A solution s prepared by mixing 1.00 g ethanol with 100.0 g water to give final volume 101 mL. What is molarity, mass %, mole fraction and molality of ethanol in solution?

Question

Wyatt Atkins · Accepted Answer

Well, here we use several definitions of concentration...

#"Molarity"="moles of solute"/"volume of solution"# #=((1.00*g)/(46.07*g*mol^-1))/(101.0*mL)=0.215*mol*L^-1# #"Molality"="moles of solute"/"kilograms of solvent"# #=((1.00*g)/(46.07*g*mol^-1))/(100.0*gxx10^-3*kg*g^-1)=0.217*mol*kg^-1# #"Mass percent"="mass of solute"/"mass of solution"xx100%=??# #chi_"the mole fraction of water"=n_"water"/"Total moles in solution"# #((100*g)/(18.01*g*mol^-1))/((1.00*g)/(46.07*g*mol^-1)+(100*g)/(18.01*g*mol^-1)#...and so #chi_"water"~=1.0# What is the relation between #chi_"water"# and #chi_"EtOH"#?

Jeremiah Adams · Answer

undefined Molarity of ethanol in the solution:
The molarity (M) of a solution is calculated by dividing the moles of solute by the volume of the solution in liters. First, we need to convert the mass of ethanol to moles using its molar mass (46.07 g/mol). Then, we divide the moles of ethanol by the total volume of the solution in liters (0.101 L).

Mass percent of ethanol in the solution:
The mass percent of ethanol in the solution is calculated by dividing the mass of ethanol by the total mass of the solution and multiplying by 100%.

Mole fraction of ethanol in the solution:
The mole fraction (χ) of ethanol in the solution is calculated by dividing the moles of ethanol by the total moles of solute in the solution.

Molality of ethanol in the solution:
Molality (m) of a solution is calculated by dividing the moles of solute by the mass of the solvent in kilograms. We need to convert the mass of water to kilograms (100.0 g = 0.100 kg) and then divide the moles of ethanol by the mass of water in kilograms.

Given:
Mass of ethanol (m₁) = 1.00 g
Mass of water (m₂) = 100.0 g
Volume of solution (V) = 101 mL = 0.101 L
Molar mass of ethanol (M₁) = 46.07 g/mol
Density of water = 1 g/mL

Calculations:
1. Calculate moles of ethanol:
moles_ethanol = mass_ethanol / molar_mass_ethanol
moles_ethanol = 1.00 g / 46.07 g/mol
moles_ethanol ≈ 0.0217 mol

2. Calculate molarity of ethanol:
Molarity_ethanol = moles_ethanol / volume_solution
Molarity_ethanol = 0.0217 mol / 0.101 L
Molarity_ethanol ≈ 0.215 M

3. Calculate mass percent of ethanol:
mass_percent_ethanol = (mass_ethanol / mass_solution) * 100%
mass_solution = mass_ethanol + mass_water
mass_solution = 1.00 g + 100.0 g
mass_solution = 101.0 g
mass_percent_ethanol = (1.00 g / 101.0 g) * 100%
mass_percent_ethanol ≈ 0.990%

4. Calculate mole fraction of ethanol:
moles_water = mass_water / molar_mass_water
moles_water = 100.0 g / 18.015 g/mol
moles_water ≈ 5.548 mol

total_moles = moles_ethanol + moles_water
total_moles = 0.0217 mol + 5.548 mol
total_moles ≈ 5.570 mol

mole_fraction_ethanol = moles_ethanol / total_moles
mole_fraction_ethanol ≈ 0.0039

5. Calculate molality of ethanol:
molality_ethanol = moles_ethanol / mass_solvent_kg
mass_solvent_kg = mass_water / 1000
mass_solvent_kg = 100.0 g / 1000
mass_solvent_kg = 0.100 kg

molality_ethanol = 0.0217 mol / 0.100 kg
molality_ethanol ≈ 0.217 mol/kg