What is $K_p$?

In chemistry, $K_p$ refers to the equilibrium constant for a chemical reaction expressed in terms of partial pressures of the gaseous reactants and products. It is a quantitative measure of the extent to which a chemical reaction proceeds towards completion.

Understanding $K_p$

Consider a general chemical reaction:

$$aA+bB\rightleftharpoons cC+dD$$

where A, B, C, and D represent chemical species, and a, b, c, and d are their respective stoichiometric coefficients. The equilibrium constant $K_p$ for this reaction is defined as the ratio of the partial pressures of the products raised to their stoichiometric coefficients to the partial pressures of the reactants raised to their stoichiometric coefficients, all at equilibrium. Mathematically, it can be expressed as:

$$K_p=\frac{p_C^c\cdot p_D^d}{p_A^a\cdot p_B^b}$$

where $p_A$, $p_B$, $p_C$, and $p_D$ represent the partial pressures of species A, B, C, and D, respectively, at equilibrium.

Significance of $K_p$

$K_p$ provides valuable insights into the behavior of chemical reactions:

• Predicting Reaction Direction: $K_p$ allows us to predict the direction in which a reaction will proceed to reach equilibrium. If $K_p$ is large, the reaction tends to proceed towards completion, favoring the formation of products. Conversely, if $K_p$ is small, the reaction favors the reactants, and the formation of products is limited.

• Quantifying Reaction Extent: The magnitude of $K_p$ indicates the extent to which a reaction proceeds towards completion. A large $K_p$ value suggests that the reaction reaches a higher degree of completion, while a small $K_p$ value indicates a limited extent of reaction.

• Comparing Reactions: $K_p$ values can be used to compare the relative tendencies of different reactions to reach equilibrium. Reactions with larger $K_p$ values are more likely to proceed towards completion compared to those with smaller $K_p$ values.

Factors Affecting $K_p$

The equilibrium constant $K_p$ is influenced by several factors:

• Temperature: $K_p$ is temperature-dependent. For exothermic reactions (reactions that release heat), $K_p$ decreases with increasing temperature, while for endothermic reactions (reactions that absorb heat), $K_p$ increases with increasing temperature.

• Pressure: $K_p$ is affected by pressure changes for reactions involving gases. Increasing pressure shifts the equilibrium towards the side with fewer moles of gas, while decreasing pressure favors the side with more moles of gas.

• Concentration: $K_p$ is independent of the initial concentrations of the reactants and products. However, changes in concentration can affect the rate at which equilibrium is reached, not the equilibrium position itself.

$K_p$ is a crucial concept in chemical equilibrium, providing a quantitative measure of the extent to which a reaction proceeds towards completion. By understanding $K_p$, chemists can gain insights into the behavior of chemical reactions, predict their direction, and compare their tendencies to reach equilibrium.

What is $K_c$?

$K_c$ is the equilibrium constant for a chemical reaction. It is a measure of the extent to which a reaction proceeds towards completion. The equilibrium constant is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to their respective stoichiometric coefficients.

For a general chemical reaction:

$$aA+bB\rightleftharpoons cC+dD$$

The equilibrium constant expression is:

$$K_c=\frac{[C{]}^c[D{]}^d}{[A{]}^a[B{]}^b}$$

where:

• $K_c$ is the equilibrium constant
• $A$, $B$, $C$, and $D$ are the chemical species involved in the reaction
• $a$, $b$, $c$, and $d$ are the stoichiometric coefficients of the respective species

The equilibrium constant is a constant at a given temperature and pressure. It is independent of the initial concentrations of the reactants and products.

The value of the equilibrium constant can be used to predict the direction of a reaction. If $K_c$ is large, the reaction will proceed towards completion. If $K_c$ is small, the reaction will not proceed very far.

The equilibrium constant can also be used to calculate the equilibrium concentrations of the reactants and products.

Applications of $K_c$

The equilibrium constant has a number of applications in chemistry. Some of these applications include:

• Predicting the direction of a reaction
• Calculating the equilibrium concentrations of reactants and products
• Designing chemical processes
• Understanding chemical equilibria

The equilibrium constant is a fundamental concept in chemistry. It is a measure of the extent to which a reaction proceeds towards completion. The equilibrium constant can be used to predict the direction of a reaction, calculate the equilibrium concentrations of reactants and products, and design chemical processes.

