Calculating Equilibrium constant

[Malgrif]

Homework Statement

Consider the system

CO2(g) + H2(g) <====> CO(g) + H2O(g)

Initially, 0.25 mol of water vapour and 0.2 mol of carbon monoxide are placed in a 1.00 L reaction vessel. At equilibrium, spectroscopic evidence shows that 0.1 mol of carbon dioxide is present. Calculate K for the reaction.

Homework Equations

equilibrium law

The Attempt at a Solution

So writing down the equilibrium law we get.
Kc = [CO][H2O]/[CO2]

Now we need to find the unknowns. We know 3/4 of the reaction's concentrations but how do you find the forth? An ice table won't work since we don't have a Kc value and without a given H2 value we can't calculate Kc. Stoichometry sounds useless since the system is in equilibrium so what the heck. How do you solve this problem?

 

[Borek]

You were already answered somewhere else, but let me repeat: stoichiometry is a key.

Think this way: you start with 25 molecules of water and 20 molecules of carbon monoxide. At equlibrium you find there are 10 molecules of carbon dixode. There were 20 atoms of carbon in the system - if 10 are in the form of dioxide, other 10 must be still in the form of monoxide. That means that 10 molecules of monoxide reacted with water molecules - stoichiometry of the reaction tells you how many molecules of water reacted and how many molecules of hydrogen were produced.

 

[Blueshift5]

it is important to approach problems systematically and logically. Let's break down the given information and use the principles of equilibrium to find the unknown values.

First, we know that the reaction is at equilibrium, meaning that the forward and reverse reactions are occurring at the same rate. This also means that the concentrations of all reactants and products remain constant.

Next, we can use the given initial and equilibrium concentrations to set up an ICE table. We know that at equilibrium, 0.1 mol of CO2 is present. Using the stoichiometry of the reaction, we can determine that 0.1 mol of CO is also present. This means that at equilibrium, 0.1 mol of H2O and 0.1 mol of H2 must have been consumed.

Using the given initial concentrations and the calculated changes, we can fill out the ICE table as follows:

CO2(g) + H2(g) <====> CO(g) + H2O(g)
Initial: 0.2 mol 0.25 mol 0 mol 0 mol
Change: -0.1 mol -0.1 mol +0.1 mol +0.1 mol
Equilibrium: 0.1 mol 0.15 mol 0.1 mol 0.1 mol

Now, using the equilibrium concentrations in the equilibrium law, we can solve for Kc:

Kc = [CO][H2O]/[CO2]

= (0.1)(0.1)/(0.1)(0.15)
= 0.67

Therefore, the equilibrium constant (Kc) for this reaction is 0.67. It is important to note that the units for Kc are not included in the given information, but they would typically be in units of mol/L.

In summary, by using the principles of equilibrium and setting up an ICE table, we were able to solve for the unknown values and calculate the equilibrium constant for this reaction.