A student added solid K₂O to a volumetric flask of volume 500.0 mL, which was then filled with water, resulting in 500.0 mL of KOH solution. Then 10.0 mL of the solution was transferred to another volumetric flask and diluted to 300.0 mL. The pH of the diluted solution is 14.12. 

(a) What is the molar concentration of hydroxide ion in (i) the diluted solution, (ii) the original solution?

(b) What mass of K₂O was added to the first flask?