<< Chapter < Page Chapter >> Page >

The equation relating K c and K P is derived as follows. For the gas-phase reaction m A + n B x C + y D:

K P = ( P C ) x ( P D ) y ( P A ) m ( P B ) n
= ( [ C] × R T ) x ( [ D] × R T ) y ( [ A] × R T ) m ( [ B] × R T ) n
= [ C ] x [ D ] y [ A ] m [ B ] n × ( R T ) x + y ( R T ) m + n
= K c ( R T ) ( x + y ) ( m + n )
= K c ( R T ) Δ n

The relationship between K c and K P is

K P = K c ( R T ) Δ n

In this equation, Δ n is the difference between the sum of the coefficients of the gaseous products and the sum of the coefficients of the gaseous reactants in the reaction (the change in moles of gas between the reactants and the products). For the gas-phase reaction m A + n B x C + y D, we have

Δ n = ( x + y ) ( m + n )

Calculation of K P

Write the equations for the conversion of K c to K P for each of the following reactions:

(a) C 2 H 6 ( g ) C 2 H 4 ( g ) + H 2 ( g )

(b) CO ( g ) + H 2 O ( g ) CO 2 ( g ) + H 2 ( g )

(c) N 2 ( g ) + 3 H 2 ( g ) 2 NH 3 ( g )

(d) K c is equal to 0.28 for the following reaction at 900 °C:

CS 2 ( g ) + 4 H 2 ( g ) CH 4 ( g ) + 2 H 2 S ( g )

What is K P at this temperature?

Solution

(a) Δ n = (2) − (1) = 1
K P = K c ( RT ) Δ n = K c ( RT ) 1 = K c ( RT )

(b) Δ n = (2) − (2) = 0
K P = K c ( RT ) Δ n = K c ( RT ) 0 = K c

(c) Δ n = (2) − (1 + 3) = −2
K P = K c ( RT ) Δ n = K c ( RT ) −2 = K c ( R T ) 2

(d) K P = K c (RT) Δ n = (0.28)[(0.0821)(1173)] −2 = 3.0 × 10 −5

Check your learning

Write the equations for the conversion of K c to K P for each of the following reactions, which occur in the gas phase:

(a) 2 SO 2 ( g ) + O 2 ( g ) 2 SO 3 ( g )

(b) N 2 O 4 ( g ) 2 NO 2 ( g )

(c) C 3 H 8 ( g ) + 5 O 2 ( g ) 3 CO 2 ( g ) + 4 H 2 O ( g )

(d) At 227 °C, the following reaction has K c = 0.0952:

CH 3 OH ( g ) CO ( g ) + 2 H 2 ( g )

What would be the value of K P at this temperature?

Answer:

(a) K P = K c ( RT ) −1 ; (b) K P = K c ( RT ); (c) K P = K c ( RT ); (d) 160 or 1.6 × 10 2

Got questions? Get instant answers now!

Heterogeneous equilibria

A heterogeneous equilibrium is a system in which reactants and products are found in two or more phases. The phases may be any combination of solid, liquid, or gas phases, and solutions. When dealing with these equilibria, remember that solids and pure liquids do not appear in equilibrium constant expressions (the activities of pure solids, pure liquids, and solvents are 1).

Some heterogeneous equilibria involve chemical changes; for example:

PbCl 2 ( s ) Pb 2+ ( a q ) + 2 Cl ( a q ) K c = [ Pb 2+ ] [ Cl ] 2
CaO ( s ) + CO 2 ( g ) CaCO 3 ( s ) K c = 1 [CO 2 ]
C ( s ) + 2 S ( g ) CS 2 ( g ) K c = [CS 2 ] [ S ] 2

Other heterogeneous equilibria involve phase changes, for example, the evaporation of liquid bromine, as shown in the following equation:

Br 2 ( l ) Br 2 ( g ) K c = [ Br 2 ]

We can write equations for reaction quotients of heterogeneous equilibria that involve gases, using partial pressures instead of concentrations. Two examples are:

CaO ( s ) + CO 2 ( g ) CaCO 3 ( s ) K P = 1 P CO 2
C ( s ) + 2 S ( g ) CS 2 ( g ) K P = P CS 2 ( P S ) 2

Key concepts and summary

For any reaction that is at equilibrium, the reaction quotient Q is equal to the equilibrium constant K for the reaction. If a reactant or product is a pure solid, a pure liquid, or the solvent in a dilute solution, the concentration of this component does not appear in the expression for the equilibrium constant. At equilibrium, the values of the concentrations of the reactants and products are constant. Their particular values may vary depending on conditions, but the value of the reaction quotient will always equal K ( K c when using concentrations or K P when using partial pressures).

A homogeneous equilibrium is an equilibrium in which all components are in the same phase. A heterogeneous equilibrium is an equilibrium in which components are in two or more phases. We can decide whether a reaction is at equilibrium by comparing the reaction quotient with the equilibrium constant for the reaction.

Questions & Answers

What is whizatron?
Frendick Reply
What is stoichometry
ngwuebo Reply
what is atom
yinka Reply
An indivisible part of an element
ngwuebo
the smallest particle of an element which is indivisible is called an atom
Aloaye
An atom is the smallest indivisible particle of an element that can take part in chemical reaction
Alieu
is carbonates soluble
Ebuka Reply
what is the difference between light and electricity
Joshua Reply
What is atom? atom can be defined as the smallest particles
Adazion
what is the difference between Anode and nodes?
Adazion
What's the net equations for the three steps of dissociation of phosphoric acid?
Lisa Reply
what is chemistry
Prince Reply
the study of matter
Reginald
what did the first law of thermodynamics say
Starr Reply
energy can neither be created or distroyed it can only be transferred or converted from one form to another
Adedeji
Graham's law of Diffusion
Ayo Reply
what is melting vaporization
Anieke Reply
melting and boiling point explain in term of molecular motion and Brownian movement
Anieke
Scientific notation for 150.9433962
Steve Reply
what is aromaticity
Usman Reply
aromaticity is a conjugated pi system specific to organic rings like benzene, which have an odd number of electron pairs within the system that allows for exceptional molecular stability
Pookieman
what is caustic soda
Ogbonna Reply
sodium hydroxide (NaOH)
Kamaluddeen
what is distilled water
Rihanat
is simply means a condensed water vapour
Kamaluddeen
advantage and disadvantage of water to human and industry
Abdulrahman Reply
a hydrocarbon contains 7.7 percent by mass of hydrogen and 92.3 percent by mass of carbon
Timothy Reply
Practice Key Terms 7

Get the best Chemistry course in your pocket!





Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask