Calculate Kc For H2(g) + I2(g) ⇌ 2 HI(g) A Step-by-Step Guide

Hey guys! Ever wondered how to calculate the equilibrium constant, Kc, for a reversible reaction? Today, we're diving into a super practical example: calculating Kc for the formation of hydrogen iodide (HI) from hydrogen (H2) and iodine (I2) at 250°C. This is a classic chemistry problem, and by the end of this article, you'll be able to tackle similar calculations with confidence. We will break down each step in detail, ensuring you grasp the underlying concepts and can apply them to various scenarios. So, buckle up and let's get started on this exciting chemical journey!

The Reaction and the Problem Setup

First, let's understand the reaction we're dealing with. We're looking at the reversible reaction where hydrogen gas (H2) and iodine gas (I2) react to form hydrogen iodide gas (HI). The balanced chemical equation is:

H2(g) + I2(g) ⇌ 2 HI(g)

This equation tells us that one mole of H2 reacts with one mole of I2 to produce two moles of HI. The double arrow (⇌) signifies that the reaction is reversible, meaning it can proceed in both forward (reactants to products) and reverse (products to reactants) directions. This reversibility is crucial for understanding chemical equilibrium.

The problem gives us specific conditions: the reaction occurs in a 10-liter container at 250°C. Initially, we have 2 moles of I2 and 4 moles of H2. After the reaction reaches equilibrium, 3 moles of HI are formed. Our mission, should we choose to accept it, is to calculate the value of Kc, the equilibrium constant, at this temperature. Kc is a quantitative measure of the extent to which a reaction proceeds to completion at a given temperature. A large Kc indicates that the reaction favors the formation of products, while a small Kc suggests the reaction favors the reactants.

Understanding the Importance of Kc

Before we jump into the calculations, let's take a moment to appreciate why Kc is such a big deal in chemistry. Kc provides invaluable insights into the behavior of chemical reactions. It tells us the relative amounts of reactants and products at equilibrium, which is essential for predicting reaction outcomes and optimizing reaction conditions. For instance, in industrial processes, knowing Kc can help chemists determine the optimal temperature and pressure to maximize product yield. In environmental chemistry, Kc can be used to assess the fate of pollutants in aquatic systems. Furthermore, in biochemistry, Kc plays a critical role in understanding enzyme-catalyzed reactions and metabolic pathways. The equilibrium constant is not just a number; it's a powerful tool for understanding and manipulating chemical reactions.

Setting Up the ICE Table

To solve this problem, we'll use a handy tool called the ICE table. ICE stands for Initial, Change, and Equilibrium. This table helps us organize the information and track the changes in the concentrations of reactants and products as the reaction reaches equilibrium. It is a systematic way to approach equilibrium problems and ensures that we account for the stoichiometry of the reaction correctly. Many students find the ICE table method to be a lifesaver when dealing with equilibrium calculations. It breaks down a potentially complex problem into manageable steps.

Here's how we set up the ICE table for our reaction:

Now, let's fill in the table with the information we have. Remember, we need to work with concentrations (moles per liter), not just moles, since Kc is defined in terms of concentrations.

1. Initial Concentrations (I)

• We start with 4 moles of H2 in a 10-liter container, so the initial concentration of H2 is 4 moles / 10 liters = 0.4 M.
• We start with 2 moles of I2 in a 10-liter container, so the initial concentration of I2 is 2 moles / 10 liters = 0.2 M.
• Initially, there's no HI, so the initial concentration of HI is 0 M.

We can now update our ICE table:

2. Change in Concentrations (C)

This is where we consider how the concentrations change as the reaction proceeds. We're told that 3 moles of HI are formed at equilibrium. This is a crucial piece of information that allows us to determine the changes in the concentrations of the reactants.

• At equilibrium, we have 3 moles of HI in 10 liters, so the equilibrium concentration of HI is 3 moles / 10 liters = 0.3 M.
• Since 2 moles of HI are formed for every 1 mole of H2 and 1 mole of I2 that react, we can deduce the changes in the concentrations of H2 and I2.
• Let's use 'x' to represent the change in concentration of H2 and I2. Since they are reactants, their concentrations will decrease, so the change will be -x.
• For HI, the concentration increases, and since 2 moles of HI are formed, the change will be +2x.

Now, we know that the equilibrium concentration of HI is 0.3 M, and the initial concentration was 0 M, so the change (2x) must be equal to 0.3 M.

