What mass of ethanol must be added to 10.0L of water to five a solution that freezes at -10.0 degrees C. Assume the density of water is q.00 g/mL. Kf of water is 1.86 degrees C/m.
You made a typo on the density of water in your post. Also, I don't understand the expression "to FIVE a solution that". I assume FIVE should be FIND.
delta T = Kf*molality
delta T = -10
Kf you know.
Solve for molality
definition of molality = mol/kg solvent.
You know molality and kg solvent, solve for mol ethanol.
Then mol ethanol = g/molar mass.
You know mol and molar mass. Solve for grams.
To find the mass of ethanol that must be added to water to get a solution that freezes at a specific temperature, we can use the equation:
ΔT = Kf × m × i
Where:
ΔT = change in freezing point (in degrees Celsius)
Kf = freezing point depression constant (in degrees Celsius per mole or degrees Celsius per kilogram)
m = molality of the solution (moles of solute per kilograms of solvent)
i = the number of particles or ions into which the solute dissociates
In this case, we know the change in freezing point (ΔT) is -10.0 degrees Celsius, the freezing point depression constant (Kf) for water is 1.86 degrees Celsius/m, and we need to find the molality (m) of the solution.
To find the molality, we need to calculate the number of moles of ethanol (solute) and the mass of water (solvent). The molecular weight of ethanol is 46.07 g/mol.
Let's begin by finding the number of moles of ethanol:
Number of moles of ethanol = mass of ethanol / molecular weight of ethanol
We have not been given the mass of ethanol, so we can use the mass of water instead. The volume of water is given as 10.0 L, and we know that the density of water is 1.00 g/mL. Therefore, the mass of water can be calculated as:
Mass of water = volume of water × density of water
Now we can substitute the mass of water into the formula for the number of moles of ethanol:
Number of moles of ethanol = mass of water / molecular weight of ethanol
Next, we can calculate the molality (m) by dividing the number of moles of ethanol by the mass of water in kilograms:
Molality (m) = Number of moles of ethanol / Mass of water (in kg)
Now let's substitute the values into the equation for freezing point depression:
-10.0 degrees C = 1.86 degrees C/m × Molality (m) × i
Assuming ethanol does not dissociate in water (i = 1), we can solve for the molality:
Molality (m) = -10.0 degrees C / (1.86 degrees C/m)
Finally, we substitute the molality obtained into the equation for molality:
Mass of ethanol = Molality (m) × Mass of water (in kg)
To convert the mass of water from grams to kilograms:
Mass of water (in kg) = Mass of water (in g) / 1000
Now, substitute the values obtained to calculate the mass of ethanol required.