Library / Solution chemistry, equilibria and kinetics / SCH-01
Solution chemistry, equilibria and kinetics
Molality from solute and solvent masses
Moles of solute per kilogram of solvent, from the solute mass ms, its molar mass M and the mass mv of the solvent alone.
- Ref
- SCH-01
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- b [mol/kg]
Molality is the amount of solute per kilogram of solvent, b = (ms/M)/(mv/1000). Unlike molarity it depends only on masses, so it does not change with temperature or when the volume changes on mixing. Use the mass of the solvent alone, not of the solution, and the molar mass in g/mol.
Moles of solute per kilogram of solvent, from the solute mass ms, its molar mass M and the mass mv of the solvent alone. Unlike molarity, it does not change with temperature or with the final solution volume.
Calculator
- Moles of solute, ms/M0.1 mol
- Solvent mass in kilograms0.5 kg
- Mass fraction of solute in the solution, ms/(ms + mv)0.01155
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Dissolving 5.844 g of solute (0.1 mol) in 500 g of solvent gives a molality of 0.2 mol/kg.
- Because molality depends on mass only, the value stays the same when the solution is heated, unlike the molarity.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/kg) | Local step | Change in result |
|---|---|---|---|---|---|---|
| mv Mass of the solvent alone | 1 to 10,000 g | 0.01 | 100 | 99.99 | +10% | −9.09 % |
| ms Solute mass | 0.001 to 1,000 g | 3.422e-5 | 34.22 | 34.22 | +10% | +10 % |
| M Molar mass of the solute | 1 to 1,000 g/mol | 0.01169 | 11.69 | 11.68 | +10% | −9.09 % |
Sweep of Mass of the solvent alone
| Mass of the solvent alone (g) | Molality (mol/kg) |
|---|---|
| 1 | 100 |
| 3.162 | 31.62 |
| 10 | 10 |
| 31.62 | 3.162 |
| 100 | 1 |
| 316.2 | 0.3162 |
| 1,000 | 0.1 |
| 3,162 | 0.03162 |
| 10,000 | 0.01 |
Sweep one variable
Variables and how each one contributes
Molality
What the equation gives you. Everything else feeds it.
Solute mass
The mass of the solute, in g. Raises the molality in direct proportion. Raising it by 10 % (to 6.428) moves the result by +10 %, from 0.2 to 0.22 mol/kg.
Molar mass of the solute
The molar mass of the solute, in g/mol. A heavier molar mass means fewer moles for the same mass, so the molality falls in inverse proportion. Raising it by 10 % (to 64.28) moves the result by −9.09 %, from 0.2 to 0.1818 mol/kg.
Mass of the solvent alone
The mass of the solvent alone, in g. More solvent dilutes the solution, so the molality falls in inverse proportion. Raising it by 10 % (to 550) moves the result by −9.09 %, from 0.2 to 0.1818 mol/kg.
Worked example with the values above
- Moles of solute: ms/M = 5.844 / 58.44 = 0.1 mol.
- Solvent mass: 500 g = 0.5 kg.
- b = 0.1 / 0.5 = 0.2 mol/kg.
Assumptions and limits
- Ideal dilute solutions, with concentrations in mol/L and masses in grams unless stated.
- Complete mixing and no evaporation or contraction on mixing unless the inputs say otherwise.
Common mistakes
- Using the mass of the solution in place of the mass of the solvent alone.
- Mixing molality with molarity, which uses the volume of the solution.
- Leaving the solvent mass in grams in the formula without the 1000 factor.
Statistics and uncertainty
Masses and volumes are usually known to 0.1 % to 1 %, and concentrations from them carry the same relative error. Volumetric glassware tolerances add up through serial dilutions, so each extra stage widens the uncertainty.
Where it is used
- Preparing standards, stocks and dilution series in the laboratory.
- Checking charge balance and ionic strength in water analysis.
Maths you need
- Amount of substance: n = m/M, in mol
- Concentration: c = n/V, in mol/L
- Electroneutrality: total positive charge equals total negative charge