15.1 Precipitation and dissolution  (Page 5/17)

Precipitation of mg(oh) ₂

The first step in the preparation of magnesium metal is the precipitation of Mg(OH) ₂ from sea water by the addition of lime, Ca(OH) ₂ , a readily available inexpensive source of OH ^– ion:

The concentration of Mg ²⁺ ( aq ) in sea water is 0.0537 M . Will Mg(OH) ₂ precipitate when enough Ca(OH) ₂ is added to give a [OH ^– ] of 0.0010 M ?

Solution

This problem asks whether the reaction:

shifts to the left and forms solid Mg(OH) ₂ when [Mg ²⁺ ] = 0.0537 M and [OH ^– ] = 0.0010 M . The reaction shifts to the left if Q is greater than K _sp . Calculation of the reaction quotient under these conditions is shown here:

Because Q is greater than K _sp ( Q = 5.4 $\times$ 10 ^–8 is larger than K _sp = 8.9 $\times$ 10 ^–12 ), we can expect the reaction to shift to the left and form solid magnesium hydroxide. Mg(OH) ₂ ( s ) forms until the concentrations of magnesium ion and hydroxide ion are reduced sufficiently so that the value of Q is equal to K _sp .

Check your learning

Use the solubility product in Appendix J to determine whether CaHPO ₄ will precipitate from a solution with [Ca ²⁺ ] = 0.0001 M and $[{\text{HPO}}_4{}^{\text{2−}}]$ = 0.001 M .

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Precipitation of agcl upon mixing solutions

Does silver chloride precipitate when equal volumes of a 2.0 $\times$ 10 ^–4 - M solution of AgNO ₃ and a 2.0 $\times$ 10 ^–4 - M solution of NaCl are mixed?

(Note: The solution also contains Na ⁺ and ${\text{NO}}_3{}^{\text{−}}$ ions, but when referring to solubility rules, one can see that sodium nitrate is very soluble and cannot form a precipitate.)

Solution

The equation for the equilibrium between solid silver chloride, silver ion, and chloride ion is:

The solubility product is 1.6 $\times$ 10 ^–10 (see Appendix J ).

AgCl will precipitate if the reaction quotient calculated from the concentrations in the mixture of AgNO ₃ and NaCl is greater than K _sp . The volume doubles when we mix equal volumes of AgNO ₃ and NaCl solutions, so each concentration is reduced to half its initial value. Consequently, immediately upon mixing, [Ag ⁺ ] and [Cl ^– ] are both equal to:

The reaction quotient, Q , is momentarily greater than K _sp for AgCl, so a supersaturated solution is formed:

Since supersaturated solutions are unstable, AgCl will precipitate from the mixture until the solution returns to equilibrium, with Q equal to K _sp .

Check your learning

Will KClO ₄ precipitate when 20 mL of a 0.050- M solution of K ⁺ is added to 80 mL of a 0.50- M solution of ${\text{ClO}}_4{}^{\text{−}}?$ (Remember to calculate the new concentration of each ion after mixing the solutions before plugging into the reaction quotient expression.)

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