A technician had to prepare a 0.450M solution of hydrated sodium trioxocarbonate (IV) of 200cm^3 but had no information regarding the molar mass and state of hydration of Na2CO3.XH2O.

However the technician dissoloved1.0g of the compound to make 5.0cm^3 solution ,he determined the concentration to be 0.520M .Calculate the molar mass,the value of X and the mass of this compound the technician needed to prepare the required solution .

You need to learn to name compounds correctly. The name you have used is NOT a name approved by IUPAC. One correct name that IS approved by IUPAC is sodium carbonate.

The molar mass is determined this way:
M = mols/L. 0.520 M = moles/0.005 L so moles = 0.520 x 0.005 = 0.0026
Then mols = grams/molar mass and molar mass = grams/mols so
molar mass = 1.0/0.0026 = 384.6 = 385
You want 200 cc of 0.450 M; therefore, you want 0.450 M x 0.200 L = 0.0900 moles of the hydrate. grams hydrate = mols x molar mass = 0.009 x 385 = ?
For the formula of the hydrate, the molar mass of the hydrate is approximately 385 and Na2CO3 is 106 for molar mass. Therefore, 385 - 106 = 279 g = mass H2O and moles H2O is 279/18 = 15.5. Therefore, the hydrate is Na2CO3.15.5 H2O. There is no such hydrate but those are the numbers.