The density of a 15.7 M methanol (CH 3 OH) solution is 0.858 g/mL. If H 2 O is the solvent, what is the molality of the solution?

The density of a 15.7 molar methanol solution is 0.858 grams per milliliter. Now methanol is c h three o h. Now if water is a solvent, what is the molality of the solution? So remember, we're gonna say that molality equals moles of solute, which in this case will be the moles of our methanol divided by kilograms of water. We're told that the sulfate here is water. Alright. So how do we approach this question? Well, they're giving us the molarity. Remember, molarity represents moles of solute over liters of solution. So when they gave us this number, they're giving us a lot of information. We have 15.7 moles of methanol divided by 1 liter of solution. And look, we have a portion of molality that we need. We know how many moles of methanol we have, 15.7. All we have to do now is figure out what my kilograms of water, which is my solvent, will be. To do that, we have 1 liter of solution and we have the density of the solution. Alright. So remember that 1 liter is the same thing as a 1,000 milliliters. And we need a 1,000 milliliters because we need to interact with the density. So here we're gonna say we have 0.858 grams of solution, and here we have 1 milliliter of solution. So those cancel out and we're gonna have 858 grams of solution. Remember, your solution is comprised of solute and solvent together. All we need though is the solvent portion, the water portion. So I'm gonna have to subtract out my grams of solute. I'm gonna take this 15.7, moles of methanol, so 15.7 moles of methanol, and then convert that into grams. So 1 mole of methanol. Methanol has a mass of 32.042 grams. Moles cancel out, and that's gonna give me here 503.0 594 grams of our solute, methanol. Subtract it from here, and what's left will be the grams of my solvent, water. When you change that into kilograms, it comes out to be 0.35 49406 kilograms. When we plug all that in, we get 44.2328 mole. And based on sig figs, that would mean that option a is my correct answer. So option a would be our final answer in terms of determining the molality of our solution.

Table of contents

Skip topic navigation

1. Intro to General Chemistry3h 48m
2. Atoms & Elements4h 16m
3. Chemical Reactions4h 10m
4. BONUS: Lab Techniques and Procedures1h 38m
5. BONUS: Mathematical Operations and Functions48m
6. Chemical Quantities & Aqueous Reactions3h 53m
7. Gases3h 49m
8. Thermochemistry2h 37m
9. Quantum Mechanics2h 58m
10. Periodic Properties of the Elements3h 9m
11. Bonding & Molecular Structure3h 29m
12. Molecular Shapes & Valence Bond Theory1h 57m
13. Liquids, Solids & Intermolecular Forces2h 23m
14. Solutions3h 1m
15. Chemical Kinetics2h 53m
16. Chemical Equilibrium2h 29m
17. Acid and Base Equilibrium5h 1m
18. Aqueous Equilibrium4h 47m
19. Chemical Thermodynamics1h 50m
20. Electrochemistry2h 42m
21. Nuclear Chemistry2h 36m
22. Organic Chemistry5h 7m
23. Chemistry of the Nonmetals2h 39m
24. Transition Metals and Coordination Compounds3h 16m

14. Solutions

Molality

General Chemistry

14. Solutions

Molality

Previous problemNext problem

Struggling with General Chemistry?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

The density of a 15.7 M methanol (CH₃OH) solution is 0.858 g/mL. If H₂O is the solvent, what is the molality of the solution?

44.2 m

18.3 m

31.2 m

23.7 m

Previous problemNext problem

Verified step by step guidance

Understand that molality (m) is defined as the number of moles of solute per kilogram of solvent. We need to find the moles of methanol and the mass of the solvent (water) in kilograms.

Calculate the mass of the solution using its density. Use the formula: \( \text{mass of solution} = \text{density} \times \text{volume} \). Assume a convenient volume of 1 L (1000 mL) for simplicity, which gives us a mass of 858 g.

Determine the moles of methanol in the solution. Use the molarity (M) definition: \( \text{moles of methanol} = \text{molarity} \times \text{volume in liters} \). For 1 L of solution, this is 15.7 moles.

Calculate the mass of methanol using its molar mass (32.04 g/mol). Use the formula: \( \text{mass of methanol} = \text{moles of methanol} \times \text{molar mass} \).

Find the mass of the solvent (water) by subtracting the mass of methanol from the total mass of the solution. Convert this mass to kilograms and use it to calculate molality: \( \text{molality} = \frac{\text{moles of methanol}}{\text{mass of water in kg}} \).