Equilibrium Constant Units

The equilibrium constant is a quantitative measure of the extent to which a chemical reaction proceeds towards completion. It is the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium, each raised to its stoichiometric coefficient.

The units of the equilibrium constant depend on the reaction being considered. For a general reaction of the form:

aA + bB ⇌ cC + dD

The equilibrium constant, Kc, is defined as:

$$K_c=\frac{[C{]}^c[D{]}^d}{[A{]}^a[B{]}^b}$$

where [A], [B], [C], and [D] are the concentrations of the respective species at equilibrium.

The units of Kc are determined by the units of the concentrations of the reactants and products. For example, if the concentrations are expressed in moles per liter (M), then the units of Kc will be M${}^{-x}$, where x is the sum of the stoichiometric coefficients of the reactants.

Units of Kp

For reactions involving gases, the equilibrium constant is often expressed in terms of partial pressures instead of concentrations. The equilibrium constant for a gas-phase reaction is called Kp and is defined as:

$$K_p=\frac{(P_C{)}^c(P_D{)}^d}{(P_A{)}^a(P_B{)}^b}$$

where P_A, P_B, P_C, and P_D are the partial pressures of the respective species at equilibrium.

The units of Kp are determined by the units of the partial pressures. For example, if the partial pressures are expressed in atmospheres (atm), then the units of Kp will be atm^x, where x is the sum of the stoichiometric coefficients of the reactants.

Units of Kw

For acid-base reactions in aqueous solutions, the equilibrium constant is called the acid dissociation constant, Kw. Kw is defined as the product of the hydrogen ion concentration ([$H^{+}$]) and the hydroxide ion concentration ([OH${}^{-}$]) at equilibrium:

$$K_w=[H^{+}][O{H}^{-}]$$

The units of Kw are (M)${}^2$, since both [$H^{+}$] and [OH${}^{-}$] are expressed in moles per liter.

Summary

The units of the equilibrium constant depend on the reaction being considered and the units used to express the concentrations or partial pressures of the reactants and products. The following table summarizes the units of the equilibrium constant for different types of reactions:

where x is the sum of the stoichiometric coefficients of the reactants.

Factors Affecting $K_p$ and $K_c$ Relation

The equilibrium constant $K_p$ is related to the equilibrium constant $K_c$ by the following equation:

$$K_p=K_c(RT{)}^{\mathrm{\Delta }n}$$

where:

• $K_p$ is the equilibrium constant in terms of partial pressures
• $K_c$ is the equilibrium constant in terms of concentrations
• $R$ is the ideal gas constant
• $T$ is the temperature in Kelvin
• $\mathrm{\Delta }n$ is the change in the number of moles of gas in the reaction

The following factors affect the relationship between $K_p$ and $K_c$:

Temperature

The temperature dependence of $K_p$ and $K_c$ is different. $K_p$ is independent of temperature, while $K_c$ varies with temperature. This is because the concentrations of the reactants and products in a reaction change with temperature, while the partial pressures do not.

Pressure

The pressure dependence of $K_p$ and $K_c$ is also different. $K_p$ is directly proportional to the pressure, while $K_c$ is independent of pressure. This is because the partial pressures of the reactants and products in a reaction change with pressure, while the concentrations do not.

Volume

The volume dependence of $K_p$ and $K_c$ is also different. $K_p$ is inversely proportional to the volume, while $K_c$ is independent of volume. This is because the concentrations of the reactants and products in a reaction change with volume, while the partial pressures do not.

Reactant and Product Concentrations

The concentrations of the reactants and products in a reaction affect both $K_p$ and $K_c$. An increase in the concentration of a reactant will increase $K_c$, while an increase in the concentration of a product will decrease $K_c$. The same is true for $K_p$, but the effect of pressure is also taken into account.

Catalyst

A catalyst affects the rate of a reaction, but it does not affect the equilibrium constant. This is because a catalyst does not change the concentrations of the reactants and products in a reaction.

The relationship between $K_p$ and $K_c$ is affected by several factors, including temperature, pressure, volume, reactant and product concentrations, and the presence of a catalyst. It is important to understand these factors in order to correctly use equilibrium constants in chemical calculations.

