Phenylcarbinol is used in nasal sprays as a preseriative. A solution of 0.52g of the compound in 25.0g of water has a melting point of -0.36C.
What is the molar mass of phenylcarbinol?
delta T = Kf*m
You know delta T and Kf for water, solve for molality.
m = mols/kg solvent
You know m and kg solvent, solve for moles.
Finally, moles = grams/molar mass.
You know moles and grams, solve for molar mass.
Thank you !
To find the molar mass of phenylcarbinol, we need to use the colligative property known as the freezing point depression. The formula to calculate the molar mass is:
Molar Mass = (Kf * mass of solute) / (molality of solution * ΔTf)
Where:
Kf = cryoscopic constant (water = 1.86 °C/m)
mass of solute = 0.52 g
molality of solution = moles of solute / mass of solvent (water)
ΔTf = decrease in freezing point of the solution
First, let's calculate the molality of the solution:
molality = moles of solute / mass of solvent
The molar mass in grams/mol of phenylcarbinol is multiplied by the number of moles to get the molality.
Next, we need to calculate the decrease in freezing point (ΔTf) using the formula:
ΔTf = initial freezing point - final freezing point
The final freezing point is given as -0.36 °C, and the initial freezing point of pure water is 0 °C.
Let's calculate the molar mass step-by-step:
Step 1: Calculate molality of the solution
molality = moles of solute / mass of solvent
mass of solvent = 25.0 g
Step 2: Calculate moles of solute
moles of solute = mass of solute / molar mass
mass of solute = 0.52 g
Step 3: Calculate ΔTf (decrease in freezing point)
ΔTf = 0 - (-0.36) °C
Step 4: Calculate the molar mass
Molar Mass = (Kf * mass of solute) / (molality of solution * ΔTf)
Substitute the values calculated in previous steps into the formula and solve for the molar mass.
To find the molar mass of phenylcarbinol, we need to use the given information.
First, we need to convert the given mass of phenylcarbinol (0.52g) and water (25.0g) into moles.
To find the moles of phenylcarbinol, we divide its mass by its molar mass. Let's use "M" to represent the molar mass of phenylcarbinol. So, the moles of phenylcarbinol (n1) can be calculated as:
n1 = mass ÷ molar mass
n1 = 0.52g ÷ M
Next, we need to find the moles of water (n2) in the solution. To do this, we divide the mass of water by its molar mass. The molar mass of water (H2O) is approximately 18.015 g/mol. So, the calculation is:
n2 = mass ÷ molar mass
n2 = 25.0g ÷ 18.015 g/mol
Now, we can use the colligative property of freezing point depression to relate the moles of solute (phenylcarbinol) to the change in freezing point. The formula for calculating the change in freezing point (ΔTf) is:
ΔTf = Kf × molality
In this case, the solution we are dealing with contains only phenylcarbinol as the solute, so it can be considered a 1 molal solution. Thus, we can say:
ΔTf = Kf × 1
Given that the freezing point depression (ΔTf) is -0.36°C, we can rearrange the equation to solve for Kf (the freezing point depression constant or cryoscopic constant). This constant is specific to the solvent being used, which in this case is water.
Kf = ΔTf ÷ 1
To solve for Kf, we substitute the given value of ΔTf (-0.36°C) into the equation:
Kf = -0.36°C ÷ 1
The units of Kf are typically °C/molal.
Finally, we can use the concept of molality to find the molar mass of phenylcarbinol (M). Molality (m) is defined as the moles of solute (n1) divided by the mass of the solvent (water) in kilograms (kg). The calculation is:
m = n1 ÷ mass of water (kg)
Now, we have all the necessary information to calculate the molar mass of phenylcarbinol:
M = mass ÷ n1
Using the given values, we can calculate the molar mass of phenylcarbinol based on this process.