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A solution is saturated with Ag_{2}SO_{4}. (a) Calculate [Ag^{+}] in this saturated solution. (b) What mass of Na_{2}SO_{4} must be added to 0.500 L of the solution to decrease [Ag^{+}] to 4.0×10^{–3} M.
(a)








Initial 



Change 



Equilibrium 


1.4×10^{–5} = [2x]^{2}[x] = 4x^{3}
x = 0.015 M = silver sulfate concentration in a saturated solution.
[Ag^{+}] = 2x = 2(0.015) = 0.030 M.
(b)








Initial 



Change 



Equilibrium 


(Note: even though the initial concentration of silver ion is not known, the equilibrium concentration is given in the problem so a solution can be obtained.)
1.4×10^{–5} = [4.0×10^{–3}]^{2}[x]
x = 0.88 M = the concentration of sulfate required to reduce the silver ion concentration to the desired level.
The number of moles required in 0.500 L = (0.88 mol/L)(0.500 L) = 0.44 mol
The molar mass of Na_{2}SO_{4} = 2(23.0) + 32.1 + 4(16.0) = 142.1 g/mol.
The number of grams required = (0.44 mol)(142.1 g/mol) = 63 g.