Difference Between $K_p$ and $K_c$

In chemical equilibrium, the equilibrium constant is a quantitative measure of the extent to which a chemical reaction proceeds. It is represented by the symbol $K$. There are two types of equilibrium constants: $K_p$ and $K_c$.

$K_p$ is the equilibrium constant expressed in terms of partial pressures. It is defined as the ratio of the partial pressures of the products to the partial pressures of the reactants, each raised to its stoichiometric coefficient.

$$K_p=\frac{P_{products}}{P_{reactants}}$$

where:

• $P_{products}$ is the partial pressure of the products
• $P_{reactants}$ is the partial pressure of the reactants

$K_c$ is the equilibrium constant expressed in terms of concentrations. It is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to its stoichiometric coefficient.

$$K_c=\frac{[products]}{[reactants]}$$

where:

• $[products]$ is the concentration of the products
• $[reactants]$ is the concentration of the reactants

Relation Between $K_p$ and $K_c$ in Chemical Equilibrium

In chemical equilibrium, the equilibrium constant $K$ is a measure of the extent to which a chemical reaction proceeds. It is defined as the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.

For a general chemical reaction,

$$aA+bB\rightleftharpoons cC+dD$$

the equilibrium constant $K_c$ is given by:

$$K_c=\frac{[C{]}^c[D{]}^d}{[A{]}^a[B{]}^b}$$

where [A], [B], [C], and [D] are the concentrations of the respective species at equilibrium.

The equilibrium constant $K_p$ is defined similarly, but it uses partial pressures instead of concentrations. For the same reaction as above, $K_p$ is given by:

$$K_p=\frac{(P_C{)}^c(P_D{)}^d}{(P_A{)}^a(P_B{)}^b}$$

where $P_A$, $P_B$, $P_C$, and $P_D$ are the partial pressures of the respective species at equilibrium.

The relationship between $K_p$ and $K_c$ can be derived using the ideal gas law. The ideal gas law states that the pressure of a gas is equal to the number of moles of gas per unit volume multiplied by the gas constant $R$ and the temperature $T$.

$$P=n/VRT$$

For a mixture of gases, the total pressure is the sum of the partial pressures of the individual gases. Therefore, for the reaction above, we have:

$$P_{total}=P_A+P_B+P_C+P_D$$

At equilibrium, the total pressure is constant. Therefore, we can write:

$$K_p=\frac{(P_C{)}^c(P_D{)}^d}{(P_A{)}^a(P_B{)}^b}=\frac{([C]/RT{)}^c([D]/RT{)}^d}{([A]/RT{)}^a([B]/RT{)}^b}$$

Simplifying this expression, we get:

$$K_p=K_c(RT{)}^{\mathrm{\Delta }n}$$

where $\mathrm{\Delta }n$ is the difference between the number of moles of products and the number of moles of reactants.

For a reaction that involves only gases, $\mathrm{\Delta }n$ is equal to the difference between the coefficients of the products and the coefficients of the reactants. For example, for the reaction

$$2H_2+O_2\rightleftharpoons 2H_{2}O$$

$\mathrm{\Delta }n$ is equal to 2 - 3 = -1. Therefore,

$$K_p=K_c(RT{)}^{-1}$$

For a reaction that involves both gases and liquids, $\mathrm{\Delta }n$ is equal to the difference between the number of moles of gaseous products and the number of moles of gaseous reactants. For example, for the reaction

$$CO(g)+H_{2}O(g)\rightleftharpoons C{O}_2(g)+H_2(g)$$

$\mathrm{\Delta }n$ is equal to 1 - 1 = 0. Therefore,

$$K_p=K_c$$

In general, the relationship between $K_p$ and $K_c$ is given by the equation:

$$K_p=K_c(RT{)}^{\mathrm{\Delta }n}$$

where $\mathrm{\Delta }n$ is the difference between the number of moles of gaseous products and the number of moles of gaseous reactants.

Relation Between $K_p$ and $K_c$ Derivation

In chemical thermodynamics, the equilibrium constant $K$ is a quantitative measure of the extent to which a chemical reaction proceeds towards completion. It is defined as the ratio of the activities of the products to the activities of the reactants, each raised to its stoichiometric coefficient.

