Question #74884

Ascorbic acid, #"HC"_6"H"_7"O"_6#, a weak acid, will react with sodium hydroxide, #"NaOH"#, a strong base, to form aqueous sodium ascorbate, #"NaC"_6"H"_7"O"_6#, and water, according to the following balanced chemical equation

#"HC"_ 6"H"_ 7"O"_ (6(aq)) + "NaOH"_ ((aq)) -> "NaC"_ 6"H"_ 7"O"_ (6(aq)) + "H"_ 2"O"_((l))#

The acid and the base react in a #1:1# mole ratio, which means that you need one mole of sodium hydroxide for every mole of ascorbic acid present in solution.

Use the molarity and volume of the sodium hydroxide solution to determine how many moles of base were needed for the reaction

#color(purple)(|bar(ul(color(white)(a/a)color(black)(c = n_"solute"/V_"solution" implies n_"solute" = c * V_"solution")color(white)(a/a)|)))#

In your case, you will have

#n_(NaOH) = "0.100 mol" color(red)(cancel(color(black)("L"^(-1)))) * overbrace(14.50 * 10^(-3)color(red)(cancel(color(black)("L"))))^(color(purple)("volume in liters")) = "0.001450 moles NaOH"#

This means that the ascorbic acid solution contained #0.001450# moles of ascorbic acid.

To find how many grams of ascorbic acid would contain this many moles, use the acid's molar mass

#0.001450 color(red)(cancel(color(black)("moles HC"_6"H"_7"O"_6))) * "176.12 g"/(1color(red)(cancel(color(black)("moles HC"_6"H"_7"O"_6)))) = "0.255374 g"#

Since the total mass of the sample is said to be equal to #"0.258 g"#, you can say that its percent purity of the ascorbic acid is

#"purity" = (0.255374 color(red)(cancel(color(black)("g"))))/(0.258color(red)(cancel(color(black)("g")))) xx 100 = "98.98%"#

Rounded to three sig figs, the answer should be

#"purity" = color(green)(|bar(ul(color(white)(a/a)"99.0%"color(white)(a/a)|)))#