What are the molality and mole fraction of solute in a 32.3 percent by mass aqueous solution of methanol (CH3OH)?
molality = ?m
mole fraction =
To calculate the molality (molality = ?m) and mole fraction of the solute in a solution, you need to know the number of moles of solute and the total mass of the solution.
Step 1: Calculate the number of moles of solute (methanol, CH3OH).
To do this, you need to know the molar mass of methanol. The molar mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and oxygen (O) is 16.00 g/mol.
Add up the molar masses of the elements in CH3OH:
(1 carbon atom x 12.01 g/mol) + (4 hydrogen atoms x 1.01 g/mol) + (1 oxygen atom x 16.00 g/mol) = 32.04 g/mol
Since the solution is 32.3% by mass, this means that in 100 grams of the solution, there are 32.3 grams of methanol (solute). Thus, the number of moles of methanol can be calculated as:
(32.3 g / 32.04 g/mol) = 1.008 mol
Step 2: Calculate the total mass of the solution.
The total mass of the solution is the sum of the mass of the solute (methanol) and the mass of the solvent (water). However, since water has a density of 1 g/mL, the mass of water can be approximated as being equal to the mass of 1 mL of water.
Therefore, the total mass of the solution is 32.3 grams (mass of methanol) + 100 grams (mass of 100 mL of water) = 132.3 grams.
Step 3: Calculate the molality (molality = ?m).
Molality is defined as the number of moles of solute per kilogram of solvent.
In this case, the solvent is water, and since the mass of water is approximately 100 grams, we can convert it to kilograms by dividing by 1000:
Mass of water in kg = 100 g / 1000 = 0.1 kg
Therefore, the molality can be calculated as:
Molality = number of moles of solute / mass of solvent in kg
Molality = 1.008 mol / 0.1 kg = 10.08 mol/kg
So, the molality of the solute in the solution is 10.08 mol/kg.
Step 4: Calculate the mole fraction.
Mole fraction is defined as the ratio of the number of moles of solute to the total number of moles in the solution.
In this case, the total number of moles in the solution is the sum of the moles of solute (methanol) and the moles of solvent (water).
Since we already have the moles of solute (methanol) as 1.008 mol, we need to calculate the moles of solvent (water).
Moles of solvent (water) = mass of solvent (water) / molar mass of water
Mass of solvent (water) = total mass of the solution - mass of solute (methanol)
Mass of solvent (water) = 132.3 g - 32.3 g = 100 g
Molar mass of water = 18.01 g/mol
Therefore, the moles of solvent can be calculated as:
Moles of solvent (water) = 100 g / 18.01 g/mol = 5.55 mol
Now, we can calculate the mole fraction:
Mole fraction = Moles of solute / Total moles in the solution
Mole fraction = 1.008 mol / (1.008 mol + 5.55 mol) = 0.153
So, the mole fraction of the solute in the solution is 0.153.