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15.1 Precipitation and dissolution  (Page 5/17)

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Predicting precipitation

The equation that describes the equilibrium between solid calcium carbonate and its solvated ions is:

CaCO 3 ( s ) ⇌ Ca 2+ ( a q ) + CO 3 2− ( a q )

We can establish this equilibrium either by adding solid calcium carbonate to water or by mixing a solution that contains calcium ions with a solution that contains carbonate ions. If we add calcium carbonate to water, the solid will dissolve until the concentrations are such that the value of the reaction quotient ( Q = [ Ca 2 + ] [ CO 3 2− ] ) is equal to the solubility product ( K sp = 8.7 × 10 –9 ). If we mix a solution of calcium nitrate, which contains Ca 2+ ions, with a solution of sodium carbonate, which contains CO 3 2− ions, the slightly soluble ionic solid CaCO 3 will precipitate, provided that the concentrations of Ca 2+ and CO 3 2− ions are such that Q is greater than K sp for the mixture. The reaction shifts to the left and the concentrations of the ions are reduced by formation of the solid until the value of Q equals K sp . A saturated solution in equilibrium with the undissolved solid will result. If the concentrations are such that Q is less than K sp , then the solution is not saturated and no precipitate will form.

We can compare numerical values of Q with K sp to predict whether precipitation will occur, as [link] shows. (Note: Since all forms of equilibrium constants are temperature dependent, we will assume a room temperature environment going forward in this chapter unless a different temperature value is explicitly specified.)

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:

Mg(OH) 2 ( s ) ⇌ Mg 2+ ( a q ) + 2OH − ( a q ) K sp = 8.9 × 10 − 12

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:

Mg(OH) 2 ( s ) ⇌ Mg 2+ ( a q ) + 2OH − ( a q )

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:

Q = [ Mg 2+ ] [ OH − ] 2 = (0.0537)( 0.0010) 2 = 5.4 × 10 − 8

Because Q is greater than K sp ( Q = 5.4 × 10 –8 is larger than K sp = 8.9 × 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 [ HPO 4 2− ] = 0.001 M .

Answer:

No precipitation of CaHPO 4 ; Q = 1 × 10 –7 , which is less than K sp

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Precipitation of agcl upon mixing solutions

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

(Note: The solution also contains Na + and NO 3 − 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:

AgCl ( s ) ⇌ Ag + ( a q ) + Cl − ( a q )

The solubility product is 1.6 × 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:

1 2 ( 2.0 × 10 − 4 ) M = 1.0 × 10 − 4 M

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

Q = [ Ag + ] [ Cl − ] = (1.0 × 10 − 4 ) ( 1.0 × 10 − 4 ) = 1.0 × 10 − 8 > K sp

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 ClO 4 − ? (Remember to calculate the new concentration of each ion after mixing the solutions before plugging into the reaction quotient expression.)

Answer:

No, Q = 4.0 × 10 –3 , which is less than K sp = 1.05 × 10 –2

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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