For a general chemical reaction:

$$aA+bB\rightleftharpoons cC+dD$$

The equilibrium constant $K_c$ is given by:

$$K_c=\frac{[\text{C}{]}^c[\text{D}{]}^d}{[\text{A}{]}^a[\text{B}{]}^b}$$

where [A], [B], [C], and [D] are the concentrations of the respective species at equilibrium.

Relation Between $K_p$ and $K_c$

The equilibrium constant $K_p$ is defined in terms of partial pressures instead of concentrations. It is given by:

$$K_p=\frac{(p_{\text{C}}{)}^c(p_{\text{D}}{)}^d}{(p_{\text{A}}{)}^a(p_{\text{B}}{)}^b}$$

where $p_{\text{A}}$, $p_{\text{B}}$, $p_{\text{C}}$, and $p_{\text{D}}$ are the partial pressures of the respective species at equilibrium.

The relation between $K_p$ and $K_c$ can be derived using the ideal gas law. The ideal gas law states that the pressure of a gas is directly proportional to its concentration and inversely proportional to its volume.

For a gas at a given temperature and volume, the partial pressure of a gas is equal to its concentration multiplied by the total pressure. Therefore, we can write:

$$p_{\text{A}}=[\text{A}]RT$$

$$p_{\text{B}}=[\text{B}]RT$$

$$p_{\text{C}}=[\text{C}]RT$$

$$p_{\text{D}}=[\text{D}]RT$$

where $R$ is the ideal gas constant and $T$ is the temperature.

Substituting these expressions into the equation for $K_p$, we get:

$$K_p=\frac{([\text{C}]RT{)}^c([\text{D}]RT{)}^d}{([\text{A}]RT{)}^a([\text{B}]RT{)}^b}$$

Simplifying this expression, we get:

$$K_p=K_c(RT{)}^{\mathrm{\Delta }n}$$

where $\mathrm{\Delta }n$ is the difference between the total number of moles of products and the total number of moles of reactants.

Conclusion

The relation between $K_p$ and $K_c$ is given by the equation $K_p=K_c(RT{)}^{\mathrm{\Delta }n}$. This equation shows that $K_p$ and $K_c$ are related by a constant factor that depends on the temperature and the change in the number of moles of gas during the reaction.

Relation Between Kp and Kc FAQs

What is the relationship between Kp and Kc?

The relationship between Kp and Kc is given by the equation:

$$Kp=Kc(RT{)}^{\mathrm{\Delta }n}$$

where:

• Kp is the equilibrium constant in terms of partial pressures
• Kc is the equilibrium constant in terms of concentrations
• R is the ideal gas constant
• T is the temperature in Kelvin
• Δn is the change in the number of moles of gas in the reaction

What is the difference between Kp and Kc?

The main difference between Kp and Kc is that Kp is expressed in terms of partial pressures, while Kc is expressed in terms of concentrations. This means that Kp is dependent on the pressure of the system, while Kc is not.

When should I use Kp instead of Kc?

Kp should be used instead of Kc when the reaction is carried out in a gas phase. This is because the partial pressures of the gases are more relevant to the equilibrium constant than the concentrations.

When should I use Kc instead of Kp?

Kc should be used instead of Kp when the reaction is carried out in a liquid phase. This is because the concentrations of the reactants and products are more relevant to the equilibrium constant than the partial pressures.

Can I convert Kp to Kc and vice versa?

Yes, you can convert Kp to Kc and vice versa using the equation:

$$Kp=Kc(RT{)}^{\mathrm{\Delta }n}$$

where:

• Kp is the equilibrium constant in terms of partial pressures
• Kc is the equilibrium constant in terms of concentrations
• R is the ideal gas constant
• T is the temperature in Kelvin
• Δn is the change in the number of moles of gas in the reaction

What are some examples of reactions where Kp and Kc are different?

Some examples of reactions where Kp and Kc are different include:

• The dissociation of hydrogen gas:

$$H_2(g)\rightleftharpoons 2H(g)$$

• The combustion of methane:

$$C{H}_4(g)+2O_2(g)\rightleftharpoons C{O}_2(g)+2H_{2}O(g)$$

• The formation of ammonia:

$$N_2(g)+3H_2(g)\rightleftharpoons 2N{H}_3(g)$$

In these reactions, the equilibrium constant in terms of partial pressures (Kp) is different from the equilibrium constant in terms of concentrations (Kc). This is because the reactions involve changes in the number of moles of gas.