# Equilibrium

Reactions don't proceed instantly, in fact, predicting the rate at which a reaction occurs is very important to ChEs.

Furthermore, reactions do not necessarily happen independently, in fact, often the reverse of the reaction we are interested in also happens!

DEFINITION

Chemical equilibrium is reached when the rates of the forward and reverse reactions are equal to each other (i.e., compositions no longer change with time!)

While we will not calculate rates in this course, we need to know what affects them (because this will affect the equilibrium!). Things that we must consider that effect reaction rates (and hence equilibrium) are:

• Temperature
• concentrations (pressure)

So how do we do equilibrium calculations? I'd wager you have already done them in a chemistry class a long time ago (in a galaxy far far away...) when dealing with acid-base chemistry.

Despite the fact that an equilibrium reaction can occur both forward and backward, we simply define one extent of reaction to that expression (forward and backward are not independent of each other, after all).

You then plug either known equilibrium concentrations or extent of reaction expressions (reactive material balances based on extents) directly into the equilibrium expression.

NOTE

The equilibrium expression will serve as one additional equation in your degrees of freedom analysis (you could call it a process specification or a physical law).

EXAMPLE

Consider the reaction of methane with oxygen:

2CH4 + 02 $\leftrightarrow$ 2CH3OH

We are given that, at equilibrium, the compositions of the components satisfy:

$K(T) = \frac{y_{CH_3OH}^2}{y_{CH_4}^2y_{O_2}}$

If you are given the feed compositions (nCH4, n02, and nCH3OH), and the equilibrium constant, K(T), how do you determine the equilibrium compositions?

OUTCOMES:

Utilize equilibrium expressions to determine equilibrium compositions and extents of reaction

TEST YOURSELF

Try an example yourselves:

At low to moderate pressures, the equilibrium state of the water-gas shift reaction:

CO + H20 $\leftrightarrow$ CO2 + H2

is approximately described by the relation:

$K(T) = 0.0247e^{[4020/T(K)]} = \frac{y_{H_2}y_{CO_2}}{y_{CO}y_{H_2O}}$

where T is the reactor temperature, K, is the reaction equilibrium constant, and y, is the mole fraction of the species in the reactor at equilibrium.

The feed to a gas-shift reactor contains 20.0 mole% CO, 10.0% CO2, 40.0% water, and the balance inert gas. The reactor is maintained at T 1123 K.

Assume a basis of 1 mol/hr feed and draw and label a flowchart. Calculate the total molar flowrate out of the reactor when it is run in such a way as to acheive equilibrium. Then, determine the equilibrium mole fraction of hydrogen in the product.