a solution was prepared by mixing ethanol (CH3CH2OH / d= 0.775 g/ml) with 350ml of water (H20 / d= 0.9940326). Assuming volumes were additive, determine the molarity of the solution knowing the mole fraction of water is 0.853.
help me resolve this please
Remember mass = volume x density and mols = grams/molar mass
XH2O = 0.853 = (mols H2O)/[(mols H2O + mols EtOH)]
0.853 = (g H2O/18)/[(g H2O/18) + (g EtOH/46)]
0.853 = (0.994*350/18)/[(0.994*350) + (0.775*V)/46]
The only unknown is V = volume of EtOH used. Solve for that.
Then 0.775 V/46 gives you mols EtOH, then mols EtOH/total volume in L give you molarity of EtOH. Post your work if you get stuck.
To determine the molarity of the solution, we need to find the number of moles of the solute (ethanol) and the total volume of the solution.
Step 1: Calculate the volume of ethanol in the solution:
Since we know the volume of water added (350 mL), we can find the volume of ethanol by subtracting it from the total volume of the solution.
Volume of ethanol = Total volume - Volume of water = Total volume - 350 mL
Step 2: Calculate the mass of ethanol:
Mass of ethanol = Volume of ethanol × Density of ethanol
Density of ethanol = 0.775 g/mL (provided in the question)
Step 3: Convert the mass of ethanol to moles:
Moles of ethanol = Mass of ethanol / Molar mass of ethanol
The molar mass of ethanol (CH3CH2OH) can be calculated as follows:
(12.01 g/mol × 2) + (1.01 g/mol × 6) + (16.00 g/mol + 1) = 46.07 g/mol
Step 4: Calculate the number of moles of water:
Since the mole fraction of water is provided (0.853), we can calculate the moles of water using the following equation:
Moles of water = Total moles of solution × Mole fraction of water
Step 5: Calculate the total volume of the solution:
Total volume = Volume of water + Volume of ethanol
Step 6: Calculate the molarity of the solution:
Molarity = Moles of ethanol / Total volume
Once you have performed these calculations, substitute the values into the respective formulas to find the molarity of the solution.