Whatare the molar concentrations of all ions in a 500 mL saturated solution of silver chloride at 25 degrees Celsius?

Question

Wyatt Atkins · Accepted Answer

#1.34 * 10^(-5)"M"#

Your strategy here will be to use the solubility product constant, #K_(sp)#, of silver chloride to find the compound's molar solubility at #25^@"C"#.

You can find the value for the #K_(sp)# of silver chloride here

bilbo.chm.uri.edu/CHM112/tables/KspTable.htm

Thus, you are aware of that

#K_(sp) = 1.8 * 10^(-10)#

Silver chloride, #"AgCl"#, is considered insoluble in aqueous solution, which means that an equilibrium will be established between the undissolved solid and the dissolved ions.

Use an ICE table to find the molar solubility of silver chloride, #s#, at this temperature

#" ""AgCl"_text((s]) " "rightleftharpoons" " "Ag"_text((aq])^(+) " "+" " "Cl"_text((aq])^(-)#

#color(purple)("I")" " " "color(white)(a)-" " " " " " " " " "0" " " " " " " " " "0# #color(purple)("C")" " " "color(white)(a)-" " " " " " " "(+s)" " " " " "(+s)# #color(purple)("E")" " " "color(white)(a)-" " " " " " " " " "s" " " " " " " " " "s#

The solubility product constant will, by definition, equal

#K_(sp) = ["Ag"^(+)] * ["Cl"^(-)]#

In your situation, you'll have

#1.8 * 10^(-10) = s * s = s^2#

This will provide you with

#s = sqrt(1.8 * 10^(-10)) = 1.34 * 10^(-5)#

This indicates that in a saturated solution of silver chloride, the concentrations of silver cations and chloride anons will be equal to

#["Ag"^(+)] = ["Cl"^(-)] = s = 1.34 * 10^(-5)"mol L"^(-1)#

Therefore, the concentration of both ions in your #"500-mL"# saturated silver chloride solution will be equal to

#["Ag"^(+)] = ["Cl"^(-)] = color(green)(|bar(ul(color(white)(a/a)1.34 * 10^(-5)"M"color(white)(a/a)|)))#

I'll round the result to three significant figures.

Do not get confused by the fact that you're dealing with a #"500-mL"# solution!

The molar solubility represents concentration, not number of moles of solute. This means that the concentration of both ions in a saturated silver chloride solution will be equal to #1.34 * 10^(-5)"M"# regardless of the volume of said solution!

Avery Adams · Answer

undefined The molar concentrations of ions in a saturated solution of silver chloride are:

- [Ag⁺]: 1.3 × 10⁻⁵ M
- [Cl⁻]: 1.3 × 10⁻⁵ M