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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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Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
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what is the change in momentum of a body?
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8m/s²
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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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