The palladium content of a steel sample was determined as follows. A 16.312 g steel sample was dissolved in concentrated HCl(aq). The solution obtained was treated to remove interfering ions, to establish the proper pH, and to obtain a final solution volume of 250.0 mL. A 10.00 mL sample of this solution was then treated with dimethylglyoxime to convert all of the palladium to palladium dimethylglyoximate, a chemical compound that is 31.61% Pd (by mass), 28.54% C, 4.19% H, 19.01% O, and 16.64% N. The mass of purified, dry palladium dimethylglyoximate obtained was 0.0784 g.

(a) What is the empirical formula of palladium dimethylglyoximate?

(b) What is the mass percent of palladium in the steel sample?