Henry's Law with Defined Units

Introduction

Henry's law turns the pressure trend for many dilute gas solutions into a calculation. The safest method is to start with the exact equation supplied: in this page, c = kP. Different references define the named constant differently, so a bare number called “Henry's constant” is not sufficient without units and convention.

Core explanation

For a suitable gas dissolved in a liquid at a fixed temperature, one common form is c = kP, where c is equilibrium dissolved concentration, P is the partial pressure of that gas above the liquid, and k depends on the gas, solvent and temperature. If c is mol L⁻¹ and P is atm, then k has units mol L⁻¹ atm⁻¹. Multiplying k by P leaves concentration units, which provides a useful dimensional check.

Suppose k = 0.020 mol L⁻¹ atm⁻¹ under specified conditions and gas partial pressure is 0.30 atm. Then c = 0.020 × 0.30 = 0.0060 mol L⁻¹. If the partial pressure doubles to 0.60 atm at the same temperature, the predicted equilibrium concentration doubles to 0.012 mol L⁻¹. A ratio form, c₂/c₁ = P₂/P₁, avoids needing the explicit k if the same gas, solvent and temperature remain. The pressure must be measured in the same unit in both numerator and denominator.

Other texts use P = kH c or define a mole-fraction form. Their numerical constants and units differ from k in c = kP. Substituting a value from one form into the other without conversion can produce a reciprocal error. Always write the supplied equation beside the constant. A dimensional check can reveal a mismatch: atm per mol L⁻¹ is not the same as mol L⁻¹ per atm.

Henry's law is approximate and has limits. It best describes sufficiently dilute gas solutions with no significant gas–solute reaction under the specified conditions. High pressures, strong interactions or chemical transformations can cause deviations. Carbon dioxide in water may enter several equilibria, so a total inorganic-carbon concentration need not equal the concentration of physically dissolved molecular CO₂ used in a simple law. Also, a sealed system's partial pressure may change as gas dissolves if the gas reservoir is small; the problem must supply or allow determination of equilibrium pressure.

Temperature alters k, so a constant quoted at 25 °C cannot be used unchanged at 40 °C without justification. The law predicts an equilibrium concentration; it does not specify the time required to dissolve or escape. A freshly opened beverage may temporarily have more dissolved gas than the concentration calculated from the new outside pressure.

Step-by-step reasoning

1. Write the exact Henry-law equation and the constant's units. 2. Identify the target gas's partial pressure, not simply the total mixture pressure. 3. Confirm that temperature and solvent match the quoted constant. 4. Calculate equilibrium concentration, checking that units cancel. 5. State whether the result describes actual current concentration or only equilibrium.

Visual explanation

Plot c against gas partial pressure P for a fixed temperature. The idealized line passes through the origin with slope k in the c = kP convention. Draw a second line with a different slope for another temperature to show why one k cannot be carried over blindly.

Real-world analogy

A price per kilogram converts a measured mass into cost only if the currency and mass units match. Here k converts gas partial pressure into equilibrium concentration only under its specified unit and condition convention.

Real-world example

When estimating dissolved oxygen from air, a calculation first finds oxygen's partial pressure from the gas composition and total pressure. The chosen Henry constant must correspond to oxygen in the stated solvent and temperature. Real water quality also depends on ongoing biological and mixing processes.

Why?

Why does the equation use partial pressure? The specific gas species exchanges between gas and liquid phases. Other gas components contribute to total pressure but do not directly supply the named gas molecules to the interface.

Common misconception

“Henry constants are interchangeable numerical values.” Two references may define reciprocal forms and report different units. Match the constant to its equation before substituting.

Worked example

At a stated temperature, let k = 1.5 × 10⁻³ mol L⁻¹ atm⁻¹ for a gas. Its mole fraction in an ideal gas mixture is 0.20 at total pressure 1.00 atm, so its partial pressure is 0.20 atm. Then c = (1.5 × 10⁻³)(0.20) = 3.0 × 10⁻⁴ mol L⁻¹. If the mixture pressure is doubled without changing composition or temperature, partial pressure becomes 0.40 atm and predicted c becomes 6.0 × 10⁻⁴ mol L⁻¹.

Quick check

1. What units must k have when c is mol L⁻¹, P is atm and c = kP? Answer: k must have units mol L⁻¹ atm⁻¹, so multiplication by atm leaves mol L⁻¹.

Exam focus

Put the equation, constant units and partial-pressure calculation on paper before computing c. State assumptions of fixed temperature and suitable dilute gas behavior.

Advanced insight

The proportional relation follows from equality of chemical potentials in the dilute limit. Thermodynamic conventions commonly express the relation using fugacity or activity for better accuracy, but those are beyond the simple school calculation.

Summary

In the c = kP convention, equilibrium gas concentration is proportional to its own partial pressure, with k in concentration-per-pressure units. The constant depends on gas, solvent and temperature, and other conventions can reverse its units. The relation predicts equilibrium, not instantaneous concentration.

Practice questions

1. If k = 0.010 mol L⁻¹ atm⁻¹ and gas partial pressure is 0.25 atm, find c. Answer: c = kP = 0.010 × 0.25 = 0.0025 mol L⁻¹ at the constant's specified temperature. 2. The same gas changes from 0.25 to 0.50 atm at fixed temperature. What happens to ideal predicted c? Answer: It doubles from 0.0025 to 0.0050 mol L⁻¹ because the pressure ratio is two. 3. Why can a constant quoted at another temperature not be used automatically? Answer: The equilibrium partitioning changes with temperature, so the Henry constant itself is temperature dependent.