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Verified Answer :

1)    Deduce
the two masses and see the amount of water was driven off when heated: 


5.03 g -
4.23 g = 0.8 g H2O given off 


2) Change
mass from grams to moles of H2O: 


0.8 g H2O
/ 18 g H2O in 1 mole = 0.044 mol H2O 


3) Change
left over mass to moles  of BaCl2 .


4.23 g
BaCl2 / 207 g BaCl2 in 1 mol = 0.021 mol BaCl2 


4)Find
the ratio of mol H2O to mol BaCl2: 


0.044 mol
H2O : 0.021 mol BaCl2 


5) The
resulting  ratio is  2:1 so two H2O for each BaCl2, thus,  the hydrate was named: 

Barium
chloride di-hydrate