A metal, , of atomic weight 96 reacts with fluorine to form a salt that can be represented as . In order to determine and therefore the formula of the salt, a boiling point elevation experiment is performed. A 9.18- sample of the salt is dissolved in 100.0 of water and the boiling point of the solution is found to be 374.38 . Find the formula of the salt.
To solve this problem, we need to use the concepts of molar mass, molality, boiling point elevation, and the formula of the salt.
1. Calculate the number of moles of the salt:
Given mass of the salt = 9.18 g
Atomic weight of the metal = 96 g/mol
Number of moles of the salt = mass / atomic weight
= 9.18 g / 96 g/mol
= 0.095625 moles
2. Calculate the molality (moles of solute per kg of solvent):
Given mass of water = 100.0 g
Mass of water in kg = mass / 1000
= 100.0 g / 1000
= 0.1000 kg
Molality (m) = moles of solute / mass of water in kg
= 0.095625 moles / 0.1000 kg
= 0.95625 mol/kg
3. Use the boiling point elevation equation to find the formula of the salt:
ΔTb = Kb * m * i
where:
ΔTb is the boiling point elevation,
Kb is the molal boiling point elevation constant of the solvent (water),
m is the molality,
and i is the Van't Hoff factor.
The Van't Hoff factor (i) represents the number of particles formed when the salt dissolves in water. In this case, the formula of the salt is required to determine i.
4. Determine the Van't Hoff factor (i) based on the formula of the salt:
The given formula of the salt is X2Y, where X represents the metal and Y represents fluorine.
The metal has an atomic weight of 96. Since the atomic weight of fluorine is 19 g/mol, there are 5 fluorine atoms in the formula X2Y.
Therefore, the formula of the salt can be written as X2Y5, and the Van't Hoff factor (i) can be calculated as follows:
i = 1 + (number of cations) + (number of anions)
= 1 + 2 + 5
= 8
5. Find the molal boiling point elevation constant (Kb) for water:
The Kb value for water is a constant that can be found in reference books or online resources. Its value is 0.512 ˚C/m at 100.0 ˚C.
6. Now, plug the values into the boiling point elevation equation and solve for ΔTb:
ΔTb = Kb * m * i
= 0.512 ˚C/m * 0.95625 mol/kg * 8
= 3.9336 ˚C
7. Finally, calculate the boiling point of the solution:
Given boiling point of pure water = 100.0 ˚C
Boiling point of the solution = boiling point of pure water + ΔTb
= 100.0 ˚C + 3.9336 ˚C
= 103.9336 ˚C
Since the boiling point of the solution is found to be 374.38 ˚C, it is clear that there is a significant difference between the calculated boiling point (103.9336 ˚C) and the observed boiling point (374.38 ˚C). This discrepancy indicates that there was likely an error in the calculation or experimental procedure. Please review the steps, assumptions, and calculations to identify any potential mistakes.