A student has a solution with a mole fraction of 0.20 of chloroform in carbon tetrachloride. What is the molality of chloroform in the solution?
XCHCl3 = 0.2
XCCl4 = 0.8
grams CCl4 = 0.8 x about 153 = about 123g.
Then m = mols CHCl3/kg CCl4.
To find the molality of chloroform in the solution, we need to use the mole fraction and the molar mass of chloroform.
Step 1: Find the molar mass of chloroform (CHCl3).
The molar mass of C = 12.01 g/mol
The molar mass of H = 1.01 g/mol
The molar mass of Cl = 35.45 g/mol
Molar mass of chloroform (CHCl3) = (12.01 * 1) + (1.01 * 4) + (35.45 * 3) = 119.36 g/mol
Step 2: Calculate the molality using the mole fraction and molar mass.
Mole fraction of chloroform = 0.20
Moles of chloroform = Mole fraction * Total moles of solution
= (0.20)(1.00 mol)
Mass of chloroform = Moles of chloroform * Molar mass
= (0.20 mol)(119.36 g/mol)
Now we need to find the mass of the solvent (carbon tetrachloride). Since we are given the mole fraction of the solute (chloroform), it can be assumed that the solvent (carbon tetrachloride) has a mole fraction of (1 - mole fraction of chloroform).
Mole fraction of carbon tetrachloride = 1 - 0.20 = 0.80
Since molality is defined as the moles of solute per kg of solvent, we need to find the mass of carbon tetrachloride (solvent) to calculate molality.
Step 3: Find the mass of the solvent.
Mass of solvent = Mass of solution - Mass of solute
Since the solution is assumed to be 1 kg (1000 g), the mass of carbon tetrachloride (solvent) can be found by subtracting the mass of chloroform (solute) from the mass of the solution.
Mass of solution = 1000 g
Mass of solute = (0.20 mol)(119.36 g/mol)
Mass of solvent = 1000 g - (0.20 mol)(119.36 g/mol)
Step 4: Calculate the molality.
Molality = Moles of solute / Mass of solvent (in kg)
First, we need to convert the mass of the solvent from grams to kilograms.
Mass of solvent (in kg) = Mass of solvent (in g) / 1000
Finally, we can calculate the molality.
Molality = (0.20 mol) / (Mass of solvent (in kg))
By substituting the known values, we can find the molality of chloroform in the solution.
To find the molality of chloroform in the solution, we need to know the mass of solvent.
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
The mole fraction of chloroform (Xchloroform) is given as 0.20, which means that there are 0.20 moles of chloroform for every mole of carbon tetrachloride.
Let's say we have 1 mole of carbon tetrachloride (CCl4) as the solvent.
Since the mole fraction of chloroform is 0.20, there will be 0.20 moles of chloroform (CHCl3) present.
Now, we need to find the mass of the solvent.
The molar mass of carbon tetrachloride (CCl4) is:
Molar mass of C + (Molar mass of Cl × 4)
Atomic mass of C = 12.01 g/mol
Atomic mass of Cl = 35.45 g/mol
Molar mass of CCl4 = (12.01 g/mol) + (35.45 g/mol × 4) = 153.82 g/mol
Assuming we have 1 mole of carbon tetrachloride (CCl4), its mass will be 153.82 grams.
To convert the mass from grams to kilograms, we divide by 1000:
Mass of solvent = 153.82 g / 1000 = 0.15382 kg
Finally, we can calculate the molality using the formula:
Molality (m) = Moles of solute / Mass of solvent in kg
Molality (m) = 0.20 moles / 0.15382 kg ≈ 1.300 mol/kg
Therefore, the molality of chloroform in the solution is approximately 1.300 mol/kg.