# 13.2 Equilibrium constants  (Page 4/14)

 Page 4 / 14

## Homogeneous equilibria

A homogeneous equilibrium is one in which all of the reactants and products are present in a single solution (by definition, a homogeneous mixture). In this chapter, we will concentrate on the two most common types of homogeneous equilibria: those occurring in liquid-phase solutions and those involving exclusively gaseous species. Reactions between solutes in liquid solutions belong to one type of homogeneous equilibria. The chemical species involved can be molecules, ions, or a mixture of both. Several examples are provided here.

${\text{C}}_{2}{\text{H}}_{2}\left(aq\right)+2{\text{Br}}_{2}\left(aq\right)⇌{\text{C}}_{2}{\text{H}}_{2}{\text{Br}}_{4}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{C}}_{2}{\text{H}}_{2}{\text{Br}}_{4}\right]}{\left[{\text{C}}_{2}{\text{H}}_{2}\right]\phantom{\rule{0.2em}{0ex}}{\left[{\text{Br}}_{2}\right]}^{2}}$
${\text{I}}_{2}\left(aq\right)+{\text{I}}^{\text{−}}\left(aq\right)⇌{\text{I}}_{3}{}^{\text{−}}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{I}}_{3}{}^{\text{−}}\right]}{\left[{\text{I}}_{2}\right]\left[{\text{I}}^{\text{−}}\right]}$
${\text{Hg}}_{2}{}^{2+}\left(aq\right)+{\text{NO}}_{3}{}^{\text{−}}\left(aq\right)+3{\text{H}}_{3}{\text{O}}^{\text{+}}\left(aq\right)⇌2{\text{Hg}}^{2+}\left(aq\right)+{\text{HNO}}_{2}\left(aq\right)+4{\text{H}}_{2}\text{O}\left(l\right)$
${K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{Hg}}^{\text{2+}}\right]}^{2}\left[{\text{HNO}}_{2}\right]}{\left[{\text{Hg}}_{2}{}^{2+}\right]\left[{\text{NO}}_{3}{}^{\text{−}}\right]{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}^{3}}$
$\text{HF}\left(aq\right)+{\text{H}}_{2}\text{O}\left(l\right)⇌{\text{H}}_{3}{\text{O}}^{\text{+}}\left(aq\right)+{\text{F}}^{\text{−}}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]\left[{\text{F}}^{\text{−}}\right]}{\left[\text{HF}\right]}$
${\text{NH}}_{3}\left(aq\right)+{\text{H}}_{2}\text{O}\left(l\right)⇌{\text{NH}}_{4}{}^{\text{+}}\left(aq\right)+{\text{OH}}^{\text{−}}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{NH}}_{4}{}^{\text{+}}\right]\left[{\text{OH}}^{\text{−}}\right]}{\left[{\text{NH}}_{3}\right]}$

In each of these examples, the equilibrium system is an aqueous solution, as denoted by the aq annotations on the solute formulas. Since H 2 O( l ) is the solvent for these solutions, its concentration does not appear as a term in the K c expression, as discussed earlier, even though it may also appear as a reactant or product in the chemical equation.

Reactions in which all reactants and products are gases represent a second class of homogeneous equilibria. We use molar concentrations in the following examples, but we will see shortly that partial pressures of the gases may be used as well.

${\text{C}}_{2}{\text{H}}_{6}\left(g\right)⇌{\text{C}}_{2}{\text{H}}_{4}\left(g\right)+{\text{H}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{\left[{\text{C}}_{2}{\text{H}}_{4}\right]\phantom{\rule{0.2em}{0ex}}\left[{\text{H}}_{2}\right]}{\left[{\text{C}}_{2}{\text{H}}_{6}\right]}$
$3{\text{O}}_{2}\left(g\right)⇌2{\text{O}}_{3}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{O}}_{3}\right]}^{2}}{{\left[{\text{O}}_{2}\right]}^{3}}$
${\text{N}}_{2}\left(g\right)+3{\text{H}}_{2}\left(g\right)⇌2{\text{NH}}_{3}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{NH}}_{3}\right]}^{2}}{\left[{\text{N}}_{2}\right]{\phantom{\rule{0.2em}{0ex}}\left[{\text{H}}_{2}\right]}^{3}}$
${\text{C}}_{3}{\text{H}}_{8}\left(g\right)+5{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⇌3{\text{CO}}_{2}\left(g\right)+4{\text{H}}_{2}\text{O}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{CO}}_{2}\right]}^{3}{\left[{\text{H}}_{2}\text{O}\right]}^{4}}{\left[{\text{C}}_{3}{\text{H}}_{8}\right]{\left[{\text{O}}_{2}\right]}^{5}}$

Note that the concentration of H 2 O( g ) has been included in the last example because water is not the solvent in this gas-phase reaction and its concentration (and activity) changes.

Whenever gases are involved in a reaction, the partial pressure of each gas can be used instead of its concentration in the equation for the reaction quotient because the partial pressure of a gas is directly proportional to its concentration at constant temperature. This relationship can be derived from the ideal gas equation, where M is the molar concentration of gas, $\frac{n}{V}.$

$PV=nRT$
$P=\left(\frac{n}{V}\right)RT$
$=MRT$

Thus, at constant temperature, the pressure of a gas is directly proportional to its concentration.

