12.5g of hydrated copper(II)sulphide were heated to constant mass 8.0g of solid residue was formed.Determine the formula of the hydrated salt
To determine the formula of the hydrated salt, we need to find the number of water molecules attached to each formula unit of copper(II) sulfide.
First, we need to find the mass of the anhydrous (without water) copper(II) sulfide. The mass of the anhydrous copper(II) sulfide is calculated by subtracting the mass of the solid residue from the mass of the hydrated copper(II) sulfide:
Mass of anhydrous copper(II) sulfide = Mass of hydrated copper(II) sulfide - Mass of solid residue
Mass of anhydrous copper(II) sulfide = 12.5g - 8.0g
Mass of anhydrous copper(II) sulfide = 4.5g
Next, we need to find the moles of anhydrous copper(II) sulfide. This is calculated using the molar mass of copper(II) sulfide. The molar mass of copper(II) sulfide is found by adding the atomic masses of copper and sulfur:
Molar mass of copper = 63.55 g/mol
Molar mass of sulfur = 32.07 g/mol
Molar mass of copper(II) sulfide = 63.55 g/mol + 32.07 g/mol = 95.62 g/mol
Moles of anhydrous copper(II) sulfide = Mass of anhydrous copper(II) sulfide / Molar mass of copper(II) sulfide
Moles of anhydrous copper(II) sulfide = 4.5g / 95.62 g/mol
Moles of anhydrous copper(II) sulfide = 0.047 moles
Finally, we need to determine the ratio of moles of water to moles of anhydrous copper(II) sulfide. This ratio can be found by dividing the molar mass of water by the molar mass of copper(II) sulfide:
Molar mass of water = 18.02 g/mol
Ratio of moles of water to moles of anhydrous copper(II) sulfide = Molar mass of water / Molar mass of copper(II) sulfide
Ratio of moles of water to moles of anhydrous copper(II) sulfide = 18.02 g/mol / 95.62 g/mol
Ratio of moles of water to moles of anhydrous copper(II) sulfide = 0.188
From this ratio, we can infer that there is approximately 0.188 moles of water for every 1 mole of anhydrous copper(II) sulfide. However, since we cannot have fractional moles in a formula, we can multiply both values by a factor of 16 to get whole number ratios:
Ratio of moles of water to moles of anhydrous copper(II) sulfide = 0.188 * 16
Simplified ratio of moles of water to moles of anhydrous copper(II) sulfide = 3:1
Therefore, the formula of the hydrated copper(II) sulfide is CuS·3H2O.