One anecdote ... Serving on a university-wide committee, I found that in one field (I think zoology?) the norm is having the advisor as co-author; and when the advisor does not appear as co-author it is taken as a sign that the advisor has a low opinion of the thesis.  

During my career, there are only two Ph.D. theses that were published with me as co-author.   

One case (Yuri Dimitrov):  After the degree was completed, the thesis had to be abridged for publication.  Dr Dimitrov would come to my office once or twice a week and show me his progress (much as he had done before the degree was completed).  In the end he suggested joint authorship for the paper.  Subsequently, we wrote another joint paper extending the work.

Another case (Jeff Golds):  This guy, upon completion of his degree, was raring to begin his career in the software industry.  It was clear he would never publish the work, but I thought it deserved publication.  So I wrote it up for publication, and it appeared as a joint paper.

When should a supervisor be a co-author?
I am trying to understand this problem and its corresponding solution (complete solution not shown)





First off, from the above one can see that the equilibrium constants when $\ce{H2ASO4-}$ donates and receives a proton are as follows:
\begin{aligned}
\ce{H2AsO4 &amp;&lt;=&gt; HAsO4^{2-} + H+} &amp; K_2 &amp;= 1.1 \cdot 10^{−7}\\
\ce{H2AsO4- + H+ &amp;&lt;=&gt; H3AsO4}    &amp; K_{-1} &amp;= 1.6 \cdot 10^{2}\\
\end{aligned}

However, if this is an amphoteric substance as the solution claims, shouldn't both $K_a$ values be comparable? It seems logical that if it is able to act as both an acid and a base, the equilibrium constants should at least be similar to each other. Instead, one is several order of magnitudes larger than the other? Why can this be true and $\ce{H2ASO4-}$ still be an amphoteric substance?



Next, how did they arrive at the statement


  We approximately have the equality relation: $$\ce{[H3AsO4]} = \ce{[HAsO4^{2−}]}$$


What is the evidence that shows this to be true? Isn't the $K_a$ value of the basic reaction ($1.6 \times 10^2$) much larger than that of the acidic reaction? Why should the concentrations be equal?



Finally, let's say you are calculating the pH for the diprotic substance $\ce{H2S}$, which undergoes the following diassociations:

$$\ce{H2S &lt;=&gt; H+ + HS-}$$
$$\ce{HS- &lt;=&gt; H+ + S^{2-}}$$

To find the pH you would assume that the first reaction is dominant, and that the effects of the second reaction consuming $\ce{HS-}$ are minimal, and then calculate the pH from there — right? 

However, why can't you treat $\ce{HS-}$ as an amphoteric substance (because it can both gain and lose a proton) and then calculate the pH as you would for an amphoteric substance (as seen in the image at the beginning)?
