The density of an aqueous solution containing 10% of ethanol (C2H5OH) by mass is 0.984 g/ml.
A) Calculate the molality of this solution.
B) Calculate its molarity.
C) What volume of the solution would contain 0.125 mol of ethanol.
10% means 10 g EtOH/100 g solution which is 10 g EtOH/(10 g EtOH + 90 g water).
A. 10 g is how many moles? moles = grams/molar mass.
m = moles/kg solvent.
Substitute moles from above. kg solvent is 0.090 kg.
B. molarity = moles/L soln.
moles you have from above.
The 10% soln has a mass of 100 grams. Use the density to convert 100 g to volume (which will be in mL), then convert to L and divide moles/L to arrive at molarity.
C. M x L = 0.125. You have M, solve for L.
Thank you!
A) To calculate the molality of the solution, we first need to determine the mass of the solvent (water) and the mass of the solute (ethanol).
Given that the solution contains 10% ethanol by mass and has a density of 0.984 g/ml, we can calculate the mass of the solution as follows:
Mass of solution = Volume of solution × Density of solution
Mass of solution = 100 g (assuming we have 100 ml of solution, for convenience) × 0.984 g/ml
Mass of solution = 98.4 g
The mass of ethanol in the solution can be calculated as:
Mass of ethanol = Mass of solution × Percentage of ethanol
Mass of ethanol = 98.4 g × 0.10
Mass of ethanol = 9.84 g
Now, we can calculate the molality using the following formula:
Molality (m) = Moles of solute / Mass of solvent (in kg)
First, we need to convert the mass of ethanol to moles:
Moles of ethanol = Mass of ethanol / Molar mass of ethanol
Molar mass of ethanol (C2H5OH) = 2(12.01 g/mol) + 6(1.01 g/mol) + 1(16.00 g/mol)
Molar mass of ethanol = 46.07 g/mol
Moles of ethanol = 9.84 g / 46.07 g/mol
Moles of ethanol = 0.2137 mol
Since the solvent is water, its mass is equal to the mass of the solution minus the mass of ethanol:
Mass of solvent = Mass of solution - Mass of ethanol
Mass of solvent = 98.4 g - 9.84 g
Mass of solvent = 88.56 g
Finally, we can calculate the molality:
Molality (m) = Moles of ethanol / Mass of solvent (in kg)
Molality (m) = 0.2137 mol / (88.56 g / 1000 g/kg)
Molality (m) = 2.413 mol/kg
Therefore, the molality of the solution is 2.413 mol/kg.
B) To calculate the molarity of the solution, we need to determine the volume of the solution in liters.
Given that the density of the solution is 0.984 g/ml, the mass of the solution is 98.4 g, we can calculate the volume of the solution as follows:
Volume of solution = Mass of solution / Density of solution
Volume of solution = 98.4 g / 0.984 g/ml
Volume of solution = 100 ml or 0.1 L
Now, we can calculate the molarity using the following formula:
Molarity (M) = Moles of solute / Volume of solution (in L)
Using the previously calculated moles of ethanol:
Molarity (M) = 0.2137 mol / 0.1 L
Molarity (M) = 2.137 M
Therefore, the molarity of the solution is 2.137 M.
C) To calculate the volume of the solution that contains 0.125 mol of ethanol, we can use the following formula:
Volume of solution = moles of ethanol / Molarity
Using the given number of moles:
Volume of solution = 0.125 mol / 2.137 moles/L
Volume of solution = 0.0584 L or 58.4 mL
Therefore, a volume of 58.4 mL of the solution would contain 0.125 mol of ethanol.
A) To calculate the molality of the solution, we need to first find the mass of ethanol in the solution.
Given:
Density of the solution = 0.984 g/ml
Mass percentage of ethanol = 10%
Mass of ethanol = ?
To find the mass of ethanol, we need to consider that it makes up 10% of the total mass of the solution. Let's assume we have 100 g of the solution, then the mass of ethanol would be 10% of 100 g, which is 10 g.
Now, we can calculate molality using the formula:
Molality (m) = moles of solute / mass of solvent (in kg)
Since the solvent is water, we need to convert the mass of water (solvent) to kg. The density of water is 1 g/ml, so 1000 g of water (since it has the same volume as 1000 ml) is equal to 1 kg.
Molality (m) = moles of solute / mass of solvent (in kg)
= moles of ethanol / mass of water (in kg)
= moles of ethanol / 1 kg
We know that the molar mass of ethanol (C2H5OH) is:
Molar mass = 2 × (atomic mass of carbon) + 5 × (atomic mass of hydrogen) + 16 × (atomic mass of oxygen)
Let's look up the atomic masses of carbon (C), hydrogen (H), and oxygen (O) and calculate the molar mass of ethanol.
Atomic mass of carbon (C) = 12.01 g/mol
Atomic mass of hydrogen (H) = 1.01 g/mol
Atomic mass of oxygen (O) = 16.00 g/mol
Molar mass of ethanol (C2H5OH) = 2 × 12.01 + 5 × 1.01 + 16.00
= 24.02 + 5.05 + 16.00
= 45.07 g/mol
Now, we can calculate the number of moles of ethanol:
moles of ethanol = mass of ethanol / molar mass of ethanol
= 10 g / 45.07 g/mol
Finally, we can calculate the molality:
molality (m) = moles of ethanol / 1 kg
= (10 g / 45.07 g/mol) / 1 kg
= (10 / 45.07) mol/kg
B) To calculate the molarity of the solution, we need to find the volume of the solution in liters.
Given:
Density of the solution = 0.984 g/ml
Mass of the solution = 100 g
Volume of the solution = ?
We know that density (d) is defined as mass (m) divided by volume (v):
Density (d) = mass (m) / volume (v)
Rearranging the equation, we can find the volume:
Volume (v) = mass (m) / density (d)
= 100 g / 0.984 g/ml
Since 1 ml is equal to 1 cm^3 and 1 L is equal to 1000 cm^3, we can convert the volume from ml to L:
Volume (v) = (100 g / 0.984 g/ml) * (1 ml / 1 cm^3) * (1 L / 1000 cm^3)
= 101.6 L
Now, we can calculate the molarity using the formula:
Molarity (M) = moles of solute / volume of solution (in liters)
Substituting the values we have:
Molarity (M) = (10 g / 45.07 g/mol) / 101.6 L
C) To find the volume of the solution that would contain 0.125 mol of ethanol, we can use the formula:
Volume of solution = (moles of ethanol / molarity)
Given:
Molarity (M) = calculated from part (B)
Moles of ethanol = 0.125 mol
Substituting the values we have:
Volume of solution = (0.125 mol / calculated Molarity)