Answer:
The value of x is 2
Explanation:
BaCl2.xH2O react with H2SO4 according to the equation:
BaCl2.xH2O + H2SO4 —> BaSO4 + 2HCl + xH2O
Data obtained from the question include:
Mass of hydrated salt (BaCl2.xH2O) = 1.80g
Mass of BaSO4 = 1.72g
Now, let us calculate the number of mole of BaSO4 present in 1.72g of BaSO4. This is illustrated below:
Molar Mass of BaSO4 = 137 + 32 + (16x4) = 137 + 32 + 64 = 233g/mol
Mass of BaSO4 = 1.72g
Number of mole of BaSO4 =?
Number of mole = Mass /Molar Mass
Number of mole BaSO4 = 1.72/233
Number of mole BaSO4 = 0.0074 mole.
From the equation above,
1 mole of BaCl2.xH2O produced 1 mole of BaSO4.
Therefore, 0.0074 mole of BaCl2.xH2O will also produce 0.0074 mole of BaSO4.
Now, with this amount (i.e 0.0074 mole) of BaCl2.xH2O, we can obtain the value of x as follow:
Molar Mass of BaCl2.xH2O = 137 + (35.5x2) + x[(2x1) + 16]
= 137 + 71 + x[2 + 16]
= 208 + 18x
Mass of BaCl2.xH2O from the question = 1.80g
Number of mole of BaCl2.xH2O =
0.0074 mole
Number of mole = Mass /Molar Mass
0.0074 = 1.80/208 + 18x
Cross multiply to express in linear form as shown below:
0.0074(208 + 18x) = 1.8
Clear the bracket
1.5392 + 0.1332x = 1.8
Collect like terms
0.1332x = 1.8 - 1.5392
0.1332x = 0.2608
Divide both side by the coefficient of x i.e 0.1332
x = 0.2608/0.1332
x = 2
Therefore the formula for the hydrated salt (BaCl2.xH2O) is BaCl2.2H2O