Using the partial pressures of the gases, we can write the reaction quotient for the system ${\text{C}}_{2}{\text{H}}_{6}\left(g\right)⇌{\text{C}}_{2}{\text{H}}_{4}\left(g\right)+{\text{H}}_{2}\left(g\right)$ by following the same guidelines for deriving concentration-based expressions:

${Q}_{P}=\phantom{\rule{0.2em}{0ex}}\frac{{P}_{{\text{C}}_{2}{\text{H}}_{4}}{P}_{{\text{H}}_{2}}}{{P}_{{\text{C}}_{2}{\text{H}}_{6}}}$

In this equation we use Q P to indicate a reaction quotient written with partial pressures: ${P}_{{\text{C}}_{2}{\text{H}}_{6}}$ is the partial pressure of C 2 H 6 ; ${P}_{{\text{H}}_{2}},$ the partial pressure of H 2 ; and ${P}_{{\text{C}}_{2}{\text{H}}_{6}},$ the partial pressure of C 2 H 4 . At equilibrium:

${K}_{P}={Q}_{P}=\phantom{\rule{0.2em}{0ex}}\frac{{P}_{{\text{C}}_{2}{\text{H}}_{4}}{P}_{{\text{H}}_{2}}}{{P}_{{\text{C}}_{2}{\text{H}}_{6}}}$

The subscript P in the symbol K P    designates an equilibrium constant derived using partial pressures instead of concentrations. The equilibrium constant, K P , is still a constant, but its numeric value may differ from the equilibrium constant found for the same reaction by using concentrations.

Conversion between a value for K c    , an equilibrium constant expressed in terms of concentrations, and a value for K P , an equilibrium constant expressed in terms of pressures, is straightforward (a K or Q without a subscript could be either concentration or pressure).

wat are hydrocarbon s
I think they are molecules that comprise only of hydrogen and carbon atoms ( they are organic if I'm not mistaken)
Mmathabo
am new here can I join
Yeko
give two properties of liquid
molecules are slightly packed and they follow the shape of a container.
Obedie
what is measurement
is the comparison of an unknown quantity with a fixed quantity of the same kind
How does an element differ from a compound? How are they similar?
an element is an indivisible particles that can take part in a reaction and consist of smaller or tiny particles i.e proton, neutrons and electron while a compound is when two or more element chemically combine together. They are similar when they are homogeneous compound. they take the same rxn.
Yusuf
an element is s chemically pure substance containing a particular type of atoms.. A COMPOUND is a substance containing atoms from different elements..
Inemesit
How to get the Lewis formula of SeCl+3
hi,I'm new here can I join the conversation
EZEA
what is the structural formula for starch
Starch is a mixture (of chemicals) of amylose and amylopectin. Both are macromolecules and polymers. You can search on wikipedia.
Abdelkarim
what is the roles of filter bed
Fathmat
what is the roles of Alu m
Fathmat
what is the roles of chlorine
Fathmat
Roles can be classified or correlate it to different areas: For example: Chlorine can be used in reactions (in industry) to manufacture HCl, which then can be used for other things. Or in swimming pools to kill bacteria. Or as a component in compounds with pharmaceutical roles (drugs). For Al:
Abdelkarim
Its dentisty value is suitable to be used in alloys (mixture of metals) in aircraft bodies. Also, Aluminium foils, Tin cans,.. Some of them are also in Al overhead cables in streets and long roads.
Abdelkarim
what is chemistry
Maxamed
what is the meaning of exceedingly
it is an adverb which means extremely
Rohini
what is atomic chemistry?
Lewis structure for no3
Lewis structure for no3
what is weak acid
It is an acid which partially ionises in water.
Abdelkarim
what is incandescence
Clifton
what makes it glow
Clifton
why is it red, irange and yellow in color
Clifton
hello am new here and I want to join you
Aliyu
hello
Clifton
hi
Aliyu
too
Gillian
hello i am new here please i want to join this group
Paul
Hi, I'm also new here
Salaudeen
Hi
Keeya
hello guys !!
Sourav
what is pressure?
The force applied to suction Area of the body
Ahmed
Matter composed of exceedingly small paticle called atom.
Yushao
questions related to metals
occurrence and preparation of the representatives metals
Regina
list the 20, periodic table and their symbols
hydrogen:h helium;he lithium:l beryllium:be Boron:b Carbon;C Nitrogen:n Oxygen:O FLUORINE:f Neon:n Sodium:s Magnesium:mg Aluminum:a Silicon:s Phosphorus:p Sulphur:s Chlorine:c Argon;a Potassium:p Calcium:c
Benita
Hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, neon, sodium, magnesium, aluminium, silicon, phosphorus, sulphur, chlorine, argon, potassium, calcium
Cudjoe
hey I'm also New here
Obedie
Welcome
Gillian
there are 118 known elements ...you numbnuts
what is a solute
Any substance that is disolved in a liqid solvent to create a solution
Fifa
sorry liquid
Fifa
it's a liquid substance
Fathmat
hello group
Ayomide
is the substance that dissolves in the solvent
Amos
so is HCl ionic compound
No, covalent compound ➡️ molecule. As both H and Cl are non-metals and and form covalent bind by sharing valence e-. But can fully ionice in water forming H+ (a proton, a reason for acidity) and Cl- (anion =Chloride) Hydrogen Chloride is a gas at room; Hydrochloric acid = HCl (aq), dissolved in w
Abdelkarim
Form covalenr bond*
Abdelkarim
The question marks are an emoji in the first sentence is an unread emoji. HCl Covalent compund -> molecule
Abdelkarim
Hi.
Queen
Hi
Calvin
Yh
Cudjoe
yes
Amos
what is chemistry
is the study of composition of substances and the way they behave under different conditions
Amos
how do calculate n1 though n6 any help on understanding the concept
Clifton
is the study of properties of matter and it's component
Grace