In a fully charged lead acid battery from your old pickup truck, with good lead plates (electrodes), the electrolyte is around 38% H2SO4 and around 62% H2Oper cell, the acidic electrolyte at this concentration of acid the specific gravity will be about 1.28 for each of the (2-volt cell) of the battery of cells.
As the battery discharges under a load the specific gravity of the acid as well as the concentration of acid changes to water as the cell discharge water from the original electrolyte and water from the chemical reactions involved.
on the discharge of the cell (9cells in a 12volt), the electrode anodes of the pure spongy lead in the cell are converted to lead sulfate, and the cathode electrodes of lead peroxide PbO2 also convert into lead sulfate lowering acid concentration and specific gravity of the solution more towards the specific gravity of water alone.
As the cell is charged the specific gravity raises back to around 1.28
0r 37%H2SO4 62% H2O for that volume of electrolyte.
a cell fully charged will have a specific gravity of about 1.28
a cell with a 70% charge will have a specific gravity of about 1.22
a cell with a 50% charge will have a specific gravity of about 1.17
a cell with a 30% charge will have a specific gravity of about 1.12
a cell with a 10% charge will have a specific gravity of about 1.07
a totally dead cell electrolyte will just be water sp. gr. 1.00
a bad cell can develop a hard sulfate, or plates can sort out, or break lowering the sp. gr. and that cell's ability to charge, this cell will have a different specific gravity from the other 5 cells in the battery.
so even most "Dead batteries may still have a good portion of the dilute acid if those cells will still hold an electric charge at the electrodes.
So charging the old battery before recovering any acid, the better the condition of the cell the more charged the more acid in volume and concentration you could recover.
Evaporation can be used to concentrate the acidic water up to its azeotrope of 98% concentration by evaporating off water from the much less volatile sulfuric acid.