Why does mercury in dilute HNO3 give mercurous nitrate while hot concentrated HNO3 produces mercuric nitrate?
“Mercury dissolves in oxidizing acids, producing either Hg${^{2+}}$ or Hg$_2$$^{2+}$, depending on which reagent (mercury or e.g., nitric acid) is in excess.” Ref 1
Wikipedia says
“Mercuric nitrate can be reacted with elemental mercury to form mercurous nitrate…(and)…If the solution is boiled or exposed to light, mercury(I) nitrate undergoes a disproportionation reaction yielding elemental mercury and mercury(II) nitrate:” Ref 2
So, dilute acid is simply acid that is insufficient to oxidize all the mercury to mercuric; excess mercury reduces mercuric to mercurous nitrate by disproportionation. The equilibrium seems labile enough. In my simplified imagination, a mercuric ion just picks up a mercury atom and brings mercury nuclei even closer together than in the metal. The $\ce{Hg-Hg}$ bond length in mercurous nitrate is 254 pm (Ref 3) and 253 pm in mercurous chloride vs 300 pm in the metal. Ref 4


Figure 1. Structure of mercurous nitrate

Figure 2. Structure of mercurous chloride
Mercury will dissolve in nitric acid because the oxidation potential of nitric acid is higher than necessary to dissolve metallic mercury. Electrochemical potentials (Ref 5) give a more quantitative picture of the possibilities (see eq 4):
eq 1: $\ce{Hg^{2+} + 2e-}$ = Hgº ..................................0.851V
eq 2: NO$^-_3$ + 3 H$^+$ + 2e- = HNO$_2$ + H$_2$O ..........0.94V
eq 3: 2 Hg${^{2+}}$ + 2e- = Hg$_2$$^{2+}$..............................0.905V
Combining equations 1 and 2 gives equation 4:
eq 4: Hgº + NO$^-_3$ + 3 H$^+$ +2e- = HNO2 + H2O + Hg${^{2+}}$ +2e- ......0.089V
The first product of dissolution of mercury will be mercuric ion. Hg${^{2+}}$ is a powerful oxidant, capable of oxidizing metallic mercury. Combine equations 1 and 3; cancel the electrons on both sides:
eq 5: 2 Hg${^{2+}}$ + Hgº + 2e- = Hg$_2$$^{2+}$ + Hg${^{2+}}$ + 2e- ............0.054V
So mercuric ion in the presence of excess mercury (or insufficient HNO3) is reduced to mercurous, but the driving forces are small. The labile reaction is well known. Excerpts from Ref 6 give equations for “excess acid” and “excess mercury”:
"eq 6: 3 Hgº + 2 NO$^-_3$ + 8 H$^+$ = 3 Hg${^{2+}}$ + 2 NO + 4 H2O (excess acid) and
eq 7: 6 Hgº + 2 NO$^-_3$ + 8 H$^+$ = 3 Hg$_2$$^{2+}$ + 2 NO + 4 H2O (excess mercury).
…the value for the potential of the reaction (Hg${^{2+}}$ + Hgº = Hg$_2$$^{2+}$) corresponds to an equilibrium concentration of Hg$_2$$^{2+}$ at 25ºC only 166 times that of Hg${^{2+}}$; hence the equilibrium is easily reversed…”(by solubility variations) “…reducing agents first reduce mercuric ion to mercurous…and…most reducing agents capable of reducing mercuric ion will, in excess, reduce the mercurous ion to mercury as a second step…”
The binuclear structure of mercurous ion is readily accepted, but it was proved meticulously, in five steps, in Ref 7. Interesting observations include that mercurous compounds are diamagnetic, ruling out Hg$^+$ with an unpaired electron. Electrical conductance of solutions of mercurous salts is consistent with a divalent mercury species. Equilibrium experiments between mercuric ion and mercury metal yield a constant only when the mercurous product is dimeric. The reference also mentions the different oxidations of mercury metal due to excess or deficiency of either reagent. But of course, X-ray diffraction is a clincher.
Interestingly, the ground state electronic configuration of neutral mercury is [Xe].4f14.5d10.6s2 Ref 8. The f electrons are supposed to be poor shielders, so the ionization potential of mercury is a little over a volt higher than might be expected. Whatever is going on (like resonance) appears to make metal-metal bonding very attractive.
Ref1:https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Qualitative_Analysis/Characteristic_Reactions_of_Select_Metal_Ions/Characteristic_Reactions_of_Mercury_Ions_(Hg²⁺_and_Hg₂²⁺)
Ref 2.https://en.wikipedia.org/wiki/Mercury(I)_nitrate
Ref 3.http://nopr.niscair.res.in/bitstream/123456789/11011/1/IJCA%2050A(2)%20137-140.pdf
Ref 4. https://en.wikipedia.org/wiki/Mercury(I)_chloride
Ref 5: CRC Handbook, p D134, 62 ed.
Ref 6: Reference Book of Inorganic Chemistry, W.M. Latimer and J.H. Hildebrand, 3rd ed, Macmillan Co., 1951, pp 140-141
Ref 7. Advanced Inorganic Chemistry, 2nd ed, F. A. Cotton and G. Wilkinson, Interscience /John Wiley, 1962, p611ff
Ref 8. https://www.webelements.com/mercury/