A metal, M, of atomic weight 96 u 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 10.9 g sample of the salt is dissolved in 100.0 g of water (for water: Kb=0.512∘Cm−1); and the boiling point of the solution is found to be 374.61 K.
Find the formula of the salt. Assume complete dissociation of the salt in solution.
Express your answer as a chemical formula.
I found out it's MoF3
Did you work it or someone told you?
To find the formula of the salt (MFx), we need to determine the value of x.
1. Calculate the molality (m) of the solution:
molality (m) = moles of solute / mass of solvent (in kg)
The mass of the solvent (water) is given as 100.0 g, which is equal to 100.0/1000 = 0.1 kg.
The moles of solute (MFx) can be calculated by dividing the mass of the salt (10.9 g) by its molar mass.
The molar mass of the salt can be calculated using the given atomic weight of the metal (M), which is 96 u.
To determine the molar mass of the salt (MFx), we need to know the atomic weight of the metal (M). Please provide this information.
To find the formula of the salt, we need to determine the value of x in MFx. In order to do that, we will use the concept of boiling point elevation.
Boiling point elevation occurs when a non-volatile solute (in this case, MFx) is dissolved in a volatile solvent (in this case, water). The boiling point of the solution is higher than the boiling point of the pure solvent.
The boiling point elevation (ΔTb) can be calculated using the formula:
ΔTb = Kbm,
where ΔTb is the boiling point elevation, Kb is the molal boiling point constant for the solvent, and m is the molality of the solute.
First, let's calculate the molality (m) of the salt in the solution. Molality is defined as the moles of solute (MFx) divided by the mass of the solvent (water) in kilograms.
Given:
Mass of water (mwater) = 100.0 g = 0.1000 kg
Mass of salt (Msalt) = 10.9 g
We need to convert the mass of salt to moles using the atomic weight of the metal (M).
Atomic weight of M = 96 u
Molar mass of M = 96 g/mol
Therefore, moles of salt (n) can be calculated as:
n = Msalt / Molar mass of M
Now, let's calculate the molality (m):
m = n / mwater
After determining the molality, we can calculate the boiling point elevation (ΔTb) using the given Kb value for water.
ΔTb = Kb * m
Given:
Kb (boiling point constant for water) = 0.512 °Cm^(-1) = 0.512 K kg mol^(-1)
Finally, we can determine the formula of the salt by analyzing the value of x in MFx. Since the salt will completely dissociate in solution, the number of moles of ions (M^+ and F^-) will be equal.
To calculate the number of moles of ions, we multiply the molality (m) by the van 't Hoff factor, which represents the number of particles formed per formula unit upon dissociation. Since the salt completely dissociates, the van 't Hoff factor is equal to x.
Therefore, the number of moles of ions can be calculated as:
moles of ions = m * x
Since the number of moles of ions is the same for both M^+ and F^-, we can set up the following equation:
n = moles of ions = m * x
Now, let's substitute the values and solve for x:
x = n / m
By expressing x as a ratio of small whole numbers, we can determine the formula of the salt (MFx).
I'll perform the calculations to find the value of x and the formula of the salt.