = 0.00995456 \, mol\).
02

Determine moles of OH-

In a titration to the equivalence point with HCl, the moles of hydronium ion (H+) from HCl will equal the moles of hydroxide ion (OH-) from the base there was originally in the mixture. Hence, moles of OH- = 0.00995456 mol.
03

Calculate mass of each hydroxide

Potassium hydroxide (KOH) and lithium hydroxide (LiOH) both provide one mole of OH- per mole. We can now write an equation representing the total OH- from KOH and LiOH as: Mass = moles OH- \times molar mass = 0.00995456 mol \times 56.1 g/mol (for KOH) + 0.00995456 mol \times 23.95 g/mol (for LiOH) = 0.5586 g + 0.23833 g = 0.79693 g. This is the maximum total mass of KOH and LiOH that could be in the sample.
04

Calculate mass percent of LiOH

Knowing maximum total mass of KOH and LiOH that could be in the sample and the actual mass of the sample, we can now subtract to get the mass of the unknown component. Subtracting from the total mass yields an estimate of the mass of LiOH: Mass of LiOH = total mass of sample - mass of KOH = 0.4324 g - 0.5586 g = -0.1262 g. Since the calculated mass of LiOH is negative, this suggests that the sample doesn't contain LiOH. Therefore, the percent by mass of LiOH in the mixture would be 0.

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