When gases dissolve into liquids we have a slightly different situation from the dissolution of a solid or a liquid into another liquid. The biggest issue is the concentration of the "pure" solute. In the case of the solid or a liquid the pure substance is the pure substance. The "molecules" are all next to each other and the concentration is the same at all conditions. For a gas, the "pure" substance has a concentration that is extremely dependent on the conditions. Thus the most important factor for a gas dissolving into a liquid is the concentration of the gas above the liquid. In chemistry we express concentrations of gases as partial pressure. The solubility of gas depends on the partial pressure of the gas above the solvent.
The solubility of a gas in the liquid is quantified using Henry’s Law. Henry’s Law states that the mole fraction of gas dissolved in the liquid (like the concentration) is directly proportional to the pressure of the gas over the liquid.
\[P_{\rm gas} = K X_{\rm gas}\]
The constant K depends on the IMFs between the solute and the solvent and thus it depends on both the chemical structure of the gas and the liquid. Xgas is the mole fraction which is the (moles of gas)/(total number of moles of the mixture).
Henry's Law is sometimes given with different units (but it is exactly the same otherwise). You may find it written as
\[C_{\rm gas} = k_{\rm H} \; P_{\rm gas} \]
Here the Henry's Law constant has units of M/atm. It might also be written as above, but with molarity instead of mole fraction. You might also find it given as the 2nd equation but with mole fraction instead of molarity. Or any number of other ways! Watch the units. (and note that mole fraction has no units).
The consequences of Henry's Law are fairly straight forward. Double the pressure. Double the concentration (mole fraction).
Gases dissolved in liquids seems a bit of a random topic, but in fact Henry’s Law shows up in every day life. Have you ever wondered how they get all the CO2 into carbonated beverages? They apply a big pressure of CO2 above the liquid and the CO2 dissolves. When the pressure goes away (the pssst when you open the can), the amount of CO2 dissolved decreases and bubbles appear.
Also, if you are a scuba diver, you know you do not come up from great depths too quickly. This is because when your body is at higher pressure, N2 dissolves into your blood and tissue. Should you come up to the surface too quickly the pressure drops and, just like the soda can, bubbles form. N2 bubbles in your body can be very painful. Worse, bubbles in your brain tissue and spinal cord are very bad for your health.
Finally, Henry’s law is important for fish (and marine life in general). Fish, if you didn’t know, manage to get O2 out of the water to live. As the earth’s atmosphere has a partial pressure of oxygen of around 0.18 atm there is always some O2 dissolved in water (rivers, lakes, oceans, the glass of water you are drinking,…) However, as we will discuss later the temperature dependence of solubility depends on the enthalpy. The fact that dissolution of gases is exothermic means that their solubility decreases with increasing temperature. Thus rising ocean temperatures mean lower dissolved O2 levels. This is turn leads to tough times for marine life.
Note: This is a very easy (if a bit boring) experiment to do at home. Put a pan of water on the stove and heat it up. What happens? Way before the solution begins to boil, little bubbles form on the bottom of the pan. Why? This is the dissolved air coming out of the water. As you raise the temperature the solubility drops and the gas comes out. (Note: The bubbles tend to form in the same place. This is because the surface tension of water makes the bubble formation slow. So the bubbles will form at little defects or scratches in the bottom of your pan.) Alternatively (and more amusing) open a very cold can of soda and a very warm can of soda and notice the difference in the solubility of the CO2 in the two situations.
Other differences for gases dissolving into liquids. For a gas dissolving in a liquid the entropy of solution is negative, \(\Delta S _{\rm solution} < 0\). The solute is in the gas phase which is the highest entropy state. So even though we are making a mixture, the entropy will be going down. A solution will form only if \(\Delta G _{\rm solution} < 0\). However, now the entropy term is causing the free energy to increase. The only way that we can a have a decrease in the free energy is if the solution process is exothermic. This is in fact the gas for gas dissolution. The reason is a key difference for the enthlapy of gases compared to other solutes. For gases we don’t have to overcome any intermolecular forces in pulling the solute molecules away from each other. They are in the gas phase and already apart. Thus \(\Delta H _{\rm solution} = \Delta H_{\rm solvation}\) since the lattice-energy term is zero (because it is a gas with no IMFs). Since the solvation term is negative, we find that \(\Delta H_{\rm solution} < 0\). A solution will form to a small extent thanks to the enthalpy term being exothermic.
Henry's Law© 2013 mccord/vandenbout/labrake