# 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).

#### Questions & Answers

what does the term carbon-12 scale mean
Amanda Reply
how can I encounter plasma
Blessing
what are the six types of elements
Rebecca Reply
carbon,hydrogen,nitrogen,oxygen,phosphorus and sulphur....#the CHNOPS element
Amanda
👍
clement
those are the six types of elements I know
Amanda
Yea
clement
thats all
Davy
which table is flammable
Blessing Reply
I haven't gotten to tables o 😥
Rebecca
pls how can I give an IUPAC nomenclature in organic chemistry
Moshood Reply
The Akanes, Akenes, Akynes, Alkanols, Alkanals and so on. you can further bring out the structural and empirical formula which also is a good example to represent it's numenclature.
Andrew
Paul's exclusion principle
Anuforo Reply
what do you mean by d block ,give more details element
Agburum Reply
d block elements are also called transition metals. It includes elements from group 3-12 and d block elements hold up to 10 electrons in their shell
Amanda
all?
Davy
they are called transition elements
Andrew
Define chemical formula
Kevin Reply
they are the mathematical representation of chemicals I guess
Uche
Bohr model of hydrogen atom
Muhammad Reply
what is important of this model
nagesh
this question is not correct, it is Boyles law.
Andrew
what is the main reaction between sodium and chlorine
Akeem Reply
when a sodium atom is transferred an electron to a chloride atom forming a sodium cation and a chlorde anoin both ions are compltely valence shells and a energetically more stable this reaction is extremely more exothermic producing a bright yellow light abd a great deal of heat energy
sani
well what kind of sodium
coland
sodium chloride
coland
Tyropanoic acid and its salt sodium tyropanoate are radiocontrast agents used in cholecystography (X-ray diagnosis of gallstones). Trade names include Bilopaque, Lumopaque, Tyropaque, and Bilopac. The molecule contains three heavy iodine atoms which obstruct X-rays in the same way as the calcium in
coland
Sodium tetradecyl sulfate (STS) is a commonly used synonym for 7-ethyl-2-methyl-4-undecanyl sulfate sodium salt which is anionic surfactant that is the active component of the sclerosant drug Sotradecol. It is commonly used in the treatment of varicose and spider veins of the leg, during the procedu
coland
Sodium stibogluconate, sold under the brand name Pentostam among others, is a medication used to treat leishmaniasis. This includes leishmaniasis of the cutaneous, visceral, and mucosal types. Some combination of miltefosine, paramycin and liposomal amphotericin B; however, may be recommended due to
coland
Sodium picosulfate (INN, also known as sodium picosulphate) is a Contact stimulant laxative used as a treatment for constipation or to prepare the large bowel before colonoscopy or surgery. It is sold under the trade names Sodipic Picofast, Laxoberal, Laxoberon, Purg-Odan, Picolax, Guttalax, Namilax
coland
Ipodate sodium (sodium iopodate) is an iodine-containing radiopaque contrast media used for X-rays. The drug is given orally and the resulting contrast allows for easy resolution of the bile duct and gall bladder. Other uses Although not FDA approved, ipodate sodium has been used to treat Graves'
coland
Sodium ferric gluconate complex (brand name ferrlecit by Sanofi), is an intravenously administered iron product indicated in the treatment of iron deficiency anemia. It is frequently used in patients undergoing hemodialysis, those undergoing erythropoietin therapy, and/or patients who have chronic k
coland
Dehydrocholic acid is a synthetic bile acid, manufactured by the oxidation of cholic acid. It acts as a hydrocholeretic, increasing bile output to clear increased bile acid load.
coland
Ethylenediaminetetraacetic acid (EDTA), also known by several other names, is an aminopolycarboxylic acid and a colourless, water-soluble solid. Its conjugate base is ethylenediaminetetraacetate. It is widely used to dissolve limescale. Its usefulness arises because of its role as a hexadentate ("s
coland
Sodium aurothiomalate (INN, known in the United States as gold sodium thiomalate) is a gold compound that is used for its immunosuppressive anti-rheumatic effects. Along with an orally-administered gold salt, auranofin, it is one of only two gold compounds currently employed in modern medicine. Med
coland
Sodium ascorbate is one of a number of mineral salts of ascorbic acid (vitamin C). The molecular formula of this chemical compound is C6H7NaO6. As the sodium salt of ascorbic acid, it is known as a mineral ascorbate. It has not been demonstrated to be more bioavailable than any other form of vitamin
coland
Diatrizoic acid (or its anionic form, diatrizoate), also known as amidotrizoic acid, or 3,5-diacetamido-2,4,6-triiodobenzoic acid, is a radiocontrast agent containing iodine. Trade names include Hypaque, Gastrografin, Iothalmate and Urografin, the latter being a combination of the sodium and meglum
coland
Sodium acetrizoate (rINN, trade names Urokon, Triurol and Salpix), the sodium salt of acetrizoic acid, is a high-osmolality, water-soluble, iodine-based radiographic contrast medium no longer in clinical use. Acetrizoate was developed by V.H. Wallingford of Mallinckrodt, and introduced in 1950; it
coland
i think some was missed
coland
what chlorine L-Alpha glycerylphosphorylcholine (alpha-GPC, choline alfoscerate) is a natural choline compound found in the brain. It is also a parasympathomimetic acetylcholine precursor which may have potential for the treatment of Alzheimer's disease and other dementias. Alpha-GPC rapidly delive
coland
Choline Theophyllinate , also known as oxtriphylline, is a cough medicine derived from xanthine that acts as a bronchodilator to open up airways in the lung. Chemically, it is a salt of choline and Theophylline. It classifies as an expectorant. The drug is available under the brand names Choledyl an
coland
Choline (/ˈkoʊlin/) is a water-soluble vitamin. It is usually grouped within the B-complex vitamins. The term cholines refers to the class of quaternary ammonium salts containing the N,N,N-trimethylethanolammonium cation (X− on the right denotes an undefined counteranion). The cation appears in the
coland
thanks
sani
please what is redox reaction
BABARINDE
the oxidation increases
Andrew
hydrogen reacting with water
Iyenge Reply
yes
Moha
what are you trying to prove
Uche
yes
Professor
what is matter
Godgift Reply
matter is anything that has Mass and can occupy space
Moshood
apart from those device there is there any device
Eke Reply
how many elements do we have
ARUOTURE Reply
Modern Electronic Theory
Levi Reply
a new way or an improvement in modern electrical products.
Andrew
find the volume of oxygen produced from the electrolysis of acidified water of a current of a 2A was passed through the electrolysis of acidified water for 2 hours
Ngwu Reply
14400J
Ese
wrong question, go through it. oxygen cannot be produced.
Andrew

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