Chemical Equilibrium Calculating Moles Of N-Butane At Equilibrium

In the realm of chemical kinetics and thermodynamics, the concept of chemical equilibrium holds immense significance. It dictates the extent to which a reversible reaction proceeds, the relative amounts of reactants and products present at the steady state, and the influence of external factors on reaction outcomes. This article delves into a practical scenario involving the isomerization of n-butane to isobutane, a reaction governed by an equilibrium constant, to illustrate the principles of chemical equilibrium and its quantitative aspects.

Chemical Equilibrium A Dynamic State

Chemical equilibrium is not a static condition where a reaction ceases to occur; rather, it's a dynamic state where the rates of the forward and reverse reactions are equal. Imagine a bustling marketplace where people are constantly moving between stalls, buying and selling goods. At equilibrium, the overall number of people at each stall remains constant, even though individuals are constantly changing positions. Similarly, in a chemical reaction at equilibrium, the concentrations of reactants and products remain constant because the rate at which reactants transform into products equals the rate at which products transform back into reactants.

The equilibrium constant, denoted as K, is a numerical value that quantifies the relative amounts of reactants and products at equilibrium. For a generic reversible reaction:

aA + bB ⇌ cC + dD

where a, b, c, and d are the stoichiometric coefficients, the equilibrium constant expression is:

K = ([C]^c [D]^d) / ([A]^a [B]^b)

A large value of K indicates that the equilibrium favors the formation of products, while a small value suggests that the equilibrium favors the reactants. The equilibrium constant is a powerful tool for predicting the direction in which a reaction will shift to reach equilibrium under a given set of conditions.

Factors Affecting Equilibrium Le Chatelier's Principle

Le Chatelier's Principle provides a qualitative framework for understanding how changes in external conditions affect chemical equilibrium. This principle states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress. These changes can include:

• Changes in Concentration: Adding reactants or removing products will shift the equilibrium towards the product side, while adding products or removing reactants will shift it towards the reactant side.
• Changes in Pressure: For reactions involving gases, increasing the pressure will favor the side with fewer moles of gas, while decreasing the pressure will favor the side with more moles of gas.
• Changes in Temperature: For exothermic reactions (releasing heat), increasing the temperature will shift the equilibrium towards the reactants, while decreasing the temperature will favor the products. For endothermic reactions (absorbing heat), the opposite is true.

Understanding these principles is critical for optimizing reaction conditions to maximize product yield in industrial processes.

The n-Butane Isobutane Equilibrium A Case Study

The isomerization of n-butane to isobutane is a classic example of a reversible reaction that establishes equilibrium. At a given temperature, n-butane can convert into isobutane, and isobutane can revert back to n-butane. The equilibrium constant (K) for this reaction is a crucial parameter that dictates the relative amounts of these two isomers at equilibrium. In this case, K = 2.5, indicating that at equilibrium, isobutane is favored over n-butane.

Problem Scenario Injecting n-Butane into a Container

Consider a scenario where 140 moles of n-butane are injected into a 20-liter container. The n-butane molecules will start to isomerize into isobutane, and simultaneously, isobutane molecules will revert to n-butane. This process continues until the system reaches equilibrium. The key question is: How many moles of n-butane will remain once equilibrium is established?

To solve this problem, we'll use the ICE table method, a systematic approach for calculating equilibrium concentrations.

Solving for Equilibrium Concentrations The ICE Table Method

The ICE table method provides a structured way to determine the equilibrium concentrations of reactants and products. ICE stands for Initial, Change, and Equilibrium, representing the three stages of the calculation.

Step 1 Initial Conditions

First, we need to determine the initial concentrations of n-butane and isobutane. Since we start with 140 moles of n-butane in a 20-liter container, the initial concentration of n-butane is:

[n-butane]Initial = (140 moles) / (20 liters) = 7.0 M

The initial concentration of isobutane is 0 M since we start with only n-butane.

Step 2 Change in Concentrations

Let's assume that 'x' moles per liter of n-butane convert to isobutane as the reaction proceeds towards equilibrium. This means the change in concentration of n-butane will be -x, and the change in concentration of isobutane will be +x. The balanced reaction is:

n-butane ⇌ isobutane

The stoichiometric coefficients are both 1, indicating a 1:1 mole ratio for the conversion.

Step 3 Equilibrium Concentrations

At equilibrium, the concentrations of n-butane and isobutane will be:

[n-butane]Equilibrium = 7.0 - x

[isobutane]Equilibrium = 0 + x = x

Step 4 Applying the Equilibrium Constant

Now, we can use the equilibrium constant expression to relate the equilibrium concentrations:

K = [isobutane] / [n-butane] = x / (7.0 - x) = 2.5

We are given that K = 2.5. Now we can solve for x:

2. 5(7.0 - x) = x
3. 5 - 2.5x = x
4. 5 = 3.5x x = 17.5 / 3.5 = 5.0 M

Step 5 Calculating Moles of n-Butane at Equilibrium

Now that we have the value of x, we can calculate the equilibrium concentration of n-butane:

[n-butane]Equilibrium = 7.0 - x = 7.0 - 5.0 = 2.0 M

To find the number of moles of n-butane at equilibrium, we multiply the equilibrium concentration by the volume of the container:

Moles of n-butane = (2.0 M) * (20 liters) = 40 moles

Therefore, when equilibrium is reached, 40 moles of n-butane will remain.

Conclusion Significance of Chemical Equilibrium

Understanding chemical equilibrium is essential in various scientific and industrial applications. In this article, we explored the concept of chemical equilibrium through the isomerization of n-butane to isobutane. We utilized the equilibrium constant and the ICE table method to calculate the equilibrium concentrations and the number of moles of n-butane remaining at equilibrium.

Applications in Industry and Research

• Industrial Chemistry: Chemical equilibrium principles are crucial in optimizing reaction conditions to maximize product yield in chemical industries. Catalysts, temperature, pressure, and reactant concentrations are carefully controlled to shift the equilibrium towards desired products.
• Environmental Science: Equilibrium considerations are vital in understanding the distribution of pollutants in the environment and designing remediation strategies. For example, the equilibrium between dissolved carbon dioxide and carbonic acid in water affects the pH of aquatic ecosystems.
• Biochemistry: Many biochemical reactions in living organisms are reversible and reach equilibrium. Enzymes play a crucial role in accelerating these reactions and maintaining optimal concentrations of reactants and products.

Final Thoughts

In conclusion, chemical equilibrium is a dynamic state that governs the extent of reversible reactions. The equilibrium constant provides a quantitative measure of the relative amounts of reactants and products at equilibrium. By understanding the factors that influence equilibrium and applying methods like the ICE table, we can predict and manipulate chemical reactions to achieve desired outcomes. This knowledge is fundamental to various fields, from chemical synthesis to environmental science and biochemistry.

By mastering the concepts of chemical equilibrium, students and professionals alike can gain a deeper understanding of the intricate chemical processes that shape our world. Whether it's optimizing industrial production or comprehending biological systems, the principles of equilibrium provide a powerful framework for analysis and problem-solving.