Some physical properties of water are shown below.
freezing point 0.00°C
boiling point 100.00°C
Kf 1.86°C/m
Kb 0.512°C/m
A 16.0 g sample of a compound known to contain 3 ion species is dissolved in 100. g of water. The boiling point of the solution is 103.6°C. What is the molar mass of the compound?
To determine the molar mass of the compound, we need to use the boiling point elevation equation. The equation is ΔTb = Kb * m * i, where ΔTb is the change in boiling point, Kb is the molal boiling point elevation constant, m is the molality of the solution, and i is the van 't Hoff factor. In this case, we know the boiling point elevation (ΔTb) is 3.6°C, and the molal boiling point elevation constant (Kb) is 0.512°C/m.
First, we need to calculate the molality of the solution. Molality (m) is defined as the moles of solute divided by the mass of the solvent in kilograms. In this case, the mass of the solute is given as 16.0 g. We need to convert this to moles by dividing by the molar mass of the compound.
To find the moles of the compound, we can use the formula: moles = mass / molar mass.
Now, to determine the moles of the compound, we need to know the number of moles of the compound (which contains three ion species). To calculate this, we need to know the van 't Hoff factor (i). The van 't Hoff factor is the number of particles produced in the solution per formula unit of solute dissolved. In this case, it is known that the compound contains three ion species, so the van 't Hoff factor (i) is 3.
Next, we can calculate the molality (m) using the formula: molality = moles of solute / mass of solvent (in kg). The mass of the solvent is given as 100.0 g. We need to convert this to kilograms by dividing by 1000.
Now that we know the molality (m), boiling point elevation constant (Kb), and the change in boiling point (ΔTb), we can rearrange the boiling point elevation equation to solve for the moles of the compound: moles = (ΔTb / (Kb * m * i).
Once we have the moles of the compound, we can calculate the molar mass by dividing the mass of the solute by the moles of the compound.
Therefore, use the boiling point elevation equation to determine the molar mass of the compound as follows:
moles = (ΔTb / (Kb * m * i)
molar mass = mass of solute / moles of the compound
Plug in the provided values and solve for the molar mass.