In general chemistry, what does “heterogeneous” mean for an equilibrium system, and how is the equilibrium constant written for AgCl(s) ⇌ Ag+(aq) + Cl−(aq)?

A heterogeneous equilibrium contains more than one phase; for AgCl(s) ⇌ Ag+(aq) + Cl−(aq), the constant is \(K_{sp}=[\text{Ag}^+][\text{Cl}^-]\) because the pure solid AgCl has activity 1 and is omitted.

Heterogeneous Equilibrium and Why Solids Don’t Appear in K Expressions

Accepted answer Answer included

Problem

The keyword “heterogeneous” is interpreted in a general chemistry equilibrium context. Consider the dissolution equilibrium:

\[ \text{AgCl(s)} \rightleftharpoons \text{Ag}^+(\text{aq}) + \text{Cl}^-(\text{aq}) \]

Determine whether the system is heterogeneous, then write the correct equilibrium constant expression and explain why the solid does not appear.

Solution

1) Meaning of “heterogeneous” in chemistry

A system is heterogeneous when it contains more than one phase. A phase is a region of matter that is uniform in composition and physical state (for example: a solid phase, a liquid phase, or a gas phase).

Key classification:

Homogeneous equilibrium: all reactants and products are in the same phase (often all gases or all aqueous species).
Heterogeneous equilibrium: at least two different phases are present (such as a solid in contact with an aqueous solution).

2) Identify phases in the given equilibrium

In \(\text{AgCl(s)} \rightleftharpoons \text{Ag}^+(\text{aq}) + \text{Cl}^-(\text{aq})\):

\(\text{AgCl(s)}\) is a solid phase.
\(\text{Ag}^+(\text{aq})\) and \(\text{Cl}^-(\text{aq})\) are in the aqueous phase (dissolved in water).

Since a solid and an aqueous solution are present, the equilibrium is heterogeneous.

3) Write the equilibrium constant using activities

A rigorous equilibrium constant is written in terms of activities \(a_i\):

\[ K = \frac{a_{\text{Ag}^+}\,a_{\text{Cl}^-}}{a_{\text{AgCl(s)}}}. \]

4) Why the solid is omitted

For a pure solid (and also for a pure liquid), the activity is defined as \(1\) under the standard-state convention used in general chemistry:

\[ a_{\text{AgCl(s)}} = 1. \]

Substituting into the activity expression gives:

\[ K = a_{\text{Ag}^+}\,a_{\text{Cl}^-}. \]

In dilute solutions, activities are commonly approximated by molar concentrations:

\[ a_i \approx [i]. \]

Result for the solubility product constant:

\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-]. \]

The term “heterogeneous” is the reason pure solids and liquids are not written in the equilibrium constant expression: their activities are constant and equal to \(1\).

5) Species checklist (included or excluded?)

Species	Phase	Appears in \(K\)?	Reason
\(\text{AgCl}\)	solid (s)	No	Pure solid has activity \(1\)
\(\text{Ag}^+\)	aqueous (aq)	Yes	Variable activity (depends on dissolved amount)
\(\text{Cl}^-\)	aqueous (aq)	Yes	Variable activity (depends on dissolved amount)

6) Short numerical illustration (optional but standard)

If a saturated solution of AgCl at a given temperature has \([\text{Ag}^+] = 1.3 \times 10^{-5}\) and \([\text{Cl}^-] = 1.3 \times 10^{-5}\), then:

\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] = (1.3 \times 10^{-5})(1.3 \times 10^{-5}) = 1.69 \times 10^{-10}. \]

Visualization

The diagram shows a solid in contact with an aqueous solution, creating a heterogeneous equilibrium. Only aqueous species appear in \(K_{sp}\); the pure solid is omitted.

Final statement

The system is heterogeneous because it contains a solid phase and an aqueous phase, and the correct expression is \(K_{sp} = [\text{Ag}^+][\text{Cl}^-]\) because \(a_{\text{AgCl(s)}}=1\).

Vote on the accepted answer

Upvotes: 0 Downvotes: 0 Score: 0