I am trying to figure out how to calculate the total amount of silver in all oceans and seas.

From what I am looking up it varies for a variety of reasons

The average concentration of silver in the surface sea-water around Monaco was found to be 0.14Mgrg Ag/l. It was also concluded that observed variations of silver content in seawater were not related to the fresh water run-off from the neighboring coast. This suggests that the variations have to be attributed to some other factor or a combination of factors.
On the basis of the observed values of the silver content of the Var River water, an upper limit of silver supply by fresh waters into the sea-area around Monaco is estimated to be 2.3Mgrg Ag per liter of fresh water. Considering the mixing of the fresh water with sea-water, an increase of up to 0.09Mgrg Ag/l in the sea-water might be expected. The fact that the increase of silver in the sea-water was not observed in connection with the fresh-water mixing suggests that some effective removal process of silver may be in operation at the immediate vicinity of the injection of fresh-water into the sea.
SpringerLink - Journal Article


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Periodic Table of the Elements for Seawater(JavaScript)