A 1.33 m solution of the solute diethyl ether dissolved in the solvent tetrahydrofuran is available. Calculate the mass(kg) of the solution that must be taken to obtain 0.4716 kg of diethyl ether.

Question

A 1.33 m solution of the solute diethyl ether dissolved in the solvent tetrahydrofuran is available. Calculate the mass(kg) of the solution that must be taken to obtain 0.4716 kg of diethyl ether.

Name/Formula:
diethyl ether = (C2H5)2O
tetrahydrofuran = C4H8O

Molar Mass(g/mol):
(C2H5)2O = 74.12
C4H8O = 72.12

Density(g/mL):
(C2H5)2O = 0.7138
C4H8O = 0.8892

Answer = 5.256 kg

This question is about molality. I've tried several ways of solving this type of problem, but I never seem to come up with the correct answer. Can someone give me a step by step explanation on how to come to the answer written above?

Answer 1

1.33 m = 1.33 moles (Et)2O in 1 kg THF.

1.33 moles = 1.33 x 74.12 grams = 98.58 g so the total solution has a mass of 1000 g + 98.58 = 1098.58 grams.

You want 471.6 grams (Et)2O which is 471.6/74.12 = 6.363 moles. So you need to take
1098.58 g solution x (6.363 moles/1.33 moles) = 5255.8 grams of the solution which rounds to 5256 grams or 5.256 kg.

Answer 2

Thank you Dr. Bob!

Answer 3

To solve this problem, we will use the concept of molality, which is defined as the number of moles of solute divided by the mass of the solvent in kilograms.

Step 1: Calculate the moles of diethyl ether (solute) required.
To do this, we will use the molar mass of diethyl ether.

Given mass of diethyl ether: 0.4716 kg
Molar mass of diethyl ether: 74.12 g/mol

First, we need to convert the given mass of diethyl ether from kg to grams:
0.4716 kg x 1000 g/kg = 471.6 g

Now, we can calculate the number of moles of diethyl ether:
n(diethyl ether) = mass(diethyl ether) / molar mass(diethyl ether)
= 471.6 g / 74.12 g/mol
≈ 6.36 moles

Step 2: Calculate the mass of the solution required.
To do this, we will use the molality formula.

Given molality of the solution: 1.33 m

Molality is defined as moles of solute / mass of solvent (in kg).
We can rearrange the formula to solve for the mass of the solvent (in kg):

mass of solvent = moles of solute / molality

mass of solvent = 6.36 moles / 1.33 m
≈ 4.78 kg

Step 3: Calculate the mass of the solution required.
We are given the mass of the solution in kilograms, so we can directly use the value from the previous step:

mass of solution = mass of solvent + mass of solute
= 4.78 kg + 0.4716 kg
≈ 5.256 kg

Therefore, the mass of the solution that must be taken to obtain 0.4716 kg of diethyl ether is approximately 5.256 kg.