What are the molality and mole fraction of solute in a 25.5 percent by mass aqueous solution of formic acid (HCOOH)?
work this one out please i didnt understand
Dr.BOB your steps are wrong. SMH
To determine the molality and mole fraction of solute in a solution, we need to first calculate the moles of solute and the moles of solvent present.
Given:
- Mass percentage of solute (formic acid) = 25.5%
- Total mass of solution = 100 g (assume)
Step 1: Calculate the mass of solute (formic acid) in the solution.
- Mass percentage = (mass of solute / mass of solution) x 100
- Rearranging the equation, we can calculate the mass of solute:
mass of solute = (mass percentage / 100) x mass of solution
mass of solute = (25.5 / 100) x 100 g
mass of solute = 25.5 g
Step 2: Calculate the moles of solute (formic acid).
- We can use the molar mass of formic acid (HCOOH) to calculate the moles of solute:
Molar mass of HCOOH = 12.01 g/mol (C) + 1.01 g/mol (H) + 16.00 g/mol (O) + 1.01 g/mol (H) = 46.03 g/mol
moles of solute = mass of solute / molar mass of solute
moles of solute = 25.5 g / 46.03 g/mol
moles of solute ≈ 0.553 mol
Step 3: Calculate the moles of solvent (water).
- To get the moles of solvent, we need to subtract the moles of solute from the total moles in the solution. Since the total mass of the solution is 100 g (assumed), we can calculate the moles of solvent using the molar mass of water:
Molar mass of H2O = 1.01 g/mol (H) + 16.00 g/mol (O) = 18.01 g/mol
moles of solvent = (total mass of solution - mass of solute) / molar mass of solvent
moles of solvent = (100 g - 25.5 g) / 18.01 g/mol
moles of solvent ≈ 3.74 mol
Now we have the moles of solute (0.553 mol) and moles of solvent (3.74 mol). Let's proceed to calculate the molality and mole fraction.
Step 4: Calculate molality (m) of solute.
- Molality is defined as the moles of solute per kilogram of solvent.
- We need to convert the mass of water to kilograms (kg) before calculating molality:
mass of solvent (H2O) = moles of solvent x molar mass of solvent
mass of solvent (H2O) = 3.74 mol x 18.01 g/mol
mass of solvent (H2O) ≈ 67.44 g ≈ 0.06744 kg
molality (m) = moles of solute / mass of solvent (in kg)
molality (m) = 0.553 mol / 0.06744 kg
molality (m) ≈ 8.20 mol/kg
Step 5: Calculate mole fraction (X) of solute.
- Mole fraction is defined as the moles of solute divided by the total moles of solute and solvent.
- Total moles = moles of solute + moles of solvent
- Knowing the moles of solute (0.553 mol) and moles of solvent (3.74 mol):
mole fraction (X) = moles of solute / (moles of solute + moles of solvent)
mole fraction (X) = 0.553 mol / (0.553 mol + 3.74 mol)
mole fraction (X) ≈ 0.129