Silver nitrate solution is often used to test for chloride ions

CHEMISTRY · Multi-part · A Level · Chemistry · Reactions of ions in aqueous solution · Reactions of ions in aqueous solution

Problem

Silver nitrate solution is often used to test for chloride ions. A student has

100.0\,\text{mL}

0.0100\,\text{M}

AgNO_{3}

25\,\text{°C}

. Chloride ions will be introduced by adding a

0.200\,\text{M}

NaCl(\text{aq})

solution. The student wishes to know the minimum volume of the

NaCl

solution that must be added before solid

AgCl

begins to precipitate.

K_{sp}[\text{AgCl}] = 1.8\times10^{-10}

25\,\text{°C}

. Assume volumes are additive. (a) Write the equilibrium dissolution equation for

AgCl(\text{s})

and the corresponding

K_{sp}

expression. (b) Let

V

be the volume (in

\text{mL}

) of

0.200\,\text{M}

NaCl

added. Derive expressions, in terms of

V

, for the molar concentrations of

Ag^{+}

and

Cl^{-}

in the mixture just after mixing but before any precipitation occurs. (c) Using your expressions from part (b), set up an inequality that determines the smallest

V

for which a precipitate of

AgCl

will form. Show all algebraic steps leading to

V

. (d) Calculate the minimum whole-number volume (to the nearest

0.1\,\text{mL}

) of the

NaCl

solution that must be added to initiate precipitation of

AgCl

, and explain why adding any smaller volume would not produce a solid.

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