How to Leverage off Henry’s Law to Get the Information You Are Looking for – Part 3

Henry's law, a gas law, states that the amount of dissolved gas in a liquid is directly proportional at equilibrium to its partial pressure above the liquid.

The depth-dependent dissolution of Oxygen and Nitrogen in the blood of underwater divers which changes during decompression, possibly causing decompression sickness if the decompression occurs too fast, is an application of Henry’s law. Scuba divers must handle high concentrations of dissolved gases in blood while breathing air at high pressure underwater. When the divers come toward the surface, the pressure gradually drops, which releases the dissolved gases as per Henry’s law forming bubbles of Nitrogen in the blood, which, in turn, blocks capillaries and gives rise to a medical condition referred to as bends, which is painful and may jeopardize life. The tanks used by scuba divers are filled with air diluted with Helium to avoid bends and the toxic effects of high concentrations of Nitrogen in the blood.

Once the bottle of a carbonated soft drink is opened, almost pure Carbon dioxide above the liquid in the container at a pressure higher than the atmospheric pressure escapes decreasing the pressure above the liquid, resulting in fast degassing as the dissolved gas is liberated from the solution. This is an everyday example of Henry’s law.

The partial pressure of Oxygen at high altitudes is less than that at the ground level, which results in low concentrations of Oxygen in the blood and tissues of climbers (or people living at high altitudes) according to Henry’s law, which, in turn, makes climbers weak and unable to think clearly, symptoms of a medical condition called anoxia.

Question:

If N₂ gas is bubbled through water at 293 K, how many millimoles of N₂ gas would dissolve in 1 L of water? Assume that N₂ exerts a partial pressure of 0.987 bar. Given that Henry’s law constant for N₂ at 293 K is 76.48 kbar.

Solution: 

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p_N2 = Partial pressure of N₂, χ_N2 = Mole fraction of N₂ in water, K_H = Henry’s law constant, C = Solubility of Nitrogen in water, n = Moles of N₂

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References:

(1)    Wikipedia Contributors. Henry’s law. Wikipedia. https://en.wikipedia.org/wiki/Henry%27s_law.

(2)    Ncert. Chemistry : Textbook for Class XII - Part.I; National Council Of Educational Research And Training: New Delhi.

‌‌(3)    Henry's Law