Calculate the molarity of a solution made by adding 20.8 mL of concentrated potassium hydroxide (34.5 % by mass, density 1.46 g/mL) to some water in a volumetric flask, then adding water to the mark to make exactly 500 mL of solution. (It is important to add concentrated acid or base to water, rather than the other way, to minimize splashing and maximize safety.)
It was said that volume of conc.KOH = 20.8 mL
Mass of the conc.KOH taken = Density x Volume = 20.8 mL x 1.46 g/mL = 30.4 g
But, the concentration is given as 34.5% mass
That is 100g of solution contains 34.5 g of KOH
Now, 30.4 g of solution contains = (34.5 x 30.4) / 100 = 10.5 g of KOH
Now, let us find moles of KOH = Mass / Molar mass
= 10.5 g / 56.1 = 0.187 mol
Total volume = 500 mL
Volume of water + Volume of KOH = 500 mL
Volume of water = 500 - 20.8 = 479.2 mL
Mass of water = 479.2 g (as density of water = 1.00 g/mL) = 0.4792 Kg
Molarity = Moles of KOH / Kg of water = 0.187 / 0.4792 = 0.390 m
Thus molarity = 0.390 m
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