2x = 0.3 M x = 0.15 M

This means the concentrations of H2 and I2 decreased by 0.15 M.

We can now update the 'Change' row in our ICE table:

3. Equilibrium Concentrations (E)

Finally, we can calculate the equilibrium concentrations by adding the 'Initial' and 'Change' rows:

• [H2]equilibrium = 0.4 M - 0.15 M = 0.25 M
• [I2]equilibrium = 0.2 M - 0.15 M = 0.05 M

We already know [HI]equilibrium = 0.3 M.

Our completed ICE table looks like this:

With our ICE table complete, we're now ready to calculate Kc. The ICE table is a powerful tool for visualizing and organizing the changes in concentrations during a reaction, making the calculation of equilibrium constants much more straightforward.

Calculating Kc

Now that we have all the equilibrium concentrations, we can finally calculate Kc. The equilibrium constant, Kc, is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their stoichiometric coefficients in the balanced chemical equation. Remember, coefficients are the numbers in front of the chemical formulas in the balanced equation.

For our reaction, H2(g) + I2(g) ⇌ 2 HI(g), the expression for Kc is:

Kc = [HI]^2 / ([H2] * [I2])

Notice that the concentration of HI is squared because its coefficient in the balanced equation is 2. The concentrations of H2 and I2 are raised to the power of 1 because their coefficients are 1.

Now, we simply plug in the equilibrium concentrations we calculated from the ICE table:

Kc = (0.3 M)^2 / (0.25 M * 0.05 M) Kc = 0.09 M^2 / 0.0125 M^2 Kc = 7.2

So, the equilibrium constant, Kc, for the formation of hydrogen iodide at 250°C is 7.2. This value tells us that at equilibrium, the ratio of products to reactants is 7.2, indicating that the reaction favors the formation of HI at this temperature.

Interpreting the Value of Kc

The magnitude of Kc provides valuable information about the extent to which a reaction proceeds to completion. In our case, Kc = 7.2 is a moderate value. This suggests that at equilibrium, there is a significant amount of both reactants and products present. If Kc were much larger (e.g., > 100), it would indicate that the reaction strongly favors the formation of products, and the equilibrium mixture would contain mostly HI. Conversely, if Kc were much smaller (e.g., < 0.01), it would indicate that the reaction favors the reactants, and the equilibrium mixture would contain mostly H2 and I2.

Key Takeaways

Let's recap the key steps we took to calculate Kc:

1. Write the balanced chemical equation: This gives us the stoichiometry of the reaction, which is crucial for setting up the Kc expression and the ICE table.
2. Set up the ICE table: This helps us organize the initial concentrations, changes in concentrations, and equilibrium concentrations.
3. Determine the changes in concentrations: Use the information given in the problem (like the amount of product formed at equilibrium) to find the value of 'x', which represents the change in concentration.
4. Calculate the equilibrium concentrations: Add the 'Initial' and 'Change' rows in the ICE table to find the concentrations at equilibrium.
5. Write the Kc expression: This is the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients.
6. Plug in the equilibrium concentrations and calculate Kc: This gives us the numerical value of the equilibrium constant.
7. Interpret the value of Kc: A large Kc indicates that the reaction favors products, while a small Kc indicates that the reaction favors reactants.

By following these steps, you can confidently calculate Kc for any reversible reaction. Understanding how to calculate and interpret equilibrium constants is a fundamental skill in chemistry, with applications in various fields, from industrial chemistry to environmental science.

Practice Makes Perfect

The best way to master calculating Kc is to practice, practice, practice! Try working through similar problems with different initial conditions and different reactions. You can find plenty of practice problems in chemistry textbooks and online resources. Don't be afraid to make mistakes – they're a valuable part of the learning process. Each time you work through a problem, you'll reinforce your understanding of the concepts and become more comfortable with the calculations.

For example, try changing the initial moles of reactants or the volume of the container and see how it affects the equilibrium concentrations and the value of Kc. You can also explore reactions with different stoichiometric coefficients to further challenge yourself. Remember, chemistry is like learning a new language – the more you practice, the more fluent you'll become!

So, there you have it! We've successfully calculated Kc for the formation of hydrogen iodide. Hopefully, this step-by-step guide has made the process clear and understandable. Remember, equilibrium is a dynamic state where the rates of the forward and reverse reactions are equal. Kc is a snapshot of this equilibrium, telling us the relative amounts of reactants and products at a given temperature. Keep practicing, and you'll become an equilibrium expert in no time!