Mercury(I) chloride, Hg2Cl2, has a reported Ksp of (1.3±0.2)×10−18 at 25 °C (uncertainty represents one standard deviation).
A chemist wishes to estimate, with propagated uncertainty, how much the solubility of Hg2Cl2 decreases when it is equilibrated with 0.0350M NaCl, assuming volumes remain constant and activity coefficients are unity.
Treat the quoted uncertainty in Ksp as the dominant source of error; uncertainties in measured concentrations are negligible by comparison.
(a) Derive an expression for the molar solubility of Hg2Cl2 in a sodium chloride solution of known chloride ion concentration CCl.
(b) Using the central value of Ksp, calculate the molar solubility in (i) pure water and (ii) 0.0350M NaCl.
(c) Compute the percent decrease in solubility produced by the added chloride ion.
(d) Propagate the uncertainty in Ksp through your calculations in part (b) to determine the uncertainty range (\pm) in the percent decrease obtained in part (c). State the final result with an appropriate number of significant figures and an accompanying uncertainty.
(e) Discuss briefly how a 5 % systematic error in the chloride concentration would influence the final percent-decrease value relative to the uncertainty you reported in part (d).