How to Calculate Ka1
Calculating the first dissociation constant (Ka1) requires several steps. Concept applicability must be established---Ka1 makes sense only with polyprotic (multiple-hydrogen) acids. Once the polyprotic acid is identified, consider the general Ka1 formula: Ka1 = [H+][HA-]/[H2A]. Detail and interpretation of this formula needs to be taken into account when deciding calculation reliability--what if [H2A]=0, for instance? As with scientific calculations in general, significant digits and error must be taken into account when reporting calculation results.
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Instructions
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Look at an example. Let's say a certain acid has a concentration of 1 mole/liter in solution. The denominator is [H2A] = 1 in this case. Furthermore, let's say that it dissociates into only [H+] and [HA-], therefore [H+]*[HA-].
At this point, our equation is: Ka1 = [H+]*[HA-]/1, or just Ka1 = [H+]*[HA-]. If H+ concentration is measured to be 0.0002 mol/liter at that point, then [H+]=[HA-]= 0.0002.
Therefore, Ka1 = (0.0002)*(0.0002)/1 = 4(10^-8).
Ka1 calculations are done in such fashion. Conceptually, they require knowing multiplying/dividing, and in case of very small numbers such as in this example, dealing with scientific notation and exponents.
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Establish the precise acid for which you want to find the first dissociation constant (Ka1). Prior to calculating an acid's Ka1 value, it makes sense to experimentally verify that its acidic effects (H+, HA-, and H2A concentrations) can be measured without excruciating cost, safety risk or error. Make sure that H+ contribution for that acid is measurable and distinguishable from any other acidic compounds and the background "noise" from all instrumentation. Label that acid as the H2A compound, with H+ and HA- being the corresponding dissociated forms of that acid.
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Determine the Ka1 numerator. The numerator (top part of the Ka1 ratio) contains a product of concentrations---hydrogen (H+) concentration multiplied by acid (HA-) concentration.
A note on notation: the "HA-" refers to a general molecular "core"---the "A"---and at least one other hydrogen atom. There must be one or more hydrogen atoms attached to the remaining acid. If not---if the acid is "A-"---then it is not polyprotic. Ka1 becomes meaningless since there is no Ka2 that corresponds to at least one other hydrogen that can be dissociated. This numerator is divided by a concentration of acid that is not dissociated (H2A).
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Plan measurement and detection schemes. To find the first dissociation constant (Ka1), all [H+], [HA-] and [H2A] values have to be known. A good first step is to use pH at a certain point in a titration. Knowing pH is useful, since pH = -log[H+]. Therefore, having the pH value gives [H+] through the relation [H+] =10^(-pH).
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Account for measurement limits. If the required concentrations are measured to, for instance, three decimal places, it makes no sense to report Ka1 calculation results to five or six decimal places. Recall that the calculation isn't "pure mathematics," and has to relate back to the real world. Therefore, significant digits and measurement error must be taken into account when reporting Ka1.
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Tips & Warnings
Consider formula limitations. Ka1 can't correspond to a strong-acid dissociation. If there's virtually no acid that is dissolved but not dissociated, the denominator becomes zero. Values divided by zero give nonsensical physical interpretations. There's little meaning in an infinite Ka1 dissociation constant. Similarly, H+ or HA- concentration measurements can be prone to large errors or are simply too low to be picked up by available techniques and instruments. In that case, once again, a Ka1 calculation cannot be performed.
On notation: When in brackets, the concentration of the bracketed substance is indicated. The [H+] refers to hydrogen ion concentration. Generally, [X] refers to concentration of X in aqueous (water-based) solution.
Measuring acid (and base) concentrations requires handling potentially dangerous substances.
Follow proper lab procedure, use safety gear, be aware of your surroundings (tight spaces, other people you could bump into, etc.), and feel free to ask an authority or supervisor if questions about lab work arise.
Ka2 (and Ka3, if applicable) can be calculated in a similar manner to Ka1. Generally, Ka1 will be much larger (several orders of magnitude) than Ka2, which would in turn be similarly larger than Ka3. If Ka1 and Ka2 values are close---within the same power of 10---it is likely there was an error and at least one of the Ka values is incorrect.
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