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The Nernst equation is a fundamental relationship between the concentration of certain substances in solution and the thermodynamic equilibrium constant for that substance. It can be found in any chemistry textbook, but the equation often gets tossed out for unknown quantities. I am taking a break from my full-length lecture on Nernst and am going to try to explain it here.
The Nernst equation shows that for certain substances, such as oxygen, water, and ammonia, the relationship between the concentration of the substance and the equilibrium constant is non-linear, depending on the temperature of the solution. The equation is based on the idea that the equilibrium constant is a function of the temperature and therefore the concentration of the substance in the solution.
As you can see in the above diagram, the equilibrium constant is a quantity that can be determined from experiments, but it is not, in general, a constant. One of the things that has to be considered when calculating the equilibrium constant is that the equilibrium constant may change as the temperature of the solution changes. This is illustrated by the fact that the equation for the equation for oxygen is shown above for temperatures of 25, 30, and 35°C.
We can’t really use the equilibrium constant as a constant since it can change depending on the temperature and the solution. The equilibrium constant is a property that depends on the solution, and as such its value may change with time, depending on temperature and other conditions. We have made the observation above that the equilibrium constant for oxygen is not constant, and that it has a minimum value. This minimum value is called the critical solution temperature, or Tcr.
Tcr is a function of the solution and the solution’s pressure. The pressure is the pressure of the gas (air or oxygen) that keeps the temperature constant over time. At any time, the pressure is less than the critical solution temperature.
The Tcr is the temperature at which the oxygen concentration equals the saturation concentration. This is the oxygen concentration at which water vapor is completely dissolved in the gas. This is called equilibrium. If the oxygen concentration increases, there is a decrease in the saturation concentration. This is called dilution. The Tcr is calculated as the solution temperature divided by the saturation concentration.
The Tcr is a function of pressure and density. So the more pressure and density, the lower the Tcr. The exact value depends on the molecule size, but in general it’s about 0.85-1.05 atmospheres. This is called the critical or absolute pressure. For the equation to work, it must have a slope of one.
If you have a temperature and pressure, and you make a solution, and you have a liquid, and it doesn’t have a slope of one, it’s at a constant temperature. It’s like a constant temperature bath. You can’t have a bath with 0.85 atmosphere of water, because at 0.85 atmosphere you would have a slope of 0.85. So you can’t have a bath made of a liquid with 0.85 atmospheres of oxygen.
When we made this derivation we looked at the same equation for the atmosphere, but with a liquid instead of a gas. It turns out that the slope really is the same. So if you’re making a liquid that has 0.85 atmospheres of air in it, you’re making a bath that has 0.85 atmospheres of air. So if you’re making a liquid that has 0.85 atmospheres of air in it, you’re making a bath that has 0.
That’s the theory behind the Nernst law of the concentration of substances in an enclosed space. The Nernst law states that if there are two concentrations of a substance in an enclosed space, the amount of one, divided by the other, will determine the concentration of that substance. To give you an idea, here’s a bath that has 0 atmospheres of oxygen (which is the same as 0.85 atmospheres of air), with 0 atmospheres of water, and 0.