A sample of mercury with a mass of 114.0g was combined with 17.9g of oxygen gas, and the resulting reaction gave 123.1g of mercury(II)oxide.?

Mercury + Oxygen yields Mercury (II) Oxide
2Hg + O₂ → 2HgO

HgO is 201+16 = 217 g/mol
Hg is 201 g/mol
O is 16 g/mol
402 g of Hg + 32 g of O₂ → 434 g of HgO

amount of oxygen needed is (32/402)114 g = 9.07 g of oxygen
17.9–9.1 = 8.8 g of oxygen remaining
due to subtraction, accuracy is only two places. 

According to the law of conservation of mass:
Total mass of reactants reacted
= Total mass of product produced
= 123.1 g

Mass of unreacted reactants left over after the reaction was complete
= (140.0 + 17.9) - 123.1 g
= 34.8 g

114.0 g + 17.9 g = 131.9 g reactants
 Mass product = 123.1 g
 Mass oxygen unreacted = 131.9-123.1 = 8.80 g oxygen unreacted.

The two previous answers answered two very different questions. Here is a third approach to answering the correct question:

123.1 g HgO / 216.6 g/mol X (1 mol O2 / 2 mol HgO) X 32.00 g/mol O2 = 9.09 g O2 consumed

Mass O2 remaining = 17.9 - 9.09 = 8.8 g O2 remaining

billrussell42's answer is correct.