What is the molar concentration of Au⁺(aq) in a saturated solution of AuCl in pure water at 25 °C?

A g C l ( s ) ⇄ A u + ( a q )   +   C l − ( a q )

Interpretation:

In saturated solution of AuCl the molar concentration of Au+(aq) has to be calculated.

Concept introduction:

The solubility of a salt is defined as the maximum amount of salt that can be dissolved in definite amount of solvent. It is expressed in moles per liter or grams per liter. Solubility in terms of moles per liter is called molar solubility and is defined as the number of moles of solute (salt) dissolved in per liter of solution.

Solubility product constant Ksp is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

For example, general salt AxBy when dissolved in water dissociates as,

  AxBy(s)⇌xAy+(aq)+yB−x(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[B−x]y (1)

The ICE table for salt AxBy, which relates the equilibrium concentration of ions in the solution is given as follows,

EquationAxBy⇌xAy++yB−xInitial(M)00Change(M)+xs+ysEquilibrium(M)xsys

From the table,

[Ay+]=xs[B−x]=ys

Substitute xs for [Ay+] and ys for [B−x] in equation (1).

Ksp=(xs)x(ys)y=xxyy(s)x+y

Rearrange for s.

s=(Kspxxyy)1/(x+y)

Here,

•  x is the coefficient of cation A+y.
• y is the coefficient of anion B−x.
• s is the molar solubility.

The value of Ksp is calculated by using molar solubility of the salt.

The molar concentration of Au+(aq) is calculated below.

Given:

Refer to the Appendix J in the textbook for the value of Ksp.

The value of solubility product Ksp of AuCl is 2.0×10−13.

The balanced chemical reaction for the dissolution of AuCl in water is,

  AuCl(s)⇌ Au+1(aq) + Cl−1(aq)

One mole of solid AuCl salt dissolve in water to give one mole each of Au+ and Cl− ions. Therefore the molar concentration of the dissolved ions (Au+ and Cl− ) present in the saturated solution of AuCl in pure water will be equal to the solubility of the salt AuCl.

The ICE table(1) is as follows,

EquationAuCl(s)⇌Au+1(aq)+Cl−1(aq)Initial (M)00Change (M)+s+sEquilibrium (M) s s

The Ksp expression for AuCl is,

Ksp = [Au+1][Cl−1] (2)

From the table,

[Au+1]=s[Cl−1]=s

Substitute s for  [Ag+1] and [Cl−1] in equation (2)