Henrys Law Example Problem

Henrys law is a gas law  formulated by the British chemist William Henry in 1803. The law states that at a constant temperature, the amount of dissolved gas in a volume of a specified liquid is directly proportional to the partial pressure of the gas in equilibrium with the liquid. In other words, the amount of dissolved gas is directly proportional to the partial pressure of its gas phase. The law contains a proportionality factor that is called Henrys law constant. This example problem demonstrates how to use Henrys law to calculate the concentration of a gas in solution under pressure. Henrys Law Problem How many grams of carbon dioxide gas is dissolved in a 1 L bottle of carbonated water if the manufacturer uses a pressure of 2.4 atm in the bottling process at 25  °C?Given: KH of CO2 in water 29.76 atm/(mol/L) at 25  °CSolutionWhen a gas is dissolved in a liquid, the concentrations will eventually reach equilibrium between the source of the gas and the solution. Henrys law shows that the concentration of a solute gas in a solution is directly proportional to the partial pressure of the gas over the solution.P KHC where:P is the partial pressure of the gas above the solution.KH is the Henrys law constant for the solution.C is the concentration of the dissolved gas in solution.C P/KHC 2.4 atm/29.76 atm/(mol/L)C 0.08 mol/LSince we have only 1 L of water, we have 0.08 mol of CO. Convert moles to grams: mass of 1 mol of CO2 12(16x2) 1232 44 g g of CO2 mol CO2 x (44 g/mol)g of CO2 8.06 x 10-2 mol x 44 g/molg of CO2 3.52 gAnswer There are 3.52 g of CO2 dissolved in a 1 L bottle of carbonated water from the manufacturer. Before a can of soda is opened, nearly all the gas above the liquid is carbon dioxide. When the container is opened, the gas escapes, lowering the partial pressure of carbon dioxide and allowing the dissolved gas to come out of solution. This is why soda is fizzy. Other Forms of Henrys Law The formula for Henrys law may be written other ways to allow for easy calculations using different units, particularly of KH. Here are some common constants for gases in water at 298 K and the applicable forms of Henrys law: Equation KH = P/C KH = C/P KH = P/x KH = Caq / Cgas units [Lsoln  · atm / molgas] [molgas / Lsoln  · atm] [atm  · molsoln / molgas] dimensionless O2 769.23 1.3 E-3 4.259 E4 3.180 E-2 H2 1282.05 7.8 E-4 7.088 E4 1.907 E-2 CO2 29.41 3.4 E-2 0.163 E4 0.8317 N2 1639.34 6.1 E-4 9.077 E4 1.492 E-2 He 2702.7 3.7 E-4 14.97 E4 9.051 E-3 Ne 2222.22 4.5 E-4 12.30 E4 1.101 E-2 Ar 714.28 1.4 E-3 3.9555 E4 3.425 E-2 CO 1052.63 9.5 E-4 5.828 E4 2.324 E-2 Where: Lsoln is liters of solution.caq is moles of gas per liter of solution.P is partial pressure of the gas above the solution, typically in atmosphere absolute pressure.xaq is mole fraction of the gas in solution, which is approximately equal to the moles of gas per moles of water.atm refers to atmospheres of absolute pressure. Applications of Henrys Law Henrys law is only an approximation that is applicable for dilute solutions. The further a system diverges from ideal solutions ( as with any gas law), the less accurate the calculation will be. In general, Henrys law works best when the solute and solvent are chemically similar to each other. Henrys law is used in practical applications. For example, it is used to determine the amount of dissolved oxygen and nitrogen in the blood of divers to help determine the risk of decompression sickness (the bends). Reference for KH Values Francis L. Smith and Allan H. Harvey (Sept. 2007), Avoid Common Pitfalls When Using Henrys Law, Chemical Engineering Progress  (CEP), pp. 33-39