Why is the hydrolysis of ATP to AMP more energetic than the hydrolysis of ATP to ADP? I am confused as to why the hydrolysis of ATP to AMP and pyrophosphate is more energetic than hydrolysis to ADP and inorganic phosphate, especially since pyrophosphates are more unstable than inorganic phosphates.
My only guess was that the pyrophosphate undergoes further hydrolysis to inorganic phosphates due to its instability and this drives the reaction forward via Le Chatelier's principle, but I think my logic is flawed. I would like to know the factors which cause this difference of -2.6 kcal/mol between the two reactions.
Dr. Larry Moran (Professor Emeritus in the Department of Biochemistry at the University of Toronto) has posted an nice article about the Free Energy of ATP Hydrolysis. Accordingly, some important concepts in biochemistry may be widely misunderstood and/or not well described in most textbooks. One of them is the free energy of ATP hydrolysis:

The traditional standard Gibbs free energy changes do not apply in biochemical system because there are $\ce{Mg^2+}$ ions, ionic strength, and $\mathrm{pH}$ involve in the transformation. The traditional standard Gibbs free energy changes are at $\pu{25 ^\circ C}$ $(\pu{298 K})$ and $\mathrm{pH} \ 7$. For reactions like ATP hydrolysis, we want a new &quot;standard&quot; that includes free $\ce{Mg^2+}$ ion concentration of $\pu{10^{-3} M}$ and an ionic strength $(I)$ of $\pu{0.25 M}$ (Ref.1).
The transformed Gibbs energy (denoted as $G'$) is defined by the following Legendre transform of the Gibbs energy $G$:
$$G' = G - n'(\ce{H+})\mu(\ce{H+}) - n'(\ce{Mg^2+})\mu(\ce{Mg^2+}) \tag1$$
where $\mu(\ce{H+})$ and $\mu(\ce{Mg^2+})$ are the specified chemical potential of $\ce{H+}$ and  $\ce{Mg^2+}$ at equilibrium, respectively, and $n'(\ce{H+})$ and $n'(\ce{Mg^2+})$ are the total amount of these ions (free and bound) in the system. Accordingly, following are the calculated new values for specific reactions:
$$
\begin{array}{l|c}
\text{Biochemical reaction} &amp; \Delta G'_\text{hydrolysis} \ (\pu{kJ mol-1})  \\
\hline
\ce{ATP + H2O -&gt; ADP + P_$i$ + H+} &amp; -32  \\
\ce{ATP + H2O -&gt; AMP + PP_$i$ + H+} &amp; -45  \\
\ce{AMP + H2O -&gt; Adinosine + P_$i$ + H+} &amp; -13  \\
\ce{PP_$i$ + H2O -&gt; 2P_$i$} &amp; -29  \\
\hline
\end{array}
$$

References:

Robert A. Alberty, Robert N. Goldberg, “Standard thermodynamic formation properties for the adenosine 5'-triphosphate series,” Biochemistry 1992, 31(43), 10610–10615 (https://doi.org/10.1021/bi00158a025).