What is the boiling point elevation of a solution of NaNO3 (85.0 g/mol, complete dissociation) made by dissolving 10.0 g of NaNO3 into 200 g of water (Kb = 0.512◦C/m)?
Well, looks like water's in hot water here! Let's dive in.
First, we need to find the number of moles of NaNO3 in the solution. To do that, we divide the mass (10.0 g) by the molar mass (85.0 g/mol):
10.0 g / 85.0 g/mol = 0.1176 mol.
Now, let's find the molality of the solution. Molality is the number of moles of solute per kilogram of solvent. In this case, the solvent is water, so we need to convert its mass from grams to kilograms:
200 g / 1000 g/kg = 0.200 kg.
Now, we can calculate molality by dividing the number of moles of NaNO3 by the mass of water in kilograms:
0.1176 mol / 0.200 kg = 0.588 mol/kg.
Next, we can use the equation for boiling point elevation:
ΔTb = Kb * m.
Substituting the values we have:
ΔTb = 0.512 ◦C/m * 0.588 mol/kg = 0.3 ◦C.
So, the boiling point elevation of this NaNO3 solution is 0.3 degrees Celsius. Don't worry, water, things will cool down eventually!
To calculate the boiling point elevation of a solution, you can use the following formula:
ΔTb = Kb × m × i
Where:
ΔTb = boiling point elevation
Kb = boiling point elevation constant (in this case, 0.512◦C/m)
m = molality of the solution (moles of solute per kilogram of solvent)
i = van't Hoff factor or the number of particles the solute dissociates into
First, let's calculate the molality (m) of the solution:
Molar mass of NaNO3 = 85.0 g/mol
Mass of NaNO3 = 10.0 g
Mass of water = 200 g
To calculate the molality, we first need to convert the mass of NaNO3 to moles:
moles of NaNO3 = mass of NaNO3 / molar mass of NaNO3
= 10.0 g / 85.0 g/mol
= 0.1176 mol
Next, let's calculate the molality (m) using the equation:
molality (m) = moles of solute / mass of solvent (in kg)
mass of solvent = mass of water / 1000
= 200 g / 1000
= 0.2 kg
molality (m) = 0.1176 mol / 0.2 kg
= 0.588 mol/kg
Now, we need to find the van't Hoff factor (i). NaNO3 fully dissociates in water, so it will have an i value of 2.
Now, let's calculate the boiling point elevation (ΔTb) using the formula:
ΔTb = Kb × m × i
= 0.512◦C/m × 0.588 mol/kg × 2
= 0.60096◦C
Therefore, the boiling point elevation of the NaNO3 solution is 0.60096◦C.
To determine the boiling point elevation of a solution, we need to use the formula:
ΔT = Kb * m * i
Where:
ΔT is the boiling point elevation
Kb is the molal boiling point elevation constant
m is the molality of the solution
i is the van't Hoff factor, which represents the number of particles the solute dissociates into
First, we need to calculate the molality of the solution. Molality (m) is defined as the moles of solute per kilogram of solvent.
Step 1: Calculate the moles of NaNO3
The given mass of NaNO3 is 10.0 g, and its molar mass is 85.0 g/mol.
moles = mass / molar mass
moles = 10.0 g / 85.0 g/mol
Step 2: Calculate the mass of water in kilograms
The given mass of water is 200 g, and we need to convert it to kilograms.
mass_water = 200 g / 1000 g/kg
Step 3: Calculate molality (m)
m = moles / mass_water
Now that we have the molality of the solution, we can calculate the boiling point elevation:
Step 4: Calculate the boiling point elevation (ΔT)
ΔT = Kb * m * i
For NaNO3, since it completely dissociates into Na+ and NO3- ions, the van't Hoff factor (i) is 2.
Now you can plug in the values and calculate the boiling point elevation.
delta T = i*Kb*m
i = 2 for NaNO3
Kb is given
m = mols/Kg. Kg is 0.2
mols = grams/molar mass NaNO3.