If 0.48 g of sulfur are added to 200 g of carbon tetracholoride, and the freezing point of the carbon tetrachloride (Kf=30 degrees C/m) is depressed by 0.28 degrees C, what is the molar mass and molecular formula of the sulfur?
delta T = Kf*m
Solve for m
m = moles/kg solvent
solve for moles
moles = grams/molar mass
solve for molar mass.
thank you :)
.48g * 1mol/32.07g= .01497 mol S
.01497/.2 kg = .07485 molality
273.28K= i * 293K * .07485
i = .08
??
To find the molar mass and molecular formula of sulfur, we need to use the concept of freezing point depression and the colligative properties of solutions. The freezing point depression is given by the equation:
ΔT = Kf * m * i,
where ΔT is the change in freezing point in degrees Celsius, Kf is the cryoscopic constant (which is 30 degrees C/m for carbon tetrachloride), m is the molality of the solution, and i is the van't Hoff factor.
In this case, we know that ΔT is -0.28 degrees C, and the molality (m) is given by the formula:
m = (moles of solute) / (mass of solvent in kg).
First, we need to convert the mass of sulfur (0.48 g) to moles. The molar mass of sulfur can be found in the periodic table, which is approximately 32.06 g/mol.
moles of sulfur = (mass of sulfur) / (molar mass of sulfur)
moles of sulfur = 0.48 g / 32.06 g/mol
Now, we need to calculate the molality (m) by dividing the moles of sulfur by the mass of the solvent (carbon tetrachloride) in kg.
mass of solvent (carbon tetrachloride) = 200 g = 0.2 kg
m = (moles of sulfur) / (mass of carbon tetrachloride in kg)
m = (0.48 g / 32.06 g/mol) / 0.2 kg
Now we have all the values to calculate the van't Hoff factor (i) using the equation:
i = ΔT / (Kf * m).
Substituting the given values:
i = -0.28 degrees C / (30 degrees C/m * ((0.48 g / 32.06 g/mol) / 0.2 kg))
Simplifying this calculation will give us the value of i.
Once we have the van't Hoff factor (i), we can determine the number of particles present in the solution. In this case, sulfur is a molecular substance, so the van't Hoff factor (i) is equal to 1.
Since sulfur is a solid, the molecular formula is the same as the empirical formula. To calculate the empirical formula, we need the molar mass of the empirical formula which can be found by dividing the molar mass of sulfur by the empirical formula factor (x):
molar mass of empirical formula = molar mass of sulfur / x.
To find the empirical formula factor (x), we need to divide the molar mass of sulfur by the molar mass of the empirical formula:
x = molar mass of sulfur / molar mass of empirical formula.
Given the molar mass of sulfur (32.06 g/mol) and using the empirical formula factor (x), we can calculate the molar mass of the empirical formula.
Finally, from the molar mass and empirical formula, we can determine the molecular formula by multiplying the empirical formula by a proper integer to match the molar mass.
Please let me know if you would like me to complete the calculations for you.