A metal, M, of atomic mass 91 amu reacts with fluorine to form a salt that can be represented as MFx. In order to determine x and therefore the formula of the salt, a boiling point elevation experiment is performed. A 9.05-g sample of the salt is dissolved in 100.0 g of water and the boiling point of the solution is found to be 374.54 K. Find the formula of the salt. Assume complete dissociation of the salt in solution.
HELP!!!!
To find the formula of the salt, we need to determine the value of x in MFx. Here's how we can approach this problem step by step:
Step 1: Calculate the number of moles of the salt.
First, we need to calculate the number of moles of the salt (MFx) using its mass and the atomic mass of the metal (M).
Given:
Atomic mass of M = 91 amu
Mass of the salt = 9.05 g
Number of moles of the salt = Mass of the salt / Atomic mass of M
= 9.05 g / 91 amu
= 0.0995 moles (approximately)
Step 2: Calculate the molality of the solution.
Next, we need to calculate the molality (mol/kg) of the solution using the mass of water and the number of moles of the salt.
Given:
Mass of water = 100.0 g (or 0.1 kg)
Molality (m) = moles of solute / mass of solvent (in kg)
= 0.0995 moles / 0.1 kg
= 0.995 mol/kg
Step 3: Determine the boiling point elevation constant (Kb) for water.
The boiling point elevation constant (Kb) is a characteristic property of the solvent and can be found in reference tables. For water, Kb is equal to 0.512 K kg/mol.
Step 4: Calculate the boiling point elevation (∆Tb).
The boiling point elevation is the difference between the boiling point of the solution and the boiling point of the pure solvent (water in this case).
Given:
Boiling point of the solution = 374.54 K
Boiling point of pure solvent (water) = 373.15 K
∆Tb = Boiling point of the solution - Boiling point of pure solvent
= 374.54 K - 373.15 K
= 1.39 K
Step 5: Calculate x (the number of moles of solute particles) using the formula:
∆Tb = Kb * m * x
Solving for x, we get:
x = ∆Tb / (Kb * m)
= 1.39 K / (0.512 K kg/mol * 0.995 mol/kg)
= 2.71
Since x represents the number of moles of solute particles, it is usually very close to a whole number. In this case, x is approximately 3.
Step 6: Determine the formula of the salt.
Now that we know x is 3, we can write the formula of the salt MFx, where x = 3.
Therefore, the formula of the salt is MF3.
Note: This calculation assumes complete dissociation of the salt in water, meaning that each formula unit of MFx breaks up into M ions and x F ions in solution.
To determine the formula of the salt, we need to find the value of x in MFx.
First, let's calculate the number of moles of the salt using its mass and molar mass:
Number of moles of the salt = mass of the salt / molar mass
Mass of the salt = 9.05 g
Molar mass of the salt (M) = 91 g/mol
Number of moles of the salt = 9.05 g / 91 g/mol
Number of moles of the salt = 0.0995 mol
Since the formula of the salt is MFx, and assuming complete dissociation in solution, 1 mole of salt will give x moles of F- ions.
Now, let's calculate the number of moles of F- ions in the solution using the boiling point elevation:
Boiling point elevation (ΔTb) = Kb * molality of the solution
Kb = boiling point elevation constant for water = 0.512 °C/m
ΔTb = change in boiling point = 374.54 K - 373.15 K = 1.39 K
Molality of the solution (m) = moles of solute / mass of solvent in kg
Mass of solvent (water) = 100.0 g = 0.100 kg
Molality of the solution (m) = 0.0995 mol / 0.100 kg
Molality of the solution (m) = 0.995 mol/kg
ΔTb = Kb * m
1.39 K = 0.512 °C/m * 0.995 mol/kg
1.39 K = 0.512 °C/m * 0.995 mol/kg
1.39 K = 0.5088 °C
Now, using the fact that 1.86 °C boiling point elevation corresponds to the presence of one mole of solute particles, we can determine the number of moles of F- ions:
1.39 K = 0.5088 °C
1.39 K / 0.5088 °C = 2.73
So, 2.73 moles of F- ions are present in the solution for every 1 mole of the salt.
Therefore, the formula of the salt is MF2.
Formula is MFx so molar mass is 91+19x
delta T = i*Kb*m and
m = mols/kg solvent and
mols = g/molar mass
374.54-273.15 = 1.39 = delta T.
mols 9.05/molar mass
m = 9.05/(91+19x)/0.1
i = 1 for M + x for F
Solve for x. My answer comes out 3.955 which rounds to 4 so I would think MF4 is the formula and the molar mass is 167. Check my work carefully because I don't see a metal that fits this MF4 category.