# What Is The Equilibrium Constant Expression For The Given System

What Is The Equilibrium Constant Expression For The Given System – Since equilibrium is reached when the rate of the forward reaction equals the rate of the reverse reaction, for a given set of conditions there must be a relationship between the composition of the system at equilibrium and the kinetics of the reaction (represented by the rate constant). We can show this relationship using the system described in equation ref, of the decomposition of (N_2O_4) into (NO_2). Both the forward and reverse reactions for this system consist of one elementary reaction, so the reaction rate is:

The ratio of the rate constants gives us a new constant, the equilibrium constant ((K)), which is defined as follows:

## What Is The Equilibrium Constant Expression For The Given System

Thus, there is a significant connection between ical kinetics and ical equilibrium: under a given set of conditions, the composition of the equilibrium mixture is determined by the values ​​of the rate constants for the forward and reverse reactions.

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The equilibrium constant is equal to the rate constant of the forward reaction divided by the rate constant of the reverse reaction.

In 1864, the Norwegians Kato Guldberg (1836-1902) and Peter Waage (1833-1900) carefully measured the compositions of many reaction systems in a state of equilibrium. They found that for any reversible reaction of the general kind

Where A and B are reactants, C and D are products, a, b, c and d are stoichiometric coefficients in the balanced chemical reaction equation, the ratio of the product of the equilibrium concentrations of the products (raised to their coefficients in the balanced chemical equation) to the product of the equilibrium concentrations of the reactants ( reduced to their coefficients in the balanced equation) is always a constant under a given set of conditions. This dependence is known as the law of mass action and can be expressed as follows:

Where (K) is the reaction equilibrium constant. The equation ref is called the equilibrium equation, and the right-hand side of the equation ref is called the expression for the equilibrium constant. The relationship shown in equation ref is valid for any pair of opposite reactions, regardless of the reaction mechanism or the number of steps in the mechanism.

### Answered] Write The Equilibrium Constant Expression…

You will also notice in the (PageIndex) table that the equilibrium constants have no units, although the ref equation suggests that the concentration units may not always cancel since the exponents may change. In fact, equilibrium constants are calculated using “effective concentrations” or reactant and product activities, which are ratios of concentrations measured under a standard condition of 1 M. As shown in equation ref, the units of concentration are offset, which also makes ( K) dimensionless:

And (K) varies from 1.9 to 4 in a wide range of temperatures (100-1000 K). Thus, the equilibrium mixture of (H_2), (D_2) and (HD) contains significant concentrations of both product and reactants.

Figure (PageIndex) summarizes the relationship between the value of K and the relative concentrations of reactants and products at equilibrium for the overall reaction, written as

Since there is a direct relationship between the reaction kinetics and the equilibrium concentrations of products and reactants (equations ref and ref), when (k_f gg k_r), (K) is a large number and the equilibrium concentration of products dominates. This corresponds to an essentially irreversible reaction. In contrast, when (k_f ll k_r), (K) is a very small number and the reaction gives almost no product as written. Systems for which (k_f ≈ k_r) have significant concentrations of both reactants and products in equilibrium.

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Figure (PageIndex): The relationship between the composition of the mixture at equilibrium and the value of the equilibrium constant. The greater K, the further to the right the reaction flows before reaching equilibrium, and the greater the ratio of products and reactants at equilibrium.

A large value of the equilibrium constant (K) means that the products prevail in the equilibrium; a small value means that reactants predominate in the equilibrium state.

Refer to equation ref. Place the arithmetic product of the concentrations of the products (reduced to their stoichiometric ratios) in the numerator and the product of the concentrations of the reactants (reduced to their stoichiometric ratios) in the denominator.

