When hafnium metal is heated in an atmosphere of chlorine gas, the product of the reaction is found to contain 62.2% hf by mass and 37.4% cl by mass. what is the empirical formula for this compound?

Clearly the percentages are weights. 
For Hafnium metal it’s 62.2%, grams per mole for Hafnium = 178.5 grams / moles 
For Chlorine gas it's 37.4%, grams per mole for Chlorine = 35.45 grams / moles 
Calculating the molar masses,  
Hafnium = 62.2 g / 178.5 grams / moles = 0.35 mol
 Chlorine = 37.4 g / 35.45 grams / moles = 1.05 mol
 Divide by the smallest to get the ratios,
 0.35 mol Hf / 0.35 mol = 1 mol Hf
 1.05 mol Cl / 0.35 mol = 3 mol Cl
 So the emperical formula would be HfCl3

They are all solids.