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?

Question

Noah Aldrich · Accepted Answer

#"0.50 M"#

The idea here is that all you have to do is concentrate on the fact that you require twice as many drops of sodium hydroxide solution as pyruvic acid solution; you don't even need to understand what a drop means in terms of volume.

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, #"CH"_3"COCOO"^(-)#, and water.

#"CH"_ 3 "COCOOH" _ ((aq)) + "OH"_ ((aq))^(-) -> "CH"_ 3"COCOO"_ ((aq))^(-) + "H"_ 2"O"_((l))#

This indicates that the quantity of pyruvic acid and hydroxide anions needed for a full neutralization will be equal.

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.

Put another way, you obtain twice as many moles of solute for the same volume of pyruvic acid solution as you do for sodium hydroxide solution.

This indicates that the molarity of the pyruvixc acid solution will be twice that of the sodium hydroxide solution due to its double concentration.

#["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)|)))#

It's crucial to keep in mind that we're making the assumption that the volumes of the sodium hydroxide and pyruvic acid solution drops are equal.

Jose Ayala · Answer

undefined To find the molar concentration of the pyruvic acid (HC3H3O3) solution, we need to use the concept of titration.

Given that 20 drops of 0.25 M NaOH are used to titrate 10 drops of pyruvic acid, we can set up an equation using the balanced chemical equation between pyruvic acid and NaOH:

HC3H3O3 + NaOH -> NaC3H3O3 + H2O

Since the mole ratio between pyruvic acid and NaOH is 1:1, we can equate the moles of NaOH used to the moles of pyruvic acid present.

Number of moles of NaOH = Volume of NaOH (in L) * Molarity of NaOH
Number of moles of NaOH = 20 drops * (1 mL / 20 drops) * (1 L / 1000 mL) * 0.25 mol/L

Once we have the number of moles of NaOH used, we know it reacts with the same number of moles of pyruvic acid. Since the number of drops is proportional to the volume of the solution, we can use the ratio of drops to determine the volume of pyruvic acid solution.

Volume of pyruvic acid solution = 10 drops * (1 mL / 20 drops)

Now, we can calculate the molar concentration of the pyruvic acid solution:

Molarity of pyruvic acid = Number of moles of pyruvic acid / Volume of pyruvic acid solution

Molarity of pyruvic acid = (Number of moles of NaOH) / (Volume of pyruvic acid solution)

Therefore, the molar concentration of the pyruvic acid solution is equal to the molarity of NaOH solution. So, the molar concentration of the pyruvic acid solution is 0.25 M.