Answer :
Final answer:
The formula for the hydrated salt of barium chloride, based on the loss of 5.4 g of water upon heating 36.6 g of the salt, is determined to be BaCl2·2H2O. The Correct Answer is Option.B.
Explanation:
The question involves finding the formula of a hydrated salt of barium chloride when a certain mass of the salt upon heating loses water to form anhydrous barium chloride. Given are 36.6 g of hydrated salt yielding 5.4 g of water upon heating.
First, we determine the moles of water lost: The molar mass of water (H2O) is 18 g/mol.
Thus, 5.4 g / 18 g/mol = 0.3 moles of water lost. To find the moles of barium chloride (BaCl2), we subtract the mass of water from the initial mass of the hydrated salt to get the mass of anhydrous BaCl2, which is 36.6 g - 5.4 g = 31.2 g.
The molar mass of BaCl2 is approximately 208 g/mol (Ba: 137 + Cl: 35.5x2). Thus, 31.2 g / 208 g/mol = 0.15 moles of BaCl2.
Since we have 0.3 moles of H2O and 0.15 moles of BaCl2, the molar ratio of H2O to BaCl2 is 2:1, which means for every mole of BaCl2, there are two moles of H2O. Therefore, the formula of the hydrated salt is BaCl2·2H2O.
"The correct formula of the hydrated salt of barium chloride, based on the given information, is BaClâ‚‚.7Hâ‚‚O.
To determine the formula of the hydrated salt, we need to find out how many moles of water are lost upon heating.
First, we calculate the mass of anhydrous barium chloride (BaClâ‚‚) by subtracting the mass of water lost from the mass of the hydrated salt:
Mass of anhydrous BaClâ‚‚ = Mass of hydrated salt - Mass of water lost
= 36.6 g - 5.4 g
= 31.2 g
Next, we find the moles of anhydrous BaClâ‚‚ using its molar mass. The molar mass of BaClâ‚‚ is calculated as:
Molar mass of BaCl₂ = Atomic mass of Ba + 2 × Atomic mass of Cl
= 137 g/mol + 2 × 35.45 g/mol
= 137 g/mol + 70.90 g/mol
= 207.90 g/mol
Moles of anhydrous BaClâ‚‚ = Mass of anhydrous BaClâ‚‚ / Molar mass of BaClâ‚‚
= 31.2 g / 207.90 g/mol
= 0.15 mol (approximately)
Since the moles of BaClâ‚‚ in the hydrated salt are the same as in the anhydrous salt, we can use this to find the moles of water that were lost:
Mass of water lost = 5.4 g
Moles of water lost = Mass of water lost / Molar mass of Hâ‚‚O
= 5.4 g / 18 g/mol
= 0.3 mol
Now, we find the ratio of moles of water to moles of BaClâ‚‚:
Ratio = Moles of water / Moles of BaClâ‚‚
= 0.3 mol / 0.15 mol
= 2
This means that for every mole of BaClâ‚‚, there are 2 moles of water in the hydrated salt. Therefore, the formula of the hydrated salt is BaClâ‚‚.2Hâ‚‚O.
However, we are given options that include hydrated salts with different numbers of water molecules. We need to find the option that matches our calculated ratio. The closest option to our calculated ratio of 2 is option (A) BaClâ‚‚.7Hâ‚‚O, which indicates that for every mole of BaClâ‚‚, there are 7/2 moles of water. Since our calculated ratio is 2, and option (A) is the closest to this value, the correct formula of the hydrated salt is BaClâ‚‚.7Hâ‚‚O.