An ethanol-water solution is prepared by dissolving 10.00 ml ethanol C2H5OH (density=0.789g/ml) in sufficient water to produce 100.00 ml of solution with a density of 0.982g/ml. What is the concentration of ethanol in this solution? Expressed as ml.
a.)%volume
b.)%mass
c.)%m/v
d.)mole fractions
e.)molarity
f.)molality
To determine the concentration of ethanol in the solution, we can use the concept of mass percent.
First, we need to find the mass of ethanol in the solution. We can do this by multiplying the volume of ethanol used (10.00 ml) by its density (0.789 g/ml):
Mass of ethanol = Volume of ethanol × Density of ethanol
= 10.00 ml × 0.789 g/ml
= 7.89 g
Next, let's find the total mass of the solution. We can do this by multiplying the volume of the solution (100.00 ml) by its density (0.982 g/ml):
Mass of solution = Volume of solution × Density of solution
= 100.00 ml × 0.982 g/ml
= 98.2 g
Now we can calculate the mass percent of ethanol in the solution:
Mass percent of ethanol = (Mass of ethanol / Mass of solution) × 100
= (7.89 g / 98.2 g) × 100
= 8.03%
So, the concentration of ethanol in the solution is 8.03% (mass/volume).
Therefore, the answer is option (c) %m/v.
To find the concentration of ethanol in the solution, we'll use three of the given pieces of information: the volume of ethanol added, the total volume of the solution, and the density of the solution.
Step 1: Calculate the mass of ethanol added.
Given: Volume of ethanol added = 10.00 ml
Density of ethanol (C2H5OH) = 0.789 g/ml
Mass of ethanol added = Volume × Density
Mass of ethanol added = 10.00 ml × 0.789 g/ml
Mass of ethanol added = 7.89 g
Step 2: Calculate the mass of the solution.
Given: Density of the solution = 0.982 g/ml
Volume of the solution = 100.00 ml
Mass of the solution = Volume × Density
Mass of the solution = 100.00 ml × 0.982 g/ml
Mass of the solution = 98.20 g
Step 3: Calculate the concentration of ethanol using the mass of ethanol added and the mass of the solution.
a) % Volume:
% Volume = (Volume of ethanol added / Volume of the solution) × 100
% Volume = (10.00 ml / 100.00 ml) × 100
% Volume = 10%
b) % Mass:
% Mass = (Mass of ethanol added / Mass of the solution) × 100
% Mass = (7.89 g / 98.20 g) × 100
% Mass = 8.02%
c) % m/v (mass/volume):
% m/v = (Mass of solute / Volume of solution) × 100
% m/v = (7.89 g / 100.00 ml) × 100
% m/v = 7.89%
d) Mole fractions:
Mole fraction of ethanol (C2H5OH) = Moles of ethanol / Moles of all components
To calculate the moles of ethanol, we need to convert the mass of ethanol added to moles using the molar mass of ethanol (46.07 g/mol).
Moles of ethanol = Mass of ethanol added / Molar mass of ethanol
Moles of ethanol = 7.89 g / 46.07 g/mol
Moles of ethanol = 0.171 mol
To calculate the moles of water, subtract the moles of ethanol from the total moles of all components (water + ethanol).
Moles of water = Total moles - Moles of ethanol
Moles of water = 1 - 0.171
Moles of water = 0.829 mol
Mole fraction of ethanol = Moles of ethanol / (Moles of ethanol + Moles of water)
Mole fraction of ethanol = 0.171 / (0.171 + 0.829)
Mole fraction of ethanol = 0.171
e) Molarity:
Molarity = Moles of solute / Volume of solution (expressed in liters)
Molarity = 0.171 mol / 0.1 L
Molarity = 1.71 M
f) Molality:
Molality = Moles of solute / Mass of solvent (expressed in kg)
Given: mass of solvent = mass of solution - mass of solute
mass of solvent = 98.20 g - 7.89 g
mass of solvent = 90.31 g
Molality = 0.171 mol / 0.09031 kg
Molality = 1.89 mol/kg
So, the concentration of ethanol in this solution is:
a) 10% (volume)
b) 8.02% (mass)
c) 7.89% (m/v)
d) 0.171 (mole fraction)
e) 1.71 M (molarity)
f) 1.89 mol/kg (molality)