Question Video: Calculating the Value of 𝐾_𝑐 for a Reaction Involving the Oxides of Sulfur Chemistry • Third Year of Secondary School

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.