Urea (NH2)2CO is dissolved in 100.0 g of water. The solution freezes at -0.085 degrees C. how many grams of urea were dissolved to make this solution.
delta T = Kf*molality
Plug in 0.085 for delta T, I assume you know Kf for water, calculate molality.
Then molality x kg solvent x molar mass = grams.
You have all but molar mass which can be calculated.
To find out how many grams of urea were dissolved in 100.0 g of water, we can make use of the concept of freezing point depression. The freezing point depression is the difference between the freezing point of a pure solvent and the freezing point of a solution. It is given by the formula:
ΔT = i * Kf * m
Where:
ΔT = change in freezing point
i = van't Hoff factor (number of particles formed when the solute dissolves)
Kf = cryoscopic constant (a constant specific to the solvent)
m = molality of the solution (moles of solute per kilogram of solvent)
In this case, the solute is urea (NH2)2CO, the solvent is water, and the freezing point depression is -0.085 degrees Celsius.
First, we need to calculate the molality of the solution. We know the mass of water (100.0 g), so we need to convert it to kilograms (since molality is expressed in moles of solute per kilogram of solvent).
m = moles of solute / kilograms of solvent
The molar mass of urea ((NH2)2CO) is:
(N: 2 * 14.01 g/mol) + (H: 2 * 1.01 g/mol) + (C: 1 * 12.01 g/mol) + (O: 1 * 16.00 g/mol) = 60.06 g/mol
To find the moles of solute, we need to use the formula:
moles of solute = grams of solute / molar mass of solute
Since we don't know the amount of urea dissolved, we'll use a variable "x" to represent it. Therefore, the equation becomes:
x / 60.06 g/mol = moles of urea
Now we can substitute this value into the molality equation:
m = (x / 60.06 g/mol) / (0.100 kg) = (x / 60.06) / 0.100
Next, we can rearrange the freezing point depression equation to solve for x:
ΔT = i * Kf * m
-0.085 = 1 * Kf * [(x / 60.06) / 0.100]
Simplifying further:
-0.085 = Kf * (x / 600.6)
Finally, solve for x (grams of urea):
x = (-0.085 * 600.6) / Kf
To find the specific value, we need to know the cryoscopic constant (Kf) for water.