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And when, as occasionally happens, a quadratic is unavoidable, we will show you some relatively painless ways of dealing with it.
In order to predict the p H of this solution, we must first find [H But don't panic!
As we will explain farther on, in most practical cases we can make some simplifying approximations which eliminate the need to solve a quadratic.
One can get around this by computing the quantity = c /Q.
(See any textbook on numerical computing for more on this and other metnods.) But who want's to bother with this stuff in order to solve typical chemistry problems?
If you are only armed with a simple calculator, then there is always the venerable quadratic formula that you may have learned about in high school, but if at all possible, you should avoid it: its direct use in the present context is somewhat laborious and susceptible to error.
|4ac|, one of the roots will require the subtraction of two terms whose values are very close; this can lead to considerable error when carried out by software that has finite precision.The only difference is that we must now take into account the incomplete "dissociation"of the acid.We will start with the simple case of the pure acid in water, and then go from there to the more general one in which salts of the acid are present.In fact, these two processes compete, but the former has greater effect because two species are involved.It is probably more satisfactory to avoid Le Châtelier-type arguments altogether, and regard the dilution law as an entropy effect, a consequence of the greater dispersal of thermal energy throughout the system.The very important first step is to make sure you understand the problem by writing down the equation expressing the concentrations of each species in terms of a single unknown, which we represent here by x: , you just substitute the x's into the latter, and you're off!If you feel the need to memorize stuff you don't need, it is likely that you don't really understand the material — and that should be a real worry!This raises the question: how "exact" must calculations of p H be?It turns out that the relation between p H and the nominal concentration of an acid, base, or salt (and especially arbitrary mixtures of these) can become quite complicated, requiring the solution of sets of simultaneous equations.The latter mixtures are known as buffer solutions and are extremely important in chemistry, physiology, industry and in the environment.will be smaller (often much smaller) than 1 M/L, while that of undissociated HA will be only slightly less than 1 M/L.