![]() ![]() This results in equimolar solution of sodium hydrogen phosphate and sodium dihydrogen phosphate. You can calculate pH of such a buffer using pH calculator - select phosphoric acid and sodium hydroxide from the databases and enter 0.05M as concentration of phosphoric acid and 0.075M as concentration of NaOH. What error are we making neglecting ionic strength of the solution? Let's see what will happen if we prepare 0.05M phosphoric buffer pH 7.2 neglecting - and not neglecting - ionic strength of the solution. Mass and charge balances should use analytical concentrations of ions. In all reaction quotients used throughout all sections we should replace concentrations of all ions with their activities. There are no extensive tables of these coefficients, so their use is rather limited. There are other theories, that work for higher ionic strengths, but they are based on experimentally determined coefficients that depend on types of ions present in the solution. Where f z denotes the activity coefficient for z-charged ions.Įquilibrium calculations made using this approach give good results for ionic strength lower than 0.1. Most popular method used to calculate ions activities is the one proposed by Debye and Hückel in 1923.įirst step in calculations is calculation of so called ionic strength, using the following formula: It is enough to add an inert salt to the solution of a known acid to observe pH change that confirms activity concept (and is in accordance with the results of calculations presented below). In fact whenever you put pH electrode into a solution you are measuring not but activity of H ions. Activities are not a theoretical construct - they can be measured for every solution. To be precise in our equilibrium calculations instead of using concentrations we should use ions activities. Whole phenomenon - although investigated for over 100 years - is still not fully understood and described. These interactions influence ions behavior and don't allow to treat every ion in the solution independently. Ions are charged so they interact in the solution attracting and repelling each other with coulomb forces. The cause of this effect is less efficient stacking of ions within the lattice, resulting in more empty space.The ionic strength and activity coefficients definitionsĪs it was already signaled in the introduction, all equilibrium calculations done using concentrations are wrong. Note, that while the increase in r r − r^ r^- r r − in the electronic repulsion term actually increases the lattice energy, the other r r − r^ r^- r r − has a much greater effect on the overall equation, and so the lattice energy decreases. As elements further down the period table have larger atomic radii due to an increasing number of filled electronic orbitals (if you need to dust your atomic models, head to our quantum numbers calculator), the factor r r − r^ r^- r r − increases, which lowers the overall lattice energy. The other trend that can be observed is that, as you move down a group in the periodic table, the lattice energy decreases. ![]() ![]() For example, we can find the lattice energy of $$\text 3430 kJ / mol. This kind of construction is known as a Born-Haber cycle. If we then add together all of the various enthalpies (if you don't remember the concept, visit our enthalpy calculator), the result must be the energy gap between the lattice and the ions. So, how to calculate lattice energy experimentally, then? The trick is to chart a path through the different states of the compound and its constituent elements, starting at the lattice and ending at the gaseous ions. These additional reactions change the total energy in the system, making finding what is the lattice energy directly difficult. This is because ions are generally unstable, and so when they inevitably collide as they diffuse (which will happen quite a lot considering there are over 600 sextillion atoms in just one mole of substance - as you can discover with our Avogadro's number calculator) they are going to react to form more stable products. While you will end up with all of the lattice's constituent atoms in a gaseous state, they are unlikely to still be in the same form as they were in the lattice. After this, the amount of energy you put in should be the lattice energy, right? Experimental methods and the Born-Haber cycleĪs one might expect, the best way of finding the energy of a lattice is to take an amount of the substance, seal it in an insulated vessel (to prevent energy exchange with the surroundings), and then heat the vessel until all of the substance is gas. You can calculate the last four using this lattice energy calculator. We will discuss one briefly, and we will explain the remaining four, which are all slight variations on each other, in more detail. Perhaps surprisingly, there are several ways of finding the lattice energy of a compound. ![]()
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