Answer:
1105.7kg of limestone must be added
Step-by-step explanation:
A solution is neutralized when pH = 7.0. That is [H+] = 1x10⁻⁷M.
The initial [H+] is 10^-5.3 = 5.01x10⁻⁶M.
That means we need to neutralize:
5.01x10⁻⁶M - 1x10⁻⁷M = 4.91x10⁻⁶M
The moles of H+ in 4.5 billion liters = 4.5x10⁹L are:
4.91x10⁻⁶M * (4.5x10⁹L) = 22095 moles of H+
That reacts with limestone (CaCO3), as follows:
2H+ + CaCO3 → H2O + CO2 + Ca²⁺
Moles of limestone needed to neutralize the lake are:
22095 moles of H⁺ * (1 mole Limestone / 2 moles H⁺) = 11047.5 moles of limestone.
Molar mass of limestone is 100.09g/mol. Mass of limestone we need to add are:
11047.5 moles of limestone * (100.09g / mol) = 1.106x10⁶g of limestone. In kg:
1.106x10⁶g of limestone * (1kg / 1000g) =
1105.7kg of limestone must be added