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Lead can undergo the following reactions when cold and hard water passes over it: $$\ce{Pb^2+ + 2Cl- -> PbCl2}$$ $$\ce{Pb^2+ + SO4- -> PbSO4}$$

All these salts are sparingly soluble in water and have a tendency to stick to lead, rendering it passive and not allowing plumbosolvency to occur: $$\ce{2Pb + 2H2O + O2 -> 2Pb(OH)2}$$

My question is:

How did lead dissolve in the water flowing through the aqueducts if most of it's salts are sparingly soluble?

I have considered erosion of the salt layer formed on the surface but according to Wikipedia, the aqueducts had a very gentle slope

Vitruvius recommends a low gradient of not less than 1 in 4800 for the channel, presumably to prevent damage to the structure through erosion and water pressure. This value agrees well with the measured gradients of surviving masonry aqueducts. The gradient of the Pont du Gard is only 34 cm per km, descending only 17 m vertically in its entire length of 50 km (31 mi):

Wikipedia also has the following to say regarding lead concentration in the water:

Where lead pipes were used, a continuous water-flow and the inevitable deposition of water-borne minerals within the pipes somewhat reduced the water's contamination by soluble lead. Nevertheless, the level of lead in this water was 100 times higher than in local spring waters.

Any insights would be much appreciated!

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Let me give an extreme example of chemical analysis. It is an anecdote. Some analytical chemists were using a very sensitive technique to analyze metals in blood. It is called neutron activation analysis. What they saw was that a very small quantity of molybdenum (Mo) was present in small quantities persistently. Nobody expected that. It turned out after a lot of hard work that Mo was coming from the stainless steel syringe needle used for drawing blood. Lesson of the story: There is nothing which is perfectly insoluble in water. It all depends on the analytical technique. If you try to weigh a hair on a "weighing machine" it will tell you that the mass is zero kg, but if you use a fine analytical balance it will tell you that hair has a mass.

The same goes for lead pipes. Natural water has plenty of minerals, dissolved oxygen anions, cations and don't forget the microorganisms. The bacteria do a lot of chemical transformations in water. As a result, Pb would slowly leach into the water at parts per million or parts per billion levels. Don't assume that Romans were drinking lead salt solutions in high concentration ranges. Not only water lead was present in water, it was also present in alcoholic beverages.

Read more here Lead in ancient Rome’s city waters

Lead in water is still a serious problem in several areas of the modern world. It is not an ancient problem.

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    $\begingroup$ More anecdote :Admiralty brass ( 70 Cu, 29 Zn, 1 Sn ) is commonly used for heat exchanger tubes in many different waters. Usually a trace of arsenic is added to stop zinc from being removed by the water ( dezincification ). $\endgroup$ – blacksmith37 Nov 23 '19 at 16:38

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