What Is $K_{\text{eq}}$ For The Reaction $N_2 + 3 H_2 \rightleftharpoons 2 NH_3$ If The Equilibrium Concentrations Are $ [ N H 3 ] = 3 M [NH_3] = 3\, \text{M} [ N H 3 ​ ] = 3 M [/tex], $[N_2] = 1, \text{M}$, And $[H_2] = 2,

by ADMIN 231 views

Introduction

In chemistry, the equilibrium constant ($K_{\text{eq}}$) is a crucial concept that helps us understand the balance between reactants and products in a chemical reaction. It is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. In this article, we will explore the concept of $K_{\text{eq}}$ and how to calculate it for the reaction $N_2 + 3 H_2 \rightleftharpoons 2 NH_3$.

What is $K_{\text{eq}}$?

The equilibrium constant ($K_{\text{eq}}$) is a numerical value that represents the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. It is a dimensionless quantity, which means it has no units. The value of $K_{\text{eq}}$ depends on the specific reaction and the conditions under which it occurs.

Calculating $K_{\text{eq}}$

To calculate $K_{\text{eq}}$, we need to know the concentrations of the reactants and products at equilibrium. The general formula for calculating $K_{\text{eq}}$ is:

Keq=[products]stoichiometric coefficients[reactants]stoichiometric coefficientsK_{\text{eq}} = \frac{[\text{products}]^{\text{stoichiometric coefficients}}}{[\text{reactants}]^{\text{stoichiometric coefficients}}}

where $[\text{products}]$ and $[\text{reactants}]$ are the concentrations of the products and reactants, respectively, and the stoichiometric coefficients are the numbers of moles of each substance that participate in the reaction.

Applying the Formula to the Reaction $N_2 + 3 H_2 \rightleftharpoons 2 NH_3$

For the reaction $N_2 + 3 H_2 \rightleftharpoons 2 NH_3$, we are given the equilibrium concentrations of the reactants and products:

[NH3]=3 M[NH_3] = 3\, \text{M}

[N2]=1 M[N_2] = 1\, \text{M}

[H2]=2 M[H_2] = 2\, \text{M}

Using the formula for $K_{\text{eq}}$, we can calculate the value of $K_{\text{eq}}$ as follows:

Keq=[NH3]2[N2][H2]3K_{\text{eq}} = \frac{[NH_3]^2}{[N_2][H_2]^3}

Substituting the given values, we get:

Keq=(3 M)2(1 M)(2 M)3K_{\text{eq}} = \frac{(3\, \text{M})^2}{(1\, \text{M})(2\, \text{M})^3}

Simplifying the expression, we get:

Keq=9 M28 M3K_{\text{eq}} = \frac{9\, \text{M}^2}{8\, \text{M}^3}

Keq=98K_{\text{eq}} = \frac{9}{8}

Conclusion

In conclusion, the equilibrium constant ($K_{\text{eq}}$) is a crucial concept in chemistry that helps us understand the balance between reactants and products in a chemical reaction. We have calculated the value of $K_{\text{eq}}$ for the reaction $N_2 + 3 H_2 \rightleftharpoons 2 NH_3$ using the given equilibrium concentrations of the reactants and products.

Understanding the Significance of $K_{\text{eq}}$

The value of $K_{\text{eq}}$ is significant because it tells us about the favorability of a reaction. If $K_{\text{eq}}$ is greater than 1, the reaction favors the products. If $K_{\text{eq}}$ is less than 1, the reaction favors the reactants. If $K_{\text{eq}}$ is equal to 1, the reaction is at equilibrium.

Real-World Applications of $K_{\text{eq}}$

The concept of $K_{\text{eq}}$ has numerous real-world applications in various fields, including:

  • Chemical Engineering: $K_{\text{eq}}$ is used to design and optimize chemical reactors, which are essential in the production of chemicals and fuels.
  • Environmental Science: $K_{\text{eq}}$ is used to understand the behavior of pollutants in the environment and to design strategies for their removal.
  • Biotechnology: $K_{\text{eq}}$ is used to understand the behavior of enzymes and other biomolecules, which are essential in the production of bioproducts.

