Question

A 0.050 mol sample of formaldehyde vapor, \(\mathrm{CH}_{2} \mathrm{O}\), was placed in a heated \(500 \mathrm{~mL}\) vessel and some of it decomposed. The reaction is $$ \mathrm{CH}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}(g) $$ At equilibrium, the \(\mathrm{CH}_{2} \mathrm{O}(g)\) concentration was \(0.066 \mathrm{~mol} \mathrm{~L}^{-1}\). Calculate the value of \(K_{\mathrm{c}}\) for this reaction.

Short answer

The equilibrium constant, Kc, for the reaction is 0.01752.

Step-by-step solution

Determine the initial concentrations

Convert the amount of formaldehyde (CH2O) to concentration using the volume of the vessel. Initial concentration is calculated by dividing the amount in moles by the volume of the vessel in liters. Since we have 0.050 mol CH2O in a 500 mL (0.500 L) vessel, the initial concentration of CH2O is 0.050 mol / 0.500 L = 0.100 M.

Calculate the change in concentration at equilibrium

The equilibrium concentration of CH2O is given as 0.066 M. The change in concentration of CH2O is the initial concentration minus the equilibrium concentration, which is 0.100 M - 0.066 M = 0.034 M. Since the reaction produces H2 and CO in a 1:1 ratio, the concentrations of H2 and CO will both be 0.034 M at equilibrium.

Write the expression for Kc

The equilibrium constant expression for this reaction is given by Kc = [H2][CO] / [CH2O].

Calculate Kc

Substitute the equilibrium concentrations into the Kc expression to find its value. Kc = (0.034 M)(0.034 M) / (0.066 M). Therefore, Kc = 0.001156 / 0.066 M, which simplifies to Kc = 0.01752.

Key concepts

Equilibrium Constant

When we talk about chemical reactions, the term equilibrium refers to a state where the rates of the forward and reverse reactions are equal. This does not necessarily mean that the amounts of reactants and products are equal, but rather that their concentrations do not change over time. The equilibrium constant, denoted as Kc, is a number that provides a quantitative measure of the position of equilibrium for a particular reaction at a given temperature.

The magnitude of the equilibrium constant gives us insight into the extent of a reaction. If Kc is much larger than 1, the concentration of products is much larger than the concentration of reactants at equilibrium, indicating a reaction that favors the formation of products. Conversely, if Kc is much less than 1, the reaction favors the reactants.

To calculate the equilibrium constant, we use the concentrations of the reactants and products measured at equilibrium. It is important to note that pure solids and liquids are not included in the Kc expression, only gases and aqueous solutions are. In the given exercise, the equilibrium constant is calculated using the equilibrium concentrations of formaldehyde (CH₂O), hydrogen (H₂), and carbon monoxide (CO) gases, resulting in a Kc value of 0.01752. This tells us that at equilibrium, a considerable amount of reactants remain compared to the products.

Equilibrium Concentration Calculations

Calculating the equilibrium concentrations of reactants and products in a chemical reaction involves understanding the reaction stoichiometry and applying the changes in concentrations that occur as the reaction approaches equilibrium. Often, this is done using an ICE table (Initial, Change, Equilibrium) to organize the data and solve for unknowns.

In our example, we started with the initial concentration of formaldehyde (CH₂O) and then calculated how much was left at equilibrium. The change in concentration (0.034 M) corresponded to the amounts of hydrogen (H₂) and carbon monoxide (CO) produced because they are formed in a 1:1 molar ratio with the decomposition of formaldehyde. Knowing these concentrations, we can solve for the equilibrium constant of the reaction. This process is crucial for predicting how a system will respond to changes in conditions such as pressure, temperature, or concentration of one of the components.

Understanding how to calculate equilibrium concentrations is a fundamental skill in chemistry. It allows us to predict the concentration of each species present when the system is at equilibrium, and can also help to determine if a system has reached equilibrium if we know the value of Kc.

Le Chatelier's Principle

Le Chatelier's Principle is a guiding rule in chemistry that predicts how a system at equilibrium will respond to changes in concentration, temperature or pressure. To put it simply, if a stress is applied to the system at equilibrium, the system will adjust itself in such a way as to counteract that stress.

For instance, if more reactants are added to a system, the principle suggests that the equilibrium will shift to form more products, thereby reducing the added reactants. Conversely, if a product is removed, the system will produce more of that product. This principle can also be applied to changes in temperature and pressure: increasing the temperature for an endothermic reaction will shift the equilibrium to the right, while increasing the pressure by decreasing the volume will favor the side of the reaction with fewer moles of gas.

In the context of our exercise, if additional formaldehyde were introduced into the system, according to Le Chatelier's Principle, the system would respond by converting some of the added formaldehyde into hydrogen and carbon monoxide, in an attempt to restore equilibrium. This concept is indispensable when attempting to increase the yield of a reaction or during the design of industrial chemical processes.