A sample of oleum consisting of a solution of SO$3$ in sulfuric acid, spent $27\mathrm{.}5$ ml of NaOH

$0\mathrm{.}2500$ M in its valuation. If the mass of the sample analyzed was $0\mathrm{.}3140$ grams, calculate:

to$.$ The richness in SO$3$ and H$2$SO$4$ of the sample, and

b$.$ The volume of sodium hydroxide that would be spent in titrating $0\mathrm{.}500$ grams of oleum containing

$10\%$ SO$3.$