2 Chemistry -- Ionic Equilibrium

The solubility product constant of Ca(OH)2 at 25°C is 4.42 x 10-5. A 500 mL of a saturated solution of Ca(OH)2 is mixed with an equal volume of 0.4 M NaOH. What mass of Ca(OH)2 is precipitated out?

The solubility product constant of Ca(OH)2 at 25°C is 4.42 x 10-5. A 500 mL of a saturated solution of Ca(OH)2 is mixed with an equal volume of 0.4 M NaOH. What mass of Ca(OH)2 is precipitated out?

Let the solubility of Ca(OH)2 in pure water
= S moles/litre
Ca(OH)2Ca2++2OH
S 2S
Then Ksp=[Ca2+][OH]
4.42×105=S×(2S)2
4.42×105=4S3
S=2.224×102=0.0223 moles litre1
 No. of moles of Ca2+ ions in 500 ml of solutions = 0.011. Now when 500 ml of saturated solution is mixed with 500 ml of 0.4 M NaOH, the resultant volume is 1000 ml. The molarity of OH ions on the resultant solution would therefore be 0.2 M
Maximum [Ca2+] that can be tolerated =ksp[OH]2
=4.42×105(0.2)2=0.0011M
Thus number of moles of Ca2+ or Ca(OH)2 precipitated =0.0110.001=0.010
Mass of Ca(OH)2 precipitated =0.010×74=0.74g

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