Free Partial Pressure Calculator

Understanding Partial Pressure and Dalton's Law

Partial pressure is the pressure a single gas in a mixture would exert if it occupied the entire volume by itself. This partial pressure calculator — often called a Dalton's law calculator — helps you determine these values using several established approaches.

Dalton's Law of Partial Pressures

Dalton's law states that the total pressure from a gas mixture equals the sum of the partial pressures of each component:

$$P_{\text{total}} = p_1 + p_2 + \dots + p_n$$

It can also be expressed with the mole fraction ($x_i$) of a gas:

$$p_i = x_i \cdot P_{\text{total}} \quad \text{where} \quad x_i = \frac{n_i}{n_{\text{total}}}$$

This relationship shows that the partial pressure of each gas is directly proportional to its mole fraction in the mixture.

Using the Ideal Gas Law

When you know the amount of a specific gas, the mixture's temperature, and its volume, you can apply the ideal gas law. For a single gas:

$$pV = nRT$$

To obtain the partial pressure of one component, rearrange the formula:

$$p_i = \frac{n_i R T_m}{V_m}$$

where:

• $p_i$ = partial pressure of the gas,
• $n_i$ = moles of that gas,
• $R$ = universal gas constant (8.3145 J/mol·K),
• $T_m$ = temperature of the mixture,
• $V_m$ = volume of the mixture.

This method is straightforward when you have measured or known the moles, temperature, and volume of the gaseous mixture.

Henry's Law and Its Two Forms

Henry's law describes the link between the partial pressure of a gas above a liquid and its concentration in that liquid. The partial pressure is proportional to the dissolved amount, with the constant of proportionality being Henry's law constant. Two common expressions are:

$$p = K_{H1} \cdot C \quad \text{(concentration in mol/L)}$$ $$p = K_{H2} \cdot x \quad \text{(mole fraction)}$$

Here, $K_{H1}$ is given in L·atm/mol and $K_{H2}$ in atm. Henry's law is most accurate at low pressures (below 1000 hPa) and at a fixed temperature (often 298 K). The constant varies by gas — at 298 K, for example, $K_{H1}$ for O₂ is 769.23 L·atm/mol, for N₂ it is 1639.34 L·atm/mol, and for CO₂ it is 29.41 L·atm/mol.

Example: Partial Pressure of Nitrogen

Suppose water contains dissolved nitrogen at a concentration of 1.5 mol/L. Using Henry's law with the constant for N₂:

$$p = 1.5 \, \text{mol/L} \times 1639.34 \, \text{L·atm/mol} = 2459 \, \text{atm} = 249159 \, \text{kPa}$$

This example shows how the gas partial pressure is quickly obtained when you have the correct constant and concentration.

Real-World Relevance

Partial pressure plays a key role in several fields:

• Underwater diving: Divers breathe oxygen‑nitrogen blends. As pressure increases with depth, oxygen can become toxic and nitrogen may cause narcosis, so the mixture must be carefully chosen.
• Medical diagnostics: Arterial blood gas tests measure the partial pressures of oxygen and carbon dioxide, allowing physicians to assess blood pH and respiratory function.

This tool integrates Dalton's law, the ideal gas law, and Henry's law into one interface. Depending on your data — mole fraction, moles, volume, concentration, or mole fraction — you can choose the most convenient partial pressure formula to get accurate results.