# 10 how does the value of the equilibrium constant depend on temperature? Ideas

Contents

Below is information and knowledge on the topic how does the value of the equilibrium constant depend on temperature? gather and compiled by the show.vn team. Along with other related topics like: What happens to equilibrium when temperature is increased, What happens to equilibrium when temperature is increased endothermic, What happens to equilibrium when temperature is increased exothermic, What happens to equilibrium when temperature is decreased, Does concentration affect equilibrium constant, How does concentration affect equilibrium, Temperature dependence of equilibrium constant formula, Does pressure affect equilibrium constant.

erature Dependence of Equilibrium Constants – the van ’t Hoff Equation

1. Last updated
2. Save as PDF
• Page ID
84349
• The value of $$K_p$$ is independent of pressure, although the composition of a system at equilibrium may be very much dependent on pressure. Temperature dependence is another matter. Because the value of $$\Delta G_{rxm}^o$$ is dependent on temperature, the value of $$K_p$$ is as well. The form of the temperature dependence can be taken from the definition of the Gibbs function. At constant temperature and pressure

$\dfrac{\Delta G^o_{T_2}}{T_2} – \dfrac{\Delta G^o_{T_1}}{T_1} = \Delta H^o \left(\dfrac{1}{T_2} – \dfrac{1}{T_1} \right)$

Substituting

$\Delta G^o = -RT \ln K$

For the two values of $$\Delta G_{}^o$$ and using the appropriate temperatures, yields

$\dfrac{-R{T_2} \ln K_2}{T_2} – \dfrac{-R{T_1} \ln K_1}{T_1} = \Delta H^o \left(\dfrac{1}{T_2} – \dfrac{1}{T_1} \right)$

And simplifying the expression so that only terms involving $$K$$ are on the left and all other terms are on the right results in the van ’t Hoff equation, which describes the temperature dependence of the equilibrium constant.

$\ln \left(\dfrac{\ K_2}{\ K_1}\right) = – \dfrac{\Delta H^o}{R} \left(\dfrac{1}{T_2} – \dfrac{1}{T_1} \right) \label{vH}$

Because of the assumptions made in the derivation of the Gibbs-Helmholtz equation, this relationship only holds if $$\Delta H^o$$ is independent of temperature over the range being considered. This expression also suggests that a plot of $$\ln(K)$$ as a function of $$1/T$$ should produce a straight line with a slope equal to $$–\Delta H^o/R$$. Such a plot is known as a van ’t Hoff plot, and can be used to determine the reaction enthalpy.

Read More:  10 how has the presence of multinational corporations in developing nations affected those nations? Ideas

Example $$\PageIndex{1}$$

A certain reaction has a value of $$K_p = 0.0260$$ at 25 °C and $$\Delta H_{rxm}^o = 32.4 \,kJ/mol$$. Calculate the value of $$K_p$$ at 37 °C.

Solution

This is a job for the van ’t Hoff equation!

• T1 = 298 K
• T2 = 310 K
• $$\Delta H_{rxm}^o = 32.4 \,kJ/mol$$
• K1 = 0.0260
• K2 = ?

So Equation \ref{vH} becomes

\begin{align*} \ln \left( \dfrac{\ K_2}{0.0260} \right) &= – \dfrac{32400 \,J/mol}{8.314 \,K/(mol \,K)} \left(\dfrac{1}{310\, K} – \dfrac{1}{298 \,K} \right) \\[4pt] K_2 &= 0.0431 \end{align*}

Note: the value of $$K_2$$ increased with increasing temperature, which is what is expected for an endothermic reaction. An increase in temperature should result in an increase of product formation in the equilibrium mixture. But unlike a change in pressure, a change in temperature actually leads to a change in the value of the equilibrium constant!

Example $$\PageIndex{2}$$

Given the following average bond enthalpies for $$\ce{P-Cl}$$ and $$\ce{Cl-Cl}$$ bonds, predict whether or not an increase in temperature will lead to a larger or smaller degree of dissociation for the reaction

$\ce{PCl_5 \rightleftharpoons PCl_3 + Cl_2} \nonumber$

X-Y D(X-Y) (kJ/mol)
P-Cl 326
Cl-Cl 240

Solution

The estimated reaction enthalpy is given by the total energy expended breaking bonds minus the energy recovered by the formation of bonds. Since this reaction involves breaking two P-Cl bonds (costing 652 kJ/mol) and the formation of one Cl-Cl bond (recovering 240 kJ/mol), it is clear that the reaction is endothermic (by approximately 412 kJ/mol). As such, an increase in temperature should increase the value of the equilibrium constant, causing the degree of dissociation to be increased at the higher temperature.

## Extra Information About how does the value of the equilibrium constant depend on temperature? That You May Find Interested

If the information we provide above is not enough, you may find more below here.

### 9.6: Temperature Dependence of Equilibrium Constants

• Author: chem.libretexts.org

• Rating: 5⭐ (856932 rating)

• Highest Rate: 5⭐

• Lowest Rate: 1⭐

• Sumary: The value of Kp is independent of pressure, although the composition of a system at equilibrium may be very much dependent on pressure. Temperature dependence is another matter. Because the value of is dependent on temperature, the value of Kp…

• Matching Result: The value of Kp is independent of pressure, although the composition of a system at equilibrium may be very much dependent on pressure.

