# If 10 drops of pyruvic acid (HC_3H_3O_3) are titrated with 20 drops of 0.25 M NaOH, what is the molar concentration of the pyruvic acid solution?

Jun 17, 2016

$\text{0.50 M}$

#### Explanation:

The idea here is that you don't need to know what a drop means in terms of volume, all you need to do is focus on the fact that you need twice as many drops of sodium hydroxide solution than of pyruvic acid solution.

Pyruvic acid, a weak acid, will react with the hydroxide anions delivered to the solution by the sodium hydroxide, a strong base, in a $1 : 1$ mole ratio to form the pyruvirate anion, ${\text{CH"_3"COCOO}}^{-}$, and water.

${\text{CH"_ 3 "COCOOH" _ ((aq)) + "OH"_ ((aq))^(-) -> "CH"_ 3"COCOO"_ ((aq))^(-) + "H"_ 2"O}}_{\left(l\right)}$

This means that a complete neutralization will require equal numbers of moles of pyruvic acid and of hydroxide anions.

You know that you have $10$ drops of pyruvic acid solution of unknown concentration that require $20$ drops of the sodium hydroxide solution for complete neutralization.

This means that the $10$ drops of pyruvic acid must contain the same number of moles of solute as the $20$ drops of sodium hydroxide.

In other words, for the same volume of pyruvic acid solution you get twice as many moles of solute than you get for the sodium hydroxide solution.

This means that the pyruvixc acid solution is twice as concentrated as the sodium hydroxide solution, which means that its molarity will be

["CH"_3"COCOOH"] = 2 xx "0.25 M" = color(green)(|bar(ul(color(white)(a/a)color(black)("0.50 M")color(white)(a/a)|)))

An important thing to note here is that we're assuming that the drops of pyruvic acid solution and the drops of sodium hydroxide solution have equal volumes.