Video Transcript
At equilibrium, 𝐾 𝑐 equals 32
moles to the negative one decimeters cubed at 325 kelvin for the following reaction
involving oxides of sulfur. Two SO2 gas plus O2 gas are in
equilibrium with two SO3 gas. Find the value of 𝐾 𝑐, including
units, at 325 kelvin for the following reaction. Two SO3 gas is in equilibrium with
two SO2 gas plus O2 gas.
In this question, we are asked to
calculate the 𝐾 𝑐 of a reaction involving oxides of sulfur. The 𝐾 𝑐, or equilibrium constant
for concentrations, can be written in its simplest form as the concentration of the
products divided by the concentration of the reactants.
We can illustrate this using a
generic equilibrium equation. The equilibrium constant for this
reaction would be the concentrations of the products C and D multiplied together
divided by the concentrations of A and B multiplied together. Brackets are used to express
concentration.
Some commonly used units for
concentration are moles per cubic decimeter. The concentrations of all species
must be raised to the power of their stoichiometric coefficients. We are given the 𝐾 𝑐 value of the
first reaction, which we will call reaction one. We need to solve for the value of
the 𝐾 𝑐 for the second reaction, which we will call reaction two. Let’s write the equilibrium
constant for concentration for both reactions to see how they relate.
We will start with reaction
one. We can write the concentration of
the product, sulfur trioxide, divided by the concentrations of the reactants, sulfur
dioxide and oxygen, multiplied together. We will raise them to the power of
their stoichiometric coefficients, with exponents of one being left unwritten. The 𝐾 𝑐 value for reaction one is
32 moles to the negative one cubic decimeters. You might also see these units
written as a fraction, or cubic decimeters per mole.
We can repeat this for reaction
two. We can compare how these two
equilibrium constant expressions relate. We can see that they are
reciprocals of each other. This means the 𝐾 𝑐 values will
also be reciprocals. So we can solve for the equilibrium
constant of reaction two by calculating the reciprocal of the equilibrium constant
of reaction one, which is 32 moles to the negative one cubic decimeters. The reciprocal of 32 is
0.03125.
To find the reciprocal units, we
change the signs of the exponents. This gives us units of moles times
decimeters to the negative three, or in other words moles per cubic decimeter. You may also see these units
written as a fraction, or moles per cubic decimeter.
Therefore, the value of 𝐾 𝑐 for
the reaction is 0.03125 moles times decimeters to the negative three.
