Ag Pool
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how do you find the equilibrium conc. of Ag^+ in parts per billion that would exist in equilibrium with Ag?
A concentration of 10-100 parts per billion (by mass) of Ag is an effective disinfectant in swimming pools. However, if the concentration exceeds this range, the can cause adverse health effects. One way to maintain an appropriate concentration of is to add a slightly soluble salt to the pool. Calculate the equilibrium concentration of Ag in parts per billion that would exist in equilibrium with AgCl. How do you do this?
Dissolved silver chloride dissociates completely according to
AgCl(s) ↔ Ag⁺(aq) + Cl⁻(aq)
In a saturated solution the ionic concentrations in mol/k satisfy the following equilibrium condition:
Ksp = [Ag⁺]∙[Cl⁻]
with
Ksp = 1.56×10⁻¹⁰ at 25°C
In absence of other sources, all silver and chloride ions are formed by dissolved AgCl. Since Each dissolved salt molecule produces on ion each type, their equilibrium concentrations are the same.
[Cl⁻] = [Ag⁺]
Hence:
Ksp = [Ag⁺]²
=>
[Ag⁺] = √Ksp = √1.56×10⁻¹⁰ = 1.25×10⁻⁵ mol/L
Multiply this by the molar mass of the ion and you get the mass concentration. You can take the mass of elementary silver because the mass of the missing electron in the ion is negligible.
ρ(Ag⁺) = [Ag⁺]∙M(Ag)
= 1.25×10⁻⁵mol/L ∙ 107.87g/mol
= 1.27×10⁻³g/L
Then divide the mass concentration by the density of the solution and you get mass fraction, your are looking for. Since the salt concentration is quite small you can assume that solution has same density as pure water at this temperature
w(Ag⁺) = ρ(Ag⁺) / ρ
= 1.27×10⁻³g/L / 997g/L
= 1.276×10⁻⁶
= 1.276 ppm (parts per million)
= 1276 ppb (parts per billion)
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