A 1.60 g sample of a mixture of naphthalene, C10H8, and anthracene, C14H10, is dissolved in 20.0 g benzene, C6H6. The freezing point of the solution is 2.81oC. What is the composition as mass percent of the sample mixture?
To find the composition of the sample mixture in terms of mass percent, we need to calculate the mass of naphthalene and anthracene in the sample.
1. Calculate the moles of benzene:
- We know the molar mass of benzene (C6H6) is 78.1134 g/mol.
- Divide the mass of benzene by its molar mass to get the moles:
20.0 g / 78.1134 g/mol = 0.256 moles
2. Calculate the molality (molal concentration) of the solution:
- We can use the formula:
ΔT = Kf * m
where ΔT is the freezing point depression, Kf is the molal freezing point depression constant, and m is the molality.
- The Kf value for benzene is 5.12 °C/m.
- Rearrange the formula to solve for m:
m = ΔT / Kf = 2.81 °C / 5.12 °C/m = 0.548 mol/kg
3. Calculate the moles of solute in the solution:
- Multiply the molality by the mass of benzene to get the moles of solute:
Moles of solute = molality * mass of benzene = 0.548 mol/kg * 20.0 g = 10.96 moles
4. Divide the total moles of solute by the number of moles in each component to find the weight percent of each component:
- Let x be the moles of naphthalene (C10H8) and y be the moles of anthracene (C14H10).
- We have the equation:
x + y = 10.96 moles (total moles of solute)
5. Determine the molecular weight of naphthalene and anthracene:
- The molecular weight of naphthalene (C10H8) is 128.17 g/mol.
- The molecular weight of anthracene (C14H10) is 178.23 g/mol.
6. Calculate the mass of each component:
- Mass of naphthalene = x (moles) * 128.17 (g/mol)
- Mass of anthracene = y (moles) * 178.23 (g/mol)
7. Calculate the mass percent of each component:
- Mass percent of naphthalene = (mass of naphthalene / mass of the mixture) * 100%
- Mass percent of anthracene = (mass of anthracene / mass of the mixture) * 100%
By following these steps, you can determine the composition of the sample mixture in terms of mass percent.
To find the composition of the sample mixture as mass percent, we need to determine the amount (in grams) of naphthalene and anthracene in the mixture. We can use the concept of freezing point depression to calculate this.
The formula to calculate the freezing point depression in a solution is:
ΔTf = Kf * m
Where:
ΔTf = freezing point depression
Kf = cryoscopic constant (for benzene, Kf = 5.12 oC/m)
m = molality of the solution (moles of solute per kilogram of solvent)
We can calculate the molality using the equation:
molality (m) = moles of solute / mass of solvent (in kg)
First, we need to convert the mass of benzene to kilograms:
Mass of benzene = 20.0 g = 0.0200 kg
Next, let's calculate the molality:
molality = moles of solute / 0.0200 kg
Since the formula of naphthalene is C10H8 and anthracene is C14H10, we can find their molar masses:
Molar mass of naphthalene (C10H8) = (10 * Atomic mass of carbon) + (8 * Atomic mass of hydrogen)
Molar mass of anthracene (C14H10) = (14 * Atomic mass of carbon) + (10 * Atomic mass of hydrogen)
Using the periodic table, we find the atomic masses of carbon and hydrogen to be approximately 12.01 g/mol and 1.01 g/mol, respectively.
Next, we need to find the number of moles of naphthalene and anthracene in the mixture. Let x be the amount (in moles) of naphthalene and y be the amount (in moles) of anthracene.
x + y = moles of solute
Now, we can calculate the freezing point depression:
ΔTf = Kf * (x + y) / 0.0200 kg
ΔTf = 2.81°C
We know that ΔTf = freezing point of pure solvent - freezing point of solution. The freezing point of pure benzene is 5.5°C. Therefore:
5.5 - 2.81 = 5.12 * (x + y) / 0.0200
Simplifying this equation, we can solve for (x + y):
2.69 = (x + y) / 0.0200
Now, we can find the ratio of moles of naphthalene to anthracene by considering their molecular formulas:
C10H8 : C14H10 = 5 : 7
Let's consider the number of moles of naphthalene to be 5n and anthracene to be 7n. Therefore:
x = 5n
y = 7n
Substituting these values into the equation, we get:
2.69 = (5n + 7n) / 0.0200
2.69 = 12n / 0.0200
Simplifying, we find:
n = (2.69 * 0.0200) / 12 = 0.00448 mol
Now, we can find the moles of naphthalene and anthracene in the mixture:
x = 5n = 5 * 0.00448 = 0.0224 mol
y = 7n = 7 * 0.00448 = 0.0314 mol
To find the mass of naphthalene and anthracene, we can multiply their respective moles by their molar masses:
Mass of naphthalene = x * molar mass of naphthalene
Mass of anthracene = y * molar mass of anthracene
Now we can calculate the mass percent composition:
Mass percent of naphthalene = (Mass of naphthalene / Mass of mixture) * 100
Mass percent of anthracene = (Mass of anthracene / Mass of mixture) * 100
Finally, we can substitute the values and calculate the composition as mass percent.
7.4%
% w/w = (mass solute/total mass solution)*100 = ?
mass solute = 1.60 grams.
mass solution = 20.0 + 1.60 = 21.60 grams.
Substitute and solve.