Answer
Compound 1: $HgO$
Compound 2: $Hg_2O$
Work Step by Step
Compound 1:
$\frac{0.6018}{0.6498}=92.6\text{ percent Mercury and $7.4$ percent Oxygen}$
$92.6\text{ grams Hg}*\frac{1\text{ mol Hg}}{200.59\text{ grams Hg}}=0.462\text{ mol Hg}$
$7.4\text{ grams O}*\frac{1\text{ mol O}}{15.9994\text{ grams O}}=0.465\text{ mol O}$
$0.462:0.465=1:1\Rightarrow HgO$
Compound 2:
$\frac{0.016}{0.4172}=3.835\text{ percent O and $96.165$ percent Hg}$
$96.165\text{ grams Hg}*\frac{1\text{ mol Hg}}{200.59\text{ grams Hg}}=0.479\text{ mol Hg}$
$3.825\text{ grams O}*\frac{1\text{ mol O}}{15.9994\text{ grams O}}=0.2397\text{ mol O}$
$0.479:0.2397\Rightarrow 2:1 \Rightarrow Hg_2O$