Finding concentrations (Achieve 6B.11)

[305769107]

I seem to be getting the wrong answer but I am not sure what I am doing wrong. Can someone please explain how they would solve this?

A student added solid Na2O to a volumetric flask of volume 200.0 mL, which was then filled with water, resulting in 200.0 mL of NaOH solution. Then 5.00 mL of the solution was transferred to another volumetric flask and diluted to 500.0 mL. The pH of the diluted solution is 13.25. (a) What is the molar concentration of hydroxide ions in (i) the diluted solution, (ii) the original solution? (b) What mass of Na2O was added to the first flask?

[Anita Sarransingh 2A]

First you would find the concentration of OH- ions by doing 10^(-pOH) or 10^(-0.75), which is around (a)(i) 0.179 M. This gives the amount of moles in one liter, so you would multiply this by 0.5 L to get amount of moles in this solution, which is 0.0889. Since this amount of moles was originally in the 0.005 L of the 0.2 L solution, that means that the entire original solution of 0.2L had 0.2/0.005, or 40 times the amount we have in the .5 L solution. For this reason we would multiply 0.0889 by 40 to get the original amount of moles of OH-, which is 3.556 moles. To get molar concentration, we would divide this value by 0.2 L, which is (a)(ii) 17.78 M. To find the mass of Na2O originally added to the flask, we would divide the total moles (3.556) by 2 since for every one Na2O molecule, 2 NaOH molecules are created. This gives the amount of moles of Na2O that were originally added. To get the mass, multiply by the molar mass, which is 61.98 g/mol. This gives the value (b) 110 grams.