Question #854b9

1 Answer
Jul 5, 2017

Answer:

#K_(sp) = 3.97 * 10^(-3)#

Explanation:

Notice that the problem provides you with the molar solubility of the salt, i.e. the number of moles that can be dissolved per liter of solution in order to have a saturated solution of #"AB"#.

In your case, you know that #0.0630# moles of #"AB"# can be dissolved in #"1.00 L"# of water to form #"1.00 L"# of saturated solution at #25^@"C"#.

You can thus say that the molar solubility of the salt, #s#, is equal to

#s = "0.0630 mol L"^(-1)#

Now, you know that when #"AB"# is dissolved in water, the following dissociation equilibrium is established

#"AB"_ ((s)) rightleftharpoons "A"_ ((Aq))^(+) + "B"_ ((aq))^(-)#

Notice that every mole of #"AB"# that dissociates produces #1# mole of #"A"# and #1# mole of #"B"#, so right from the start, you can say that the saturated solution will contain

#["A"] = ["B"]#

Since you already know the molar solubility of the salt at #25^@"C"#, i.e. the maximum number of moles of #"AB"# that dissociate to produce solvated ions, you can say that

#["A"] = ["B"] = s#

which means that you have

#["A"] = ["B"] = "0.0630 mol L"^(-1)#

By definition, the solubility product constant, #K_(sp)#, is equal to

#K_(sp) = ["A"] * ["B"]#

This means that you have--I won't add the units here

#K_(sp) = 0.0630 * 0.0630 = color(darkgreen)(ul(color(black)(3.97 * 10^(-3))))#

The answer is rounded to three sig figs.