The only product is ammonia, which has a coefficient of 2. For reactants (N_2) has a coefficient of 1, and H2 has a coefficient of 3. The equilibrium constant has the following expression:

## Answered: Write The Equilibrium Constant…

The only product is carbon dioxide, the coefficient of which is equal to 1. The reactants are (CO), with a coefficient of 1, and (O_2), with a coefficient of (frac). Thus, the expression of the equilibrium constant has the following form:

This reaction is the reverse of the reaction in part b, with all coefficients multiplied by 2 to remove the fractional coefficient for (O_2). Thus, the expression for the equilibrium constant is the inverse of the expression in part b, where all exponents are multiplied by 2:

Predict which systems at equilibrium will (a) contain only products, (b) contain only reactants, and (c) contain significant amounts of both products and reactants.

Use the value of the equilibrium constant to determine whether the equilibrium mixture will contain essentially only products, essentially only reactants, or significant amounts of both.

## Law Of Mass Action Definition And Equation

At what temperature would you expect to find the largest percentage of (H_2) and (N_2) in the equilibrium mixture?

Assuming the reaction rate is high enough to reach equilibrium quickly, at what temperature would you design a commercial reactor to operate to maximize ammonia yield?

Since equilibrium can be approached from any direction in an exit reaction, the expression for the equilibrium constant and thus the value of the equilibrium constant depend on the form in which the exit reaction is written. For example, if we write the reaction described in equation 15.2.6 in reverse order, we get the following:

This expression is the inverse of the expression for the initial equilibrium constant, i.e. (K′ = 1/K). That is, when we write the reaction in the opposite direction, the expression for the equilibrium constant changes to the opposite. For example, the equilibrium constant for the reaction (N_2O_4) rightleftharpoons 2NO_2) has the following form:

## Writing An Equilibrium Constant

But for the reverse reaction, (2 NO_2 right-leftharpoons N_2O_4), the equilibrium constant K′ is determined by the opposite expression:

Writing the equation in a different but equivalent form also causes the expression for the equilibrium constant and the magnitude of the equilibrium constant to differ. For example, we can write the reaction equation

Write an expression for the equilibrium constant for this reaction and for each related reaction. From these expressions, calculate (K) for each reaction.

The expression of the equilibrium constant for this reaction (N_) with (H_) with the formation of (NH_) at 745 K is as follows:

#### Solved: Write The Equilibrium Constant Expression For The Following Reaction. Cacoâ‚ƒ(s) â†’ Cao(s) + Coâ‚‚(g) Group Of Answer Choices: K = [cao][coâ‚‚]/[cacoâ‚ƒ] K = [coâ‚‚]/[cao] K = [cacoâ‚ƒ]/[cao] K = P(coâ‚‚)

In this reaction, the stoichiometric coefficients of this reaction are divided by 2, so the equilibrium constant is calculated as follows:

The ratio of the rate constants of forward and reverse reactions at equilibrium is the equilibrium constant (K), a unitless quantity. Therefore, the composition of the equilibrium mixture is determined by the value of the forward and reverse velocity constants in the equilibrium state. Under this set of conditions, the reaction will always have the same (K). For an equilibrium system, the law of mass action relates (K) to the ratio of the equilibrium concentrations of the products to the concentrations of the reactants raised to appropriate powers to match the coefficients in the equilibrium equation. The ratio is called the expression of the equilibrium constant. When the reaction is written in the opposite direction, (K) and the expression for the equilibrium constant are reversed. For gases, the expression for the equilibrium constant can be written as the ratio of the partial pressures of the products to the partial pressures of the reactants, each raised to the power corresponding to its coefficient in the equation ik. Equilibrium constant calculated based on partial pressures ((K_p)) related to (K) based on ideal gas constant ((R)), temperature ((T)) and change in number of moles gas during the reaction. An equilibrium system containing products and reactants in one phase is a homogeneous equilibrium; a system in which reactants, products, or both are in more than one phase is a heterogeneous equilibrium. If a reaction can be expressed as the sum of two or more reactions, its equilibrium constant is equal to the product of the equilibrium constants for the individual reactions.

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