Conclusion

Q: What is the difference between $K_{\text{eq}}$ and $K_{\text{c}}$?

A: $K_{\text{eq}}$ and $K_{\text{c}}$ are both equilibrium constants, but they are used in different contexts. $K_{\text{c}}$ is used to describe the equilibrium constant in terms of concentrations, while $K_{\text{eq}}$ is used to describe the equilibrium constant in terms of activities.

Q: How do I calculate $K_{\text{eq}}$ for a reaction?

A: To calculate $K_{\text{eq}}$, you need to know the concentrations of the reactants and products at equilibrium. You can use the formula:

Keq=[products]stoichiometric coefficients[reactants]stoichiometric coefficientsK_{\text{eq}} = \frac{[\text{products}]^{\text{stoichiometric coefficients}}}{[\text{reactants}]^{\text{stoichiometric coefficients}}}

Q: What is the significance of $K_{\text{eq}}$?

A: The value of $K_{\text{eq}}$ tells us about the favorability of a reaction. If $K_{\text{eq}}$ is greater than 1, the reaction favors the products. If $K_{\text{eq}}$ is less than 1, the reaction favors the reactants. If $K_{\text{eq}}$ is equal to 1, the reaction is at equilibrium.

Q: How do I determine the equilibrium constant ($K_{\text{eq}}$) for a reaction?

A: To determine the equilibrium constant ($K_{\text{eq}}$) for a reaction, you need to know the concentrations of the reactants and products at equilibrium. You can use the formula:

Keq=[products]stoichiometric coefficients[reactants]stoichiometric coefficientsK_{\text{eq}} = \frac{[\text{products}]^{\text{stoichiometric coefficients}}}{[\text{reactants}]^{\text{stoichiometric coefficients}}}

Q: What is the relationship between $K_{\text{eq}}$ and the reaction quotient ($Q$)?

A: The reaction quotient ($Q$) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at a given point in time. The equilibrium constant ($K_{\text{eq}}$) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. If $Q = K_{\text{eq}}$, the reaction is at equilibrium.

Q: How do I use $K_{\text{eq}}$ to predict the direction of a reaction?

A: To predict the direction of a reaction, you can use the formula:

Q=[products]stoichiometric coefficients[reactants]stoichiometric coefficientsQ = \frac{[\text{products}]^{\text{stoichiometric coefficients}}}{[\text{reactants}]^{\text{stoichiometric coefficients}}}

If $Q > K_{\text{eq}}$, the reaction will shift to the left, favoring the reactants. If $Q < K_{\text{eq}}$, the reaction will shift to the right, favoring the products.

Q: What is the relationship between $K_{\text{eq}}$ and the temperature of a reaction?

A: The equilibrium constant ($K_{\text{eq}}$) is a function of temperature. As the temperature increases, the value of $K_{\text{eq}}$ also increases. This is because higher temperatures provide more energy for the reactants to form products.

Q: How do I calculate the equilibrium constant ($K_{\text{eq}}$) for a reaction at a given temperature?

A: To calculate the equilibrium constant ($K_{\text{eq}}$) for a reaction at a given temperature, you need to know the concentrations of the reactants and products at equilibrium. You can use the formula:

Keq=[products]stoichiometric coefficients[reactants]stoichiometric coefficientsK_{\text{eq}} = \frac{[\text{products}]^{\text{stoichiometric coefficients}}}{[\text{reactants}]^{\text{stoichiometric coefficients}}}

You also need to know the temperature at which the reaction occurs. You can use the formula:

ΔG∘=−RTln⁡Keq\Delta G^{\circ} = -RT \ln K_{\text{eq}}

to calculate the change in Gibbs free energy ($\Delta G^{\circ}$) for the reaction. You can then use the formula:

Keq=e−ΔG∘/RTK_{\text{eq}} = e^{-\Delta G^{\circ}/RT}

to calculate the equilibrium constant ($K_{\text{eq}}$) for the reaction.

Conclusion

In conclusion, the equilibrium constant ($K_{\text{eq}}$) is a fundamental concept in chemistry that helps us understand the balance between reactants and products in a chemical reaction. We have answered some frequently asked questions about $K_{\text{eq}}$ and provided examples of how to calculate it for a reaction.