# 3.3 The equilibrium constant

 Page 1 / 2

## The equilibrium constant

Equilibrium constant

The equilibrium constant (K ${}_{c}$ ), relates to a chemical reaction at equilibrium. It can be calculated if the equilibrium concentration of each reactant and product in a reaction at equilibrium is known.

## Calculating the equilibrium constant

Consider the following generalised reaction which takes place in a closed container at a constant temperature :

$A+B⇌C+D$

We know from "Factors affecting reaction rates" that the rate of the forward reaction is directly proportional to the concentration of the reactants. In other words, as the concentration of the reactants increases, so does the rate of the forward reaction. This can be shown using the following equation:

Rate of forward reaction $\propto$ [A][B]

or

Rate of forward reaction = k ${}_{1}$ [A][B]

Similarly, the rate of the reverse reaction is directly proportional to the concentration of the products. This can be shown using the following equation:

Rate of reverse reaction $\propto$ [C][D]

or

Rate of reverse reaction = k ${}_{2}$ [C][D]

At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. This can be shown using the following equation:

${k}_{1}\left[A\right]\left[B\right]={k}_{2}\left[C\right]\left[D\right]$

or

$\frac{{k}_{1}}{{k}_{2}}=\frac{\left[C\right]\left[D\right]}{\left[A\right]\left[B\right]}$

or, if the constants k ${}_{1}$ and k ${}_{2}$ are simplified to a single constant, the equation becomes:

${k}_{c}=\frac{\left[C\right]\left[D\right]}{\left[A\right]\left[B\right]}$

A more general form of the equation for a reaction at chemical equilibrium is:

$aA+bB⇌cC+dD$

where A and B are reactants, C and D are products and a, b, c, and d are the coefficients of the respective reactants and products. A more general formula for calculating the equilibrium constant is therefore:

${K}_{c}=\frac{{\left[C\right]}^{c}{\left[D\right]}^{d}}{{\left[A\right]}^{a}{\left[B\right]}^{b}}$

It is important to note that if a reactant or a product in a chemical reaction is in either the liquid or solid phase, the concentration stays constant during the reaction. Therefore, these values can be left out of the equation to calculate K ${}_{c}$ . For example, in the following reaction:

$C\left(s\right)+{H}_{2}O\left(g\right)⇌CO\left(g\right)+{H}_{2}\left(g\right)$

${K}_{c}=\frac{\left[CO\right]\left[{H}_{2}\right]}{\left[{H}_{2}O\right]}$
1. The constant ${K}_{c}$ is affected by temperature and so, if the values of ${K}_{c}$ are being compared for different reactions, it is important that all the reactions have taken place at the same temperature.
2. K ${}_{c}$ values do not have units. If you look at the equation, the units all cancel each other out.

## The meaning of k ${}_{c}$ Values

The formula for K ${}_{c}$ has the concentration of the products in the numerator and the concentration of reactants in the denominator. So a high K ${}_{c}$ value means that the concentration of products is high and the reaction has a high yield. We can also say that the equilibrium lies far to the right. The opposite is true for a low K ${}_{c}$ value. A low K ${}_{c}$ value means that, at equilibrium, there are more reactants than products and therefore the yield is low. The equilibrium for the reaction lies far to the left.

When you are busy with calculations that involve the equilibrium constant, the following tips may help:

1. Make sure that you always read the question carefully to be sure of what you are being asked to calculate. If the equilibrium constant is involved, make sure that the concentrations you use are the concentrations at equilibrium , and not the concentrations or quantities that are present at some other time in the reaction.
2. When you are doing more complicated calculations, it sometimes helps to draw up a table like the one below and fill in the mole values that you know or those you can calculate. This will give you a clear picture of what is happening in the reaction and will make sure that you use the right values in your calculations.
 Reactant 1 Reactant 2 Product 1 Start of reaction Used up Produced Equilibrium

how does cell look like
What is impulse and how does it = to momentum
what is physics
what is a catanation ?
The ability of a few elements, most especially carbon, to yield chains and rings by forming covalent bonds with atoms of the same element.
Ofentse
different structural formula
different type of structural formula
Lucas
primary,secondary and tertiary
Snowy
how does the earth revolute
What is the momentum
The product of the object's mass and it's velocity
Mvula
electric field def
FREENCO
what is secondary alcohol?
Raymond
is when Carbon that is bonded with OH is also bonded to 2 carbons of the chain.
Gontse
Electric field is the region of space around a charged object where other charged objects will experience an electrostatic force ( coulomb forces) without coming into contact with the object that is generating the field.
Kagiso
Electric field is the region of space around a charged object where other charged objects will experience an electrostatic force ( coulomb forces) without coming into contact with the object that is generating the field.
Kagiso
how is ester formed
how is n ester formed
Aubrey
Alcohol reacts with a carboxylic acid
Texas
and the reaction is catalysed by sulphuric acid
Vhulenda
An ester is form when an alcohol reacts a carboxylic acid and sulphuric acid is used as a catalyst which therefore eliminates water.
Azola
an athlete with a mass of 70kg runs at a velocity of 45km . determine the athlete's momentum
Is that a velocity or something else
msawenkosi
45km/h i guess
Texas
Change to m/s
Texas
45km/h = 12.5 m/s p=mv =70×12.5 =875 kg.m/s
Thato
what are the measures of the rates of reaction
Volume Concentration Temperature Pressure Surface Area
Thato
the principle of superposition of waves
what is work
is this a group chat
Hey can y'all define newton's 2nd law
mthebzification
If a resultant force act on an object...the object will accelerate in the direction of a resultant force,the acceleration of the object is directly proportional to the net force and inversely proportional to the mass of the object
mosa
how do you calculate tension force
Bulumko
use the formula Fnet=ma if there is tension connecting two objects
Sboniso
to calculate Tension, usually calculate acceleration first Draw separate free body diagrams for each body. Apply Fnet = ma to calculate Tension
Kevin
Hi people
Paul
when a resultant force acting on an object the object will accelerate in the direction of a force at an acceleration directly proportional to the force and invesly proportional to the mass of the object.
Raymond
Hey people
Kaytee
how does temperature affect the equilibrium position
an increased temperature increases the average kinetic energy thus in turn increases the number of effective collisions........
Lwando
so...which reaction is favored between endothermic and exothermic .when temperature is increased..?
Blessing
exothermic reaction because energy is realised to the surroundings as heat and light energy ....graphical so much energy is realised as reactants to form product and because temperature is high rate of reaction is fast which means there is a successful collision
Code
INTEMENDO - INCREASE IN TEMPERATURE FAVOURS ENDOTHERMIC DETEMEXO - DECREASE IN TEMPERATURE FAVOURS EXOTHERMIC
Thato
an object will continue in a state of rest unless it is acted upon an unbalanced force
Newton's Law 1
Code
First Newton's Law
Azola
Newton's first law
Surprise
newton first law
Thinavhuyo
Newton's first law
Blessing  By By    By  By Abishek Devaraj By