• Intro: 9.6: Temperature Dependence of Equilibrium Constants – the van ’t Hoff Equation Last updated Save as PDF Page ID84349 The value of $$K_p$$ is independent of pressure, although the composition of a system at equilibrium may be very much dependent on pressure. Temperature dependence is another matter. Because the value…
Read More:  10 a moon that is full will appear to rise (just at the horizon) at what time of the night or day? Ideas

### How does the equilibrium constant change with temperature?

• Author: socratic.org

• Rating: 5⭐ (856932 rating)

• Highest Rate: 5⭐

• Lowest Rate: 1⭐

• Sumary: For an exothermic reaction (ΔH is negative), K decreases with an increase in temperature. For an endothermic reaction (ΔH is positive), K increases with an increase temperature. You can calculate the effect…

• Matching Result: Jan 11, 2014 · 1 answer

• Intro: How does the equilibrium constant change with temperature? | SocraticFor an exothermic reaction (#ΔH# is negative), #K# decreases with an increase in temperature. For an endothermic reaction (#ΔH# is positive), #K# increases with an increase temperature. You can calculate the effect of changing temperature on the equilibrium constant by using…

### equilibrium constants and Le Chatelier's Principle – Chemguide

• Author: chemguide.co.uk

• Rating: 5⭐ (856932 rating)

• Highest Rate: 5⭐

• Lowest Rate: 1⭐

• Sumary: A look at the relationship between equilibrium constants and Le Chatelier’s Principle.

• Matching Result: Equilibrium constants are changed if you change the temperature of the system. Kc or Kp are constant at constant temperature, but they vary as the temperature …

• Intro: equilibrium constants and changing conditions EQUILIBRIUM CONSTANTS and LE CHATELIER’S PRINCIPLE This page looks at the relationship between equilibrium constants and Le Chatelier’s Principle. Students often get confused about how it is possible for the position of equilibrium to change as you change the conditions of a reaction, although the…

### How Does Temperature Affect the Equilibrium Constant?

• Author: lavelle.chem.ucla.edu

• Rating: 5⭐ (856932 rating)

• Highest Rate: 5⭐

• Lowest Rate: 1⭐

• Matching Result: For endothermic reactions, the relationship between temperature and the equilibrium constant is direct. Raising the temperature of …

• Intro: How Does Temperature Affect the Equilibrium Constant? Moderators: Chem_Mod, Chem_Admin Lilyana Villa 3L Posts: 100 Joined: Sat Aug 17, 2019 12:15 am How Does Temperature Affect the Equilibrium Constant? Postby Lilyana Villa 3L » Thu Jan 28, 2021 10:15 pm Hello! Could someone tell me how raising the temperature affects…

### How does the equilibrium constant change with … – Vedantu

• Author: vedantu.com

• Rating: 5⭐ (856932 rating)

• Highest Rate: 5⭐

• Lowest Rate: 1⭐

• Sumary: How does the equilibrium constant change with temperature?. Ans: Hint : In order to answer the question, to know how the equilibrium constant changes with temperature, we should go through both the exothermic reaction and the endothermic reaction. A…

• Matching Result: Note : Le Chatelier’s principle states that a change in temperature, pressure, or concentration of reactants in an equilibrated system will stimulate a response …

• Intro: How does the equilibrium constant change with temperature?AnswerVerifiedHint : In order to answer the question, to know how the equilibrium constant changes with temperature, we should go through both the exothermic reaction and the endothermic reaction. And we will discuss more about this topic.Complete Step By Step Answer:Yes, the equilibrium…
Read More:  10 this carbohydrate is produced by animals for energy storage Ideas

### Equilibrium constant depends on: A.) The actual quantities of …

• Author: vedantu.com

• Rating: 5⭐ (856932 rating)

• Highest Rate: 5⭐

• Lowest Rate: 1⭐

• Sumary: Equilibrium constant depends on:A.) The actual quantities of reactants and productsB.) The presence of a catalystC.) TemperatureD.) The presence of inert material. Ans: Hint:Value of equilibrium constant inversely depends on temperature. As we increa…

• Intro: Equilibrium constant depends on:A.) The actual quantities of reactants and productsB.) The presence of a catalystC.) TemperatureD.) The presence of inert materialAnswerVerifiedHint:Value of equilibrium constant inversely depends on temperature. As we increase the temperature, the value of equilibrium constant decreases and when we decrease the temperature, the value of equilibrium…

## Frequently Asked Questions About how does the value of the equilibrium constant depend on temperature?

If you have questions that need to be answered about the topic how does the value of the equilibrium constant depend on temperature?, then this section may help you solve it.

### Is K equilibrium temperature-dependent?

The magnitude of K decreases with increasing temperature for exothermic reactions (?H° 0), whereas for endothermic reactions (?H° > 0), the magnitude of K increases with increasing temperature, assuming that?H° and?S° are temperature independent.

### How is K equilibrium impacted by temperature?

The equilibrium will shift in favor of reactant formation and a decrease in Keq as a result of an increase in temperature, which is why the answer is “Keq will decrease.”

### Why does temperature cause the K value to rise?

The Arrhenius Equation states that as T increases, the value of the exponential part of the equation becomes less negative, increasing the value of k. This means that increasing the temperature of a reaction generally speeds up the process (increases the rate) because the rate constant increases.

### What occurs to constant K as the temperature rises?

The reaction is exothermic because the K value decreases as the temperature rises.