What is the molality of a solution consisting of 34.0 mL of benzene (C6H6; d = 0.877 g/mL) in 187 mL of hexane (C6H14 ; d = 0.660 g/mL)?
654f
from the densities, figure the grams of each.
molality=(gramsBenzene/molmassC6H6)/kg of hexane
notice the denominator is in kg.
To find the molality of a solution, we need to calculate the number of moles of solute (benzene) and the mass of the solvent (hexane).
Step 1: Calculate the moles of benzene.
The number of moles (n) can be calculated using the formula:
n = mass / molar mass
The molar mass of benzene (C6H6) is:
C: 12.01 g/mol x 6 = 72.06 g/mol
H: 1.01 g/mol x 6 = 6.06 g/mol
Total molar mass of C6H6 = 72.06 g/mol + 6.06 g/mol = 78.12 g/mol
The mass of benzene can be calculated using the density and volume:
mass = volume x density
mass = 34.0 mL x 0.877 g/mL = 29.818 g
Now, calculate the moles of benzene:
n_benzene = mass / molar mass
n_benzene = 29.818 g / 78.12 g/mol = 0.381723 mol (rounded to 6 decimal places)
Step 2: Calculate the mass of hexane.
The mass of hexane can be calculated using the density and volume:
mass_hexane = volume_hexane x density_hexane
mass_hexane = 187 mL x 0.660 g/mL = 123.42 g
Step 3: Calculate the molality of the solution.
Molality is defined as the number of moles of solute per kilogram of solvent.
molality = moles_benzene / kg_hexane
Convert the mass of hexane from grams to kilograms:
mass_hexane_kg = mass_hexane / 1000
mass_hexane_kg = 123.42 g / 1000 = 0.12342 kg
Now, calculate the molality:
molality = n_benzene / mass_hexane_kg
molality = 0.381723 mol / 0.12342 kg = 3.09042 mol/kg (rounded to 5 decimal places)
Therefore, the molality of the solution is 3.09042 mol/kg.
To find the molality of a solution, you need to know the amount of solute in moles and the amount of solvent in kilograms. Here's how you can calculate the molality of the given solution:
Step 1: Calculate the moles of benzene (solute):
To calculate the moles of benzene, you need to know its mass. The mass of benzene can be calculated by multiplying its volume (34.0 mL) by its density (0.877 g/mL):
Mass of benzene = Volume of benzene x Density of benzene
= 34.0 mL x 0.877 g/mL
Step 2: Convert the mass of benzene to moles:
To convert the mass of benzene to moles, you need to divide the mass by its molar mass. The molar mass of benzene (C6H6) can be found by adding up the atomic masses of its constituent elements from the periodic table.
Molar mass of C6H6 = (6 x Atomic mass of carbon) + (6 x Atomic mass of hydrogen)
Step 3: Calculate the mass of hexane (solvent):
To calculate the mass of hexane, you first need to calculate its volume. The volume of hexane can be obtained by subtracting the volume of benzene (34.0 mL) from the total volume of the solution (187 mL):
Volume of hexane = Total volume of solution - Volume of benzene
= 187 mL - 34.0 mL
Next, you can calculate the mass of hexane by multiplying its volume by its density:
Mass of hexane = Volume of hexane x Density of hexane
= (187 mL - 34.0 mL) x 0.660 g/mL
Step 4: Convert the mass of hexane to kilograms:
To convert the mass of hexane from grams to kilograms, divide the mass by 1000:
Mass of hexane (in kg) = Mass of hexane (in g) / 1000
Step 5: Calculate the molality of the solution:
Molality is defined as moles of solute per kilogram of solvent. Now that you have the moles of benzene and the mass of hexane in kilograms, you can calculate the molality:
Molality = Moles of benzene / Mass of hexane (in kg)
Plug in the values obtained from the previous steps into this equation to find the molality of the solution.