Henry's Law Calculator

What is Henry's Law?

Henry's Law is a fundamental gas law formulated in physical chemistry that describes the solubility of gases in liquids. It states that at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

The mathematical formulation of Henry's Law is:

If the pressure of the gas above a liquid is doubled, the concentration of the dissolved gas in the liquid will also double, assuming temperature is held constant.

History and William Henry

Henry's Law was formulated in 1803 by the British chemist and physician William Henry. Henry was a close friend of John Dalton and studied the behavior of gas mixtures. His experiments on the absorption of gases by water under pressure led to the discovery of this linear relationship. His work helped establish early concepts of chemical equilibrium and phase behavior in solutions.

Detailed Step-by-Step Example Calculation

Let's calculate the concentration of dissolved oxygen ($O_2$) in a freshwater lake at sea level:

• Given Partial Pressure of Oxygen ($P$): $0.21\text{ atm}$ (since oxygen makes up about 21% of the atmosphere).
• Henry's Law Constant ($k_H$) for $O_2$ in water at $25^\circ\text{C}$: $1.3 \times 10^{-3}\text{ M/atm}$.

Step 1: State the Formula

$C = k_H \cdot P$

Step 2: Substitute the Values

$C = \left(1.3 \times 10^{-3}\text{ M/atm}\right) \cdot 0.21\text{ atm}$

Step 3: Perform the Multiplication

$C = 0.000273\text{ M}$ Convert to millimoles per liter ($mM$) for readability: $C = 0.273\text{ mM} = 0.273 \text{ mmol/L}$ The concentration of dissolved oxygen in the water under standard atmospheric conditions is $0.273\text{ mmol/L}$ (or about $8.7\text{ mg/L}$).

Industrial, Clinical, and Environmental Applications

1. Scuba Diving Physiology (Decompression Sickness): As a diver descends, water pressure increases, forcing more nitrogen gas to dissolve into their blood and tissues. If the diver ascends too quickly, the pressure drops rapidly, causing the dissolved nitrogen to form gas bubbles in blood vessels, leading to the painful and dangerous condition known as "the bends".
2. Carbonated Beverage Industry: Soda, beer, and sparkling water factories use Henry's Law to carbonate drinks. They bottle liquids under high pressures of carbon dioxide ($CO_2$), forcing a large concentration of gas to dissolve. When the container is opened, the pressure drops to atmospheric level, reducing solubility, and causing $CO_2$ to bubble out.
3. Aquatic Ecology: The survival of fish and aquatic organisms depends on dissolved oxygen ($DO$) levels. Environmental scientists use Henry's Law to monitor how changes in atmospheric pressure and rising water temperatures (which lower $k_H$) affect oxygen levels in lakes and oceans.

Common Pitfalls and Tips

• Temperature Dependency: Henry's Law constants are highly sensitive to temperature. Generally, gas solubility decreases as temperature increases because dissolved gas molecules gain kinetic energy and escape into the gas phase. Always use the $k_H$ value specific to your system's temperature.
• Chemical Reactivity: Henry's Law only holds true for dilute solutions where the gas does not chemically react with the solvent. For example, it fails for ammonia ($NH_3$) or hydrogen chloride ($HCl$) in water because these gases react to form ions, dramatically increasing solubility.
• Different Constant Definitions: Be careful with units. Some databases express Henry's constant as volatility ($k_{H,pc} = P/C$) or as dimensionless solubility ($k_{H,cc} = C_{liquid}/C_{gas}$). Check the formula definition before entering constants.