Dalton’s law of partial pressures
A daltons law real life example appears whenever several nonreacting gases share the same container volume and temperature (air, anesthesia mixtures, breathing gas, industrial gas blends). Each gas contributes to the total pressure as if it were alone in the container.
\[ P_{\text{total}}=\sum_i P_i \]
\[ P_i=x_i\,P_{\text{total}}, \qquad x_i=\frac{n_i}{n_{\text{total}}} \]
Physical meaning in general chemistry
In the ideal-gas model, pressure reflects molecular collisions with container walls. For a mixture, collisions from different species add, so each species contributes an additive pressure term. The mole fraction \(x_i\) becomes the natural weighting because, at fixed \(T\) and \(V\), the ideal gas relation implies pressure scales with moles:
\[ P=\frac{nRT}{V}\quad\Longrightarrow\quad P_i=\frac{n_iRT}{V} \quad\Longrightarrow\quad \frac{P_i}{P_{\text{total}}}=\frac{n_i}{n_{\text{total}}}=x_i \]
Additivity works best for nonreacting gases close to ideal behavior (moderate pressures, not too low temperatures). At high pressures or with strong intermolecular attractions, real-gas effects shift partial-pressure predictions.
Real-life example: humid air and the “dry-gas” correction
Air that contains water vapor is a mixture. Water vapor contributes its own partial pressure \(P_{\ce{H2O}}\), reducing the pressure available for the “dry” components (nitrogen, oxygen, argon, carbon dioxide) at the same total pressure reading.
\[ P_{\text{dry}}=P_{\text{total}}-P_{\ce{H2O}} \]
The partial pressure of a dry component \(i\) (for example oxygen) follows:
\[ P_i=x_i\,P_{\text{dry}} \]
Numerical illustration
Consider air at \(P_{\text{total}}=101.3\ \text{kPa}\) and \(25^\circ\text{C}\). A typical water-vapor partial pressure at this temperature is about \(P_{\ce{H2O}}\approx 3.2\ \text{kPa}\) (order of magnitude shown; actual humidity and temperature set the value).
\[ P_{\text{dry}}=101.3-3.2=98.1\ \text{kPa} \]
Using common dry-air mole fractions (approximately \(x_{\ce{N2}}=0.7808\), \(x_{\ce{O2}}=0.2095\), and a remainder “other” of \(0.0097\)):
| Component (dry air) | Mole fraction \(x_i\) | Partial pressure \(P_i=x_iP_{\text{dry}}\) (kPa) | Chemical significance |
|---|---|---|---|
| \(\ce{N2}\) | 0.7808 | \(0.7808\times 98.1\approx 76.6\) | Largest contributor to total pressure; mostly inert under normal conditions. |
| \(\ce{O2}\) | 0.2095 | \(0.2095\times 98.1\approx 20.6\) | Controls oxidation chemistry and biological oxygen availability via \(P_{\ce{O2}}\). |
| Other (\(\ce{Ar}\), \(\ce{CO2}\), …) | 0.0097 | \(0.0097\times 98.1\approx 0.95\) | Small partial pressures; \(\ce{CO2}\) still matters for equilibria in aqueous solutions. |
| \(\ce{H2O(g)}\) (water vapor) | — | \(\approx 3.2\) | Consumes part of \(P_{\text{total}}\), shifting “dry-gas” partial pressures. |
Visualization: how partial pressures add to the total
Other common real-world settings
- Anesthesia and medical gas blends. Oxygen, nitrous oxide, and anesthetic vapors share a breathing circuit; physiological effects correlate with partial pressures rather than volume percentages alone.
- Scuba and hyperbaric environments. Increasing \(P_{\text{total}}\) increases each \(P_i\) proportionally at fixed composition, so oxygen and nitrogen partial pressures rise with depth and influence toxicity and narcosis thresholds.
- Industrial cylinders and welding gases. Argon–\(\ce{CO2}\) and similar mixtures rely on controlled partial pressures for consistent arc characteristics and shielding performance.
Common pitfalls
- Dry vs humid gas confusion. Total pressure readings for humid mixtures require the correction \(P_{\text{dry}}=P_{\text{total}}-P_{\ce{H2O}}\) when a dry-gas partial pressure is needed.
- Mole fraction vs “percent by volume.” For ideal gases at the same \(T\) and \(P\), volume fraction equals mole fraction; mixing rules fail when condensation or strong nonideality occurs.
- Unit inconsistency. Summation in \(P_{\text{total}}=\sum_i P_i\) requires a single pressure unit throughout (kPa, atm, mmHg, bar).
- Nonreacting assumption. Gas-phase reactions or strong association/dissociation can change composition and invalidate a simple fixed-\(x_i\) calculation.