Mike,
I'm not a chemist, so I may not be able to explain it in a technically accurate way. When you dissolve something in a solvent, chemical bonds in the substance to be dissolved have to be broken to form ions, and the bonds of the solvent are disrupted to hold the ions in solution.
Every substance has a solubility limit - only so much of it can be dissolved in a given amount of the solvent. So if you put a little sugar in some water, it dissolves. If you keep adding sugar, you'll reach a point where no more will dissolve and the excess will simply drop to the bottom. But if you add more water, more sugar will dissolve.
HNO3 is more soluble in water than AgNO3. At 20°C. (68°F.), a liter of water can hold about 2,200 grams of AgNO3. The molecular weight of AgNO3 is 169.874 grams per mole. Dividing 2,200 grams by 169.874 shows us that about 12.95 moles of AgNO3 can dissolve in 1 liter of water.
Concentrated nitric acid (68 - 70%) is about 15.8 molar, meaning there are 15.8 moles of HNO3 dissolved in each liter of acid. Note that is 15.8 moles of HNO3 per liter of acid, not per liter of water. Concentrated nitric acid has a density of about 1.42, so 1 liter of acid weighs about 1,420 grams. We know that there are 15.8 moles of HNO3 in that weight. Each mole of HNO3 weighs 68.012 grams, so 15.8 moles times 68.012 grams per mole means we have 1,074.59 grams of HNO3 in that liter of acid. That leaves about 345 grams of water (1,420 grams per liter of acid - 1,074.59 grams of HNO3) in the liter of acid. Since the density of water is 1.00, we find we only have about 345 ml. of water in each liter of concentrated acid.
So if we try to dissolve our silver into concentrated HNO3, we can only get about 4.47 moles of silver to dissolve in the 345 ml. of water in each liter of acid, leaving excess, unused HNO3 still in the solution. Diluting the acid with water provides a greater volume of water into which the silver can dissolve. A 50/50 mix of 1 liter of concentrated HNO3 and 1 liter of water will give us 1.345 liters of water containing 15.8 moles of HNO3. 1.345 liters of water can hold 17.42 moles of AgNO3. The 50/50 ratio allows us to completely consume the HNO3 with a little excess water left.
I know that's a long explanation, but you did ask. :lol: I hope it makes sense.
Adding your acid in small increments will help to avoid those boil overs, but you are right in using a vessel with plenty of extra room as well.
Dave