Question Video: Calculating the Units of a 𝐾_c Equation Chemistry • Third Year of Secondary School

Video Transcript

Find the units for the following 𝐾 𝑐 equation: 𝐾 𝑐 equals HI squared over H2 times I2. (A) Mole to the negative two decimeter to the power of six. (B) Mole to the power of two decimeters to the negative six. (C) No units. (D) Moles decimeters to the negative three. (E) Mole to the negative one decimeter to the power of three.

In this question, we need to determine the units for an equilibrium constant for concentration. Let’s first understand the 𝐾 𝑐 equation for this question. We can then replace variable, denominator, and numerator terms with appropriate concentration units. We can then simplify the 𝐾 𝑐 equation and determine the answer to this question.

Let us first clarify that, in its simplest form, the 𝐾 𝑐 can be written as the concentration of products over the concentration of reactants. The brackets are used to indicate concentration. Concentration is commonly measured in moles per cubic decimeter or in moles per liter. We can see from the answer choices that we can use moles per cubic decimeter for this question.

Let’s now have a look at the equilibrium reaction that the 𝐾 𝑐 equation represents. As hydrogen iodide is in the numerator, it is a product in this reaction. The exponent of two in the 𝐾 𝑐 equation mirrors the value of the stoichiometric coefficient in the chemical equation. The reactants of this equilibrium reaction are molecular hydrogen and iodine. This reaction generally occurs when the reactants and products are gases. The equilibrium reaction between molecular hydrogen and iodine to produce hydrogen iodide gives this 𝐾 𝑐 expression.

We can now replace the unit for concentration for each of the terms into the 𝐾 𝑐 equation. We end up with the term moles times decimeters to the negative three squared in the numerator. In the denominator, we have moles times decimeters to the negative three multiplied by moles times decimeters to the negative three. A term multiplied by itself is the same mathematical operation as raising to the power of two. Thus, the units in the numerator and the denominator are the same. These units would then cancel out. When we simplify, we get no units for this 𝐾 𝑐 equation.

Therefore, the correct answer for this question is answer choice (C) no units.