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Solution chemistry, equilibria and kinetics
Bubble pressure of an ideal binary liquid
Pressure at which vapour first appears above an ideal binary liquid of fixed composition at a given temperature, from the mole fraction xA and the pure-component saturation pressures.
- Ref
- SCH-47
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- Pbub [kPa]
For an ideal binary liquid, the total vapour pressure above a liquid of composition xA is the sum of the two Raoult’s-law partial pressures, Pbub = xA pA* + (1 − xA) pB*. The first vapour bubble appears when the applied pressure falls to this value. It is a straight line between pB* and pA*, which is the liquid line on a pressure–composition diagram. The vapour composition is richer in the more volatile component.
Pressure at which vapour first appears above an ideal binary liquid of fixed composition at a given temperature, from the mole fraction xA and the pure-component saturation pressures. It is a straight line in xA.
Calculator
- Vapour mole fraction of A at the bubble point, yA0.64
- Partial pressure of A, xA pA*32 kPa
- Partial pressure of B, (1 − xA) pB*18 kPa
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.
- The mixture starts to boil at 50 kPa, and the first vapour is 64 mol % A, richer in A than the 40 mol % in the liquid.
- That enrichment of the more volatile component in the vapour is what distillation uses to separate the mixture.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| pB* Pure B saturation pressure | 0.1 to 1,000 kPa | 32.06 | 632 | 599.9 | +10% | +3.6 % |
| pA* Pure A saturation pressure | 0.1 to 1,000 kPa | 18.04 | 418 | 400 | +10% | +6.4 % |
| xA Liquid mole fraction of A | 0 to 1 | 30 | 80 | 50 | +10% | +4 % |
Sweep of Liquid mole fraction of A
| Liquid mole fraction of A | Bubble pressure (kPa) |
|---|---|
| 0 | 30 |
| 0.125 | 36.25 |
| 0.25 | 42.5 |
| 0.375 | 48.75 |
| 0.5 | 55 |
| 0.625 | 61.25 |
| 0.75 | 67.5 |
| 0.875 | 73.75 |
| 1 | 80 |
Sweep one variable
Variables and how each one contributes
Bubble pressure
What the equation gives you. Everything else feeds it.
Liquid mole fraction of A
The liquid mole fraction of A, between 0 and 1. Moves the bubble pressure linearly from pB* towards pA*. Raising it by 10 % (to 0.44) moves the result by +4 %, from 50 to 52 kPa.
Pure A saturation pressure
The pure-A saturation pressure at the temperature, in kPa. Raises the bubble pressure in proportion to xA. Raising it by 10 % (to 88) moves the result by +6.4 %, from 50 to 53.2 kPa.
Pure B saturation pressure
The pure-B saturation pressure at the temperature, in kPa. Raises the bubble pressure in proportion to 1 − xA. Raising it by 10 % (to 33) moves the result by +3.6 %, from 50 to 51.8 kPa.
Worked example with the values above
- Partial pressure of A: 0.4 × 80 = 32 kPa.
- Partial pressure of B: 0.6 × 30 = 18 kPa.
- Pbub = 50 kPa.
Assumptions and limits
- Dilute or ideal solutions with a non-volatile solute, unless a second volatile component is stated.
- Constant temperature (or constant pressure for boiling-point elevation) and a membrane that passes only the solvent for osmosis.
Common mistakes
- Using molarity where molality is needed for freezing and boiling points.
- Forgetting the van’t Hoff factor for salts.
- Adding the elevation or depression to the temperature in the wrong direction.
Statistics and uncertainty
Colligative formulas assume ideal behaviour, which holds only for dilute solutions. The effective particle factor i of an electrolyte is below its ideal value, by 5 % to 30 % even at 0.1 mol/kg.
Where it is used
- Estimating antifreeze, de-icing and desalination behaviour.
- Finding molar masses and reading simple phase diagrams.
Maths you need
- Raoult’s law: partial pressure = mole fraction × pure vapour pressure
- Colligative properties: properties that depend on particle number
- Molality: moles of solute per kilogram of solvent