A 4.14 m solution of the solute methylene chloride dissolved in the solvent ethanol is available. Calculate the mass ( kg ) of the solution that must be taken to obtain 1487 g of methylene chloride
density:
CH2Cl2-1327(kg/m^3)
C2H5OH-789.3(kg/m^3)
I worked this for you below although I made a typo in the first post but I followed up with a correction post.
To calculate the mass of the solution required to obtain a given amount of methylene chloride, we'll need to consider the concentration of the solution and the density of the solute and the solvent.
Given information:
Concentration of the solution: 4.14 m (molality)
Density of CH2Cl2 (methylene chloride): 1327 kg/m^3
Density of C2H5OH (ethanol): 789.3 kg/m^3
Step 1: Calculate the amount of methylene chloride required.
We are given that we need to obtain 1487 g of methylene chloride. To convert this mass to moles, we need to divide it by the molar mass of methylene chloride (CH2Cl2).
The molar mass of CH2Cl2 = (12.01 x 2) + (1.01 x 2) + 35.45 = 84.93 g/mol
1487 g / 84.93 g/mol ≈ 17.49 moles of CH2Cl2.
Step 2: Calculate the mass of the solvent required to form the solution.
Since we know the concentration of the solution (4.14 m), we can calculate the number of moles of the solvent (ethanol) needed to dissolve the 17.49 moles of CH2Cl2.
To convert from molality (m) to moles, we need to multiply by the mass of the solvent in kg.
m = moles of solute / mass of solvent in kg
Rearranging the equation:
mass of solvent (kg) = moles of solute / m
mass of solvent (kg) = 17.49 moles / 4.14 m
mass of solvent (kg) ≈ 4.22 kg
Step 3: Calculate the total mass of the solution.
The mass of the solution will be the sum of the mass of the solute (methylene chloride) and the mass of the solvent (ethanol).
mass of solution (kg) = mass of solute (kg) + mass of solvent (kg).
mass of solution (kg) = 1487 g / 1000 (to convert to kg) + 4.22 kg
mass of solution (kg) ≈ 5.707 kg
Therefore, approximately 5.707 kg of the solution must be taken to obtain 1487 g of methylene chloride.