Calculating K For Overall Reaction: Videos & Practice Problems

Chemical reactions often occur in multiple steps, each with its own equilibrium constant. To calculate the equilibrium constant (K_eq) for the overall reaction, you must consider the equilibrium constants of the individual steps. The process involves locating each compound from the overall reaction within the partial reactions, ensuring they match in number and phase. If a compound appears in multiple reactions, skip it. You may need to reverse or multiply the partial reactions, affecting the equilibrium constant. After aligning the reactions correctly, combine them, canceling out intermediates—compounds that appear as both reactants and products. The overall Keq is then found by multiplying the constants of the partial reactions. This method ensures the accurate determination of the equilibrium constant for complex reactions, which is crucial for predicting the reaction's behavior and understanding chemical kinetics and thermodynamics.

Overall Reaction Equilibrium Constant

In many chemical reactions, achieving the final product requires multiple steps, each with its own equilibrium constant. The overall equilibrium constant, denoted as \( K_{eq} \), can be calculated by multiplying the equilibrium constants of the individual steps. This process involves several systematic steps to ensure accuracy.

To illustrate this, consider a reaction where 1 mole of solid carbon reacts with 1 mole of carbon dioxide gas to produce 2 moles of carbon monoxide gas. To find the overall equilibrium constant, we start by identifying the relevant partial reactions and their equilibrium constants.

First, locate the compounds from the overall reaction in the partial reactions. For instance, if solid carbon appears as a product in a partial reaction, it must be reversed to match its role as a reactant in the overall reaction. Reversing a reaction changes the equilibrium constant to its inverse. For example, if the equilibrium constant for the reversed reaction is \( K \), the new constant becomes \( \frac{1}{K} \).

Next, if a compound appears in multiple partial reactions, it should be skipped to avoid double counting. If the required amount of a compound differs from what is available in a partial reaction, the entire reaction can be multiplied by a factor to match the coefficients. This multiplication also affects the equilibrium constant, raising it to the power of the factor used.

After adjusting the reactions, any intermediates—compounds that appear as both reactants and products—should be canceled out. This step ensures that only the relevant reactants and products remain, allowing for the reconstruction of the overall reaction.

Finally, to find the overall equilibrium constant, multiply the adjusted equilibrium constants from the partial reactions. For example, if the adjusted constants are \( K_1 \) and \( K_2 \), the overall constant is calculated as:

\[ K_{eq} = K_1 \times K_2 \]

In our example, if \( K_1 \) is derived from squaring a previous constant and \( K_2 \) is the inverse of another, the final calculation yields an overall \( K_{eq} \) of approximately 2.13 when rounded to three significant figures. This value represents the equilibrium constant for the overall reaction, encapsulating the contributions of each step in the process.

Calculate K_c for: C(s) + ½ O₂(g) + H₂(g) ⇌ ½ CH₃OH(g) + ½ CO(g)  K_c = ?
Given the following reactions:
4 C(s) + 2 O₂(g) ⇌ 4 CO(g)                               K_p = 2.11 x 10⁴³
CH₃OH(g) + H₂O(g) ⇌ CO₂(g) + 3 H₂(g)          K_p = 7.17 x 10^–2
CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g)                     K_p = 2.00 x 10³

• A. 1.13×10¹³
• B. 5.60×10¹³
• C. 1.37×10¹⁵
• D. 5.35×10¹³

Answer: (B)

Here’s what students ask on this topic:

When we add two reactions together, how can we determine the value of the equilibrium constant for the new reaction?

When you add two chemical reactions together to form a new reaction, the equilibrium constant for the new reaction can be determined by multiplying the equilibrium constants of the original reactions. This is because the equilibrium constant, denoted as K, is a reflection of the ratio of the concentrations of the products to reactants, each raised to the power of their stoichiometric coefficients.

For example, if you have two reactions:

1. A → B with equilibrium constant K₁
2. B → C with equilibrium constant K₂

And you add them to get the new reaction:

A → C

The equilibrium constant for this new reaction, K₃, is the product of K₁ and K₂:

K₃ = K₁ * K₂

This relationship holds because the equilibrium constant is derived from the rate constants of the forward and reverse reactions, and when reactions are added, their rate constants multiply in a way that leads to the multiplication of their equilibrium constants. Remember, this only applies if the reactions are added in such a way that intermediates like B in this example are the same (i.e., they cancel out).

The table above provides the Keq values for two reactions. What is the correct mathematical expression needed to determine the equilibrium constant of the reaction shown below?

To answer your question, I need to clarify that the table mentioned is not visible in your query. However, I can guide you on how to determine the equilibrium constant (K_eq) for a given reaction using the K_eq values of other reactions.

If you have two reactions:

1. A -> B with K_eq = K_eq1
2. C -> D with K_eq = K_eq2

And you want to determine the K_eq for a new reaction that is a combination of the two, such as:

A + C -> B + D

You would use the following mathematical expression:

$K{\mathrm{eq}}_{\text{new reaction}}=K{\mathrm{eq}}_1\cdot K{\mathrm{eq}}_2$

This is because the equilibrium constants of individual reactions multiply when reactions are added together.

If the new reaction is the reverse of one of the given reactions, you would take the reciprocal of the K_eq value for that reaction. If the stoichiometry of a reaction is multiplied by a coefficient, you would raise the K_eq to the power of that coefficient.

For example, if the new reaction is the reverse of Reaction 1, the expression would be:

$K{\mathrm{eq}}_{}$