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ChemWiki: The Dynamic Chemistry E-textbook > Physical Chemistry > Equilibria > Le Ch√Ętelier's Principle > Effect of Temperature on Equilibrium > Exothermic vs. Endothermic and K

Exothermic vs. Endothermic and K

An exothermic reaction occurs when the temperature of a system increases due to the evolution of heat. This heat is then released into the surroundings, resulting in an overall negative quantity for the heat of reaction (\(q_{rxn}< 0\)). An endothermic reaction occurs when the temperature of an isolated system decreases while the surroundings of a non-isolated system gains heat. Endothermic reactions result in an overall positive heat of reaction (\(q_{rxn}> 0\)).

Exothermic Reactions

Exothermic and endothermic reactions cause energy level differences and thus differences in enthalpy (\(\Delta{H}\)), the sum of all potential and kinetic energies. \(\Delta{H}\) is determined by the system, not the surrounding environment in a reaction. A system that releases heat to the surroundings, an exothermic reaction, has a negative \(\Delta{H}\) by convention because the enthalpy of the products is lower than the enthalpy of the reactants of the system (Figure 1). 

\[ C(s) + O_{2\;(g)} \rightarrow CO_{2\; (g)} \tag{ΔH = –393.5 kJ} \]

\[ H_{2\;(g)} + 1/2 O_{2\;(g)} \rightarrow H_2O_{(l)} \tag{ΔH = –285.8 kJ} \]

The enthalpies of these reactions are less than zero and are thus exothermic reactions.

Endothermic Reactions

A system of reactants that absorbs heat from the surroundings in an endothermic reaction has a positive \(\Delta{H}\), because the enthalpy of the products is higher than the enthalpy of the reactants of the system.

\[N_{2\;(g)} + O_{2\;(g)} \rightarrow 2NO_{(g)} \tag{ΔH = +180.5 kJ > 0}\]

\[C(s) + 2S_{(s)} \rightarrow CS_{2\;(l)} \tag{ΔH = +92.0 kJ > 0}\]

Because the enthalpies of these reactions are greater than zero, they are endothermic reactions. 

The Equilibrium Constant K

The equilibrium constant (\(K\)) defines the relationship among the concentrations of chemical substances involved in a reaction at the time of equilibrium. The Le Châtelier's Principle states that if a stress, such as changing temperature, pressure, or concentration, is inflicted on an equilibrium reaction, the reaction will either shift to restore the equilibrium. When using exothermic and endothermic reactions, this added stress is a change in temperature. The equilibrium constant shows how far the reaction will progress at a specific temperature by determining the ratio of products to reactions using equilibrium concentrations.

In an equilibrium expression: \( aA + bB \rightleftharpoons cC + dD \)

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

where

  • \(K_c\) is the equilibrium constant
  • [A], [B], [C], [D] are concentrations
  • a, b, c, and d are the stoichiometric coefficients of the balanced equation

Exothermic Reactions

  • If \(K_c\) decreases with an increase in temperature, the reaction moves to the left.
  • If \(K_c\) increases with a decreases in temperature, the reaction to moves to the right.

Endothermic Reactions

  • If \(K_c\) increases with an increase in temperature, the reaction to moves to the right.
  • If \(K_c\) decreases with a decrease in temperature, the reaction to move to the left.

K Values

If the products dominate in a reaction, the value for K is greater than 1. The larger the K value, the more the reaction will tend toward the right and thus to completion. 

  • If \(K=1\), neither the reactants nor the products are favored. Note that this is not the same as both being favored.
  • If the reactants dominate in a reaction, then \(K< 1\). The smaller the K value, the more the reaction will tend toward the left. 

 

Example: The Haber Process

Lets say that the following reaction is at equilibrium and that the concentration of \(N_2\) is 2 M, the concentration of \(H_2\) is 4 M and that concentration of \(NH_3\) is 3 M. What is the value of \(K_c\)? 

\[ N_2 + 3H_2 \rightleftharpoons 2NH_3 \]

The coefficients and the concentrations are plugged into the \(K_c\) equation to calculate its value. 

\[\begin{eqnarray} K_c &=& \dfrac{[NH_3]^2}{[N_2]^1[H_2]^3} \\ &=& \dfrac{[3]^2}{[2]^1[4]^3} \\ &=& \dfrac{9}{32} \\ &=& 0.3 \end{eqnarray}\]

Practice Problems

1. Determine the equilibrium constant, K, for the following chemical reaction at equilibrium if the molar concentrations of the molecules are 0.20 M H2, 0.10 M NO, 0.20 M H2O, and 0.10M N2

\[2H_2 (g) + 2NO (g) \rightleftharpoons 2H_2O (g) + N_2 (g) \]

2. In the previous equation, in which way will the equilibrium shift? 

3. In the following reaction, the temperature is increased and the K value decreases from 0.75 to 0.55. Is this an exothermic or endothermic reaction?

\[N_2 (g) + 3H_2 \rightleftharpoons 2NH_3 (g) \]

4. In the following reaction, in which direction will the equilibrium shift if there is an increase in temperature and the enthalpy of reaction is given such that \(ΔH = -92.5\, kJ\)?

\[PCl_3(g) + Cl_2(g) \rightleftharpoons PCl_5(g) \tag{ΔH = -92.5 kJ}\]

Solutions

1. Using the equilibrium constant equation and plugging in the concentration values of each molecule:

\[ \begin{eqnarray} K_c &=& \dfrac{[C]^c[D]^d}{[A]^a[B]^b} \\ &=& 0.2 \end{eqnarray}\]

2. Because K_c = 0.2, which is less than 1, the reaction will shift to the left. 

3. Because the K value decreases with an increase in temperature, the reaction is an exothermic reaction. 

4. In the initial reaction, the energy given off is negative and thus the reaction is exothermic. However, an increase in temperature allows the system to absorb energy and thus favor an endothermic reaction; the equilibrium will shift to the left.

References

  1. Petrucci, Harwood, Herring, Madura. General Chemistry Principles & Modern Applications. Prentice Hall. New Jersey, 2007 

Contributors

  • Alyson Salmon, Nikita Patel (UCD), Deepak Nallur (UCD)

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Last Modified
08:48, 23 Sep 2014

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