Question #f96a9
1 Answer
Here's what's going on here.
Explanation:
The idea here is that silver carbonate,
#"Ag"_2"CO"_text(3(s]) rightleftharpoons color(red)(2)"Ag"_text((aq])^(+) + "CO"_text(2(aq])^(2-)#
The solubility product constant,
#K_(sp) = ["Ag"^(+)]_0^color(red)(2) * ["CO"_3^(2-)]_0#
Here
The actual value of the solubility product constant is not important here, all that matters is the fact that you can assume it to be constant, i.e. the temperature of the solution remains unchanged after water is added.
Now, this equilibrium, like any other dynamic equilibrium, is governed by Le Chatelier's Principle, which as you know states that a system at equilibrium will react to a stress applied to the current position of the equilibrium by shifting in such a way as to counteract that stress.
So, what happens when water is added to the solution?
As a first observation, one could say that the volume of the solution increases. Since molarity is
#color(blue)("molarity" = "moles of solute"/"liters of solution")#
an increase in volume would cause a decrease in concentration.
So, after water is added to the solution, you will have
#overbrace(["Ag"^(+)])^(color(purple)("molarity AFTER adding water")) < overbrace(["Ag"^(+)]_0)^(color(brown)("molarity BEFORE adding water"))#
and
#overbrace(["CO"_3^(2-)])^(color(purple)("molarity AFTER adding water")) < overbrace(["CO"_3^(2-)]_0)^(color(brown)("molarity BEFORE adding water"))#
Now, if the concentrations of the two ions decreased, the product of their new concentrations will be smaller than what you had initially.
#["Ag"^(+)]^color(red)(2)["CO"_3^(2-)] < ["Ag"^(+)]_0^color(red)(2) * ["CO"_3^(2-)]_0#
But remember, this product must be equal to
In order for that to happen, more moles of
#"Ag"_2"CO"_text(3(s]) rightleftharpoons color(red)(2)"Ag"_text((aq])^(+) + "CO"_text(2(aq])^(2-)#
This means that the number of moles of
Remember, the molar solubility of the compound remains unchanged because an increase in the number of moles of ions comes after an increase in the volume of the solution.