How long since the oceans were fresh-water?

[Ian]

This may seem odd but I see the oceans as a collective 'sump' that is gradually becoming more saline.
The salt and other minerals in the oceans must have been dissolved into the oceans as a result of the perpetual rainfall cycle of evaporation and precipitation and emptying into the seas through the earth's rivers.
If that could be said to be the case, how far back can we extrapolate until the seas were fresh?
There must be some measure of the amount of solvents entering the oceans through the rivers, so given the present state of the seas we ought to be able to calculate/estimate how long it has taken to reach the present concentrations.
also, how long before the sea dies of salt?

[Bystander]

You have assumed a unidirectional transport of solutes. Fluxes from land to sea and from sea to land are both fairly well known (give or take a factor of two or three). Sodium chloride as an example has a residence time of 70 Ma (this is a thirty year old number, and may have changed a bit); that means that the quantity of salt in the oceans is "increasing" by some rate that is approximately equal to the rate at which it is aerosolized for aeolian transport to land, trapped in salt pans/evaporite deposits (Dead Sea, Great Rift area, Death Valley, Lake Bonneville, etc.), and those rates are of a magnitude that integrated over the residence time, there is a total exchange of the salt in the oceans.

[HallsofIvy]

In the 19th century this was used to "prove" that the earth is not millions of years old: that the seas would have to be much saltier if it were. The flaw in the reasoning is that the salt in the water is in equilibrium with salt in the soil at the bottom of the sea. More salt coming into the sea causes salt to be dropped out of solution into the soil so that the 'saltiness' of the sea remains constant.

[Andre]

It seems AFAIK that the salinity of all body fluids of the majority of creatures (including salt water fish, fresh water fish and mammals) is roughly the same. The natural salinity. I couldn't find numbers but some biologist could help us out here. It is assumed that this resembled the salinity of the oceans during some stage in the evolution some millions to a billion of years ago, to prevent adverse effects of osmosis (http://www.tvdsb.on.ca/westmin/science/sbi3a1/Cells/Osmosis.htm). Not an unreasonable idea.