When 3.78 g of nonvolatile solute is dissolved in 300.0 g of water, the freezing point depression is 0.646 o C. Calculate the molar mass of the solute. The cryoscopic constant of water is 1.86 K kg mol -1.
When 3.78 g of nonvolatile solute is dissolved in 300.0 g of water, the freezing point depression is 0.646 o C. Calculate the molar mass of the solute. The cryoscopic constant of water is 1.86 K kg mol -1.
DeltaTf= molality*Kf
.646=molrSolute/.3 * 1.86
.646=3.78/molmass/.3 * 1.86
solve for molmass.
To calculate the molar mass of the solute, we can use the formula:
ΔTf = molality * Kf
Where:
ΔTf = freezing point depression (in degrees Celsius)
molality = moles of solute / mass of solvent (in kg)
Kf = cryoscopic constant of the solvent (in K kg mol^-1)
In this case, we are given the freezing point depression (ΔTf = 0.646 o C), the mass of solvent (300.0 g of water), and the cryoscopic constant of water (Kf = 1.86 K kg mol^-1). We need to find the molar mass of the solute, which is represented by molmass.
First, let's convert the mass of the solvent to kg:
mass of solvent = 300.0 g = 300.0 g / 1000 = 0.300 kg
Next, rearrange the equation to solve for the moles of solute:
ΔTf = molrSolute / (mass of solvent * Kf)
Multiply both sides of the equation by (mass of solvent * Kf) to isolate molrSolute:
ΔTf * (mass of solvent * Kf) = molrSolute
Now, substitute the given values into the equation:
0.646 * (0.300 * 1.86) = molrSolute
Calculate the right side of the equation to find the moles of solute:
molrSolute = 0.646 * 0.300 * 1.86 = 0.360516 mol
Now, we can calculate the molar mass of the solute by rearranging the formula for molality:
molality = moles of solute / mass of solute (in kg)
Rearrange the equation to solve for the molar mass:
moles of solute = molar mass / mass of solute
molarity = moles of solute / mass of solvent (in kg)
Substitute the given values into the equation:
0.646 = (molar mass / 3.78) / 0.300
Multiply both sides by 0.300 and 3.78 to isolate molar mass:
0.646 * 0.300 * 3.78 = molar mass
Calculate the right side of the equation to find the molar mass:
molar mass = 0.731676 g/mol
Therefore, the molar mass of the solute is approximately 0.731676 g/mol.