For which of the following mixtures will Ag2SO4(s) precipitate?

• A. Mixing 0.10 M AgNO3 and 0.10 M Na2SO4
• B. Mixing 0.01 M AgNO3 and 0.01 M Na2SO4
• C. Mixing 0.001 M AgNO3 and 0.001 M Na2SO4
• D. Mixing 0.10 M NaNO3 and 0.10 M Na2SO4

Answer: (A)

Verified step by step guidance

1. Identify the solubility product constant (Ksp) for silver sulfate, Ag\_2SO\_4. This value is essential to determine whether precipitation occurs when solutions are mixed.
2. Write the dissociation equation for Ag\_2SO\_4: \[Ag_2SO_4 (s) \rightleftharpoons 2Ag^+ (aq) + SO_4^{2-} (aq)\]
3. Express the ion product (Q) for the mixture in terms of the concentrations of Ag\^+ and SO\_4^{2-}: \[Q = [Ag^+]^2 [SO_4^{2-}]\]
4. Calculate Q for each mixture by substituting the given concentrations of AgNO\_3 and Na\_2SO\_4, remembering that AgNO\_3 provides Ag\^+ ions and Na\_2SO\_4 provides SO\_4^{2-} ions. For example, if the concentration of AgNO\_3 is C, then [Ag\^+] = C, and if the concentration of Na\_2SO\_4 is C, then [SO\_4^{2-}] = C.
5. Compare the calculated Q values to the Ksp of Ag\_2SO\_4. If Q > Ksp, precipitation of Ag\_2SO\_4 will occur; if Q < Ksp, no precipitation occurs. Identify which mixtures satisfy Q > Ksp.