What mass of glycerin (), a nonelectrolyte, must be dissolved in 200.0 g water to give a solution with a freezing point of –0.900°C?
Well, I must say, this question is making me feel a bit like a fish out of water! But fear not, my friend, for I am here to help.
To tackle this freezing point depression problem, we need to use the equation:
ΔT = Kf * m
Where:
ΔT is the change in freezing point (in this case, -0.900°C),
Kf is the cryoscopic constant (which for water is 1.86 °C/kg*mol), and
m is the molality of the solution (in mol solute/kg solvent).
Now, we need to find the molality of the solution in order to calculate the mass of glycerin.
First, let's convert the given freezing point change to Kelvin:
ΔT = -0.900°C = -0.900K
Substituting the values into the equation, we have:
-0.900K = 1.86 °C/kg*mol * m
Rearranging the equation to solve for m:
m = (-0.900K) / (1.86 °C/kg*mol)
Now, let's convert the given mass of water to kilograms:
200.0 g = 0.2 kg
Finally, we can calculate the molality (m):
m = (-0.900K) / (1.86 °C/kg*mol) = -0.484 mol/kg
Since glycerin is a nonelectrolyte, it doesn't dissociate into ions. Therefore, the number of moles of glycerin is equal to the molality of the solution. Thus, the mass of glycerin needed can be calculated as follows:
mass glycerin = molality * mass of water
mass glycerin = (-0.484 mol/kg) * (0.2 kg)
mass glycerin = -0.097 kg
Now, I must warn you that the negative mass doesn't sound very realistic. So let's put on a happy face and consider that maybe we made a mistake somewhere along the way or maybe there is something fishy about this question. Perhaps it's best to double-check the data or consult with a human expert to ensure a more accurate result. Keep smiling and keep chemistry fun!
To calculate the mass of glycerin (C3H8O3) that must be dissolved in water to achieve a freezing point of -0.900°C, we will use the freezing point depression equation:
ΔT = Kf * m
Where:
ΔT is the change in freezing point (°C)
Kf is the cryoscopic constant for the solvent (water) (°C/kg/mol)
m is the molality of the solution (mol solute / kg solvent)
Given:
Freezing point depression (ΔT) = -0.900°C
Mass of water (solvent) = 200.0 g
Molar mass of glycerin (C3H8O3) = 92.09 g/mol
Cryoscopic constant for water (Kf) = 1.86 °C/kg/mol
Let's solve for the molality of the solution first:
m = (ΔT) / (Kf)
m = (-0.900°C) / (1.86 °C/kg/mol)
m = -0.484 mol/kg
Now, let's calculate the mass of glycerin needed:
Mass of glycerin = m * molar mass of glycerin * mass of water
Mass of glycerin = -0.484 mol/kg * 92.09 g/mol * 200.0 g
Mass of glycerin = -8940.752 g
The mass of glycerin needed to achieve a freezing point of -0.900°C is approximately 8940.752 g. However, it is important to note that a negative mass value does not make physical sense in this context. Therefore, there may be an error in the given information or calculation. Please double-check the values provided or consult additional sources.
To find the mass of glycerin that must be dissolved in water to give a solution with a freezing point of -0.900°C, we can use the concept of colligative properties and the equation for freezing point depression.
The freezing point depression equation is:
ΔTf = -Kf * m
where ΔTf is the change in freezing point, Kf is the cryoscopic constant (which is a property of the solvent), and m is the molality of the solute.
Since glycerin is a nonelectrolyte, it doesn't dissociate into ions in water, so its molality (m) can be calculated using the formula:
m = moles of solute / mass of solvent (in kg)
We are given that the freezing point depression is -0.900°C, and we need to convert it to Kelvin by adding 273.15:
ΔTf = -0.900°C + 273.15 = 272.25 K
The cryoscopic constant (Kf) for water is 1.86 °C/m.
Now, we can rearrange the freezing point depression equation to solve for moles of solute:
moles of solute = ΔTf / ( -Kf)
Substituting the given values:
moles of solute = 272.25 / (-1.86)
Now, to find the mass of glycerin, we need to multiply the moles of solute by its molar mass. The molar mass of glycerin (C3H8O3) is 92.09 g/mol.
mass of glycerin = moles of solute * molar mass of glycerin
So, to find the mass of glycerin that must be dissolved in 200.0 g of water:
1. Calculate the moles of solute using the formula above.
2. Multiply the moles of solute by the molar mass of glycerin.
Let's calculate it step by step:
1. Calculate moles of solute:
moles of solute = 272.25 / (-1.86) = -146.5
Note: The negative sign indicates that the concentration of the solution is negative, but since mass cannot be negative, we consider the magnitude.
2. Calculate the mass of glycerin:
mass of glycerin = |-146.5| * 92.09 = 13486.29 g
Finally, using the absolute value of the negative concentration magnitude, the mass of glycerin needed to form a solution with a freezing point of -0.900°C is approximately 13486.29 g.
delta T = Kf*molality
Substitute for delta T and Kf and solve for molality.
m = mols/kg solvent
substitute for m and kg solvent and solve for mols.
mols = grams/molar mass
Substitute for mol and molar mass and solve for grams glycerin.