Collision Theory in Equilibrium – HSC Chemistry

 

This is part of the HSC Chemistry syllabus under the topic of Static and Dynamic Equilibrium.

HSC Chemistry Syllabus

  • Investigate the relationship between collision theory and reaction rate in order to analyse chemical equilibrium reactions (ACSCH070, ACSCH094

      Collision Theory in Equilibrium Explained

      This video will explore what collision theory is and how it relates to how we understand equilibrium systems

       

      What is Collision Theory?

      Collision theory is a theory which states chemical reactions are the result of collisions between molecules or atoms.

      It utilises our understanding of the particle model to explain that the rate of reaction depends on:

      1. Rate of collision between molecules. This is the frequency at which molecules collide. Greater rate of collision leads to greater reaction rate.
       
      2. Activation energy of the reaction. For a reaction to occur, the reactants must overcome a certain amount of activation energy. Even if the collision rate is high, if the particles don’t have enough energy reaction will still not occur.
       Molecular orientation in collision theory


      Figure: Molecular orientation is an important factor of reaction rate as stated by collision theory. If the orientation of reactants is not correct (effective) during collision, reaction does not occur.

       

      3. Molecular orientation of reactants. Rate of reaction can increase if reactants collide in the right orientation. Conversely, rate can decrease if the orientation of molecules is not favourable for the formation of product(s).
       

      What Affects Collision Rate?

      Effect of concentration on collision rate between molecules

      Collision rate increases at a higher concentration

      • Concentration of particles/molecules. A higher concentration means there are more particles moving about in a given volume, increasing the frequency at which particles collide.

      Effect of pressure or volume on collision rate between molecules

      Collision rate increases at a higher pressure for gases

      • Pressure/volume. Changes in pressure and volume affect the collision rate between gaseous particles as they occupy the most volume. An increase in pressure (or reduction in volume) increases the rate of collision.
      • Temperature is the measurement of the average kinetic energy in a system. A higher temperature (greater energy) means particles move about quicker at greater kinetic energy. This in turn increases the collision rate between them.

      What Affects Activation Energy?

      Effect of catalyst on the energy profile of a reactionCatalyst reduces the activation energy

      • Catalysts reduce the activation energy of a reaction, resulting in an increased rate.

      Molecular Energy Distribution

      • In addition to increasing the collision rate, a higher temperature also allows more collisions to result in a chemical reaction (more successful collisions). This is because, at a higher temperature, more molecules have energy greater than the activation energy to react. This causes the Maxwell-Boltzmann energy distribution graph to shift to the right, without changing the activation energy.

       

      Effect of temperature on the energy of molecules in a chemical system

       

      • Catalysts reduce the activation energy of a reaction. This does not affect the energy distribution of molecules as it does not change the energy inside the system. However, by reducing the activation energy, more molecules have enough energy to result in a chemical reaction when collisions occur.

       

      Effect of catalyst on the activation energy of a reaction

       

      • In both cases (higher temperature and adding a catalyst), the frequency of a successful collision (one that results in a chemical reaction) increases, and so does the reaction rate.

      Collision Theory in Dynamic Equilibrium

      • A dynamic equilibrium refers to a state whereby the forward and reverse rates of a reversible reaction are equal.
      • An example of a reversible reaction that can exist in equilibrium is the reaction between N2O4 and NO2. Suppose a closed system initially has some amount of N2O4 and no NO2. Molecules of N2O4 can decompose to produce twice as many NO2.

        $$2NO_2(g) \rightleftharpoons N_2O_4(g)$$

         

         Collision theory and equilibrium

        • As the N2O4 molecules decompose to produce NO2, their concentration decreases and so does their collision rate. This in turn reduces the rate of the forward reaction.
        • As NO2 molecules form, they can also collide and result in a reaction to re-form N2O4. This is represented by the reverse reaction.
        • In the beginning, the forward reaction rate is greater than the reverse reaction rate as there are far more N2O4 than NO2 molecules. This results in a net decrease in [N2O4] and a net increase in [NO2]

         Collision theory and equilibrium

         

        • However, as the reaction proceeds, the rate of the forward reaction gradually decreases, and the rate of the reverse reaction gradually increases.

        Collision theory and equilibrium


        • This continues until the rates of the forward and reverse reaction become equal, where equilibrium is established. At this point, forward and reverse reactions still occur due to the collision between molecules but no changes in concentration are observed.

        Practice Question

        Consider a closed chemical system will only N2Omolecules. 

        Using collision theory, explain the changes in [N2O4] and [NO2] shown by the two graphs below. 

         

        Figure: change in reaction rate with time. At t1, rate of forward and backward reactions becomes equal, and equilibrium is reached. 

         

         


        Figure: change in concentration of reactants and products of a reversible reaction.
        [`N_2O_4`] decreases while [`NO_2`] increases. A reaction can reach equilibrium starting with any quantities of reactants and products.

         

        Sample answer:

        • Initially, N2O4 collide and will result in a reaction to produce NO2 if the activation energy is met. This causes [NO2] to increase and [N2O4] to decrease.
        • As [N2O4] falls, there are fewer collisions between N2O4 molecules, so the rate of the forward reaction decreases.
        • As [NO2] increases, there are more collisions between NO2 molecules, so the rate of the reverse reaction increases.
        • Forward and backward reaction rates will continue to change until they become equal in value. When this occurs, the reaction reaches dynamic equilibrium. Since the two rates are equal, there is no change in [N2O4] and [NO2]

        Figure: Reaction between dinitrogen tetroxide and nitrogen dioxide can be monitored by its colour change. Nitrogen tetroxide is colourless whereas nitrogen dioxide has a distinctive brown colour. 

         

        • Nitrogen dioxide (`NO_2`) has a distinctive brown colour while dinitrogen tetroxide (`N_2O_4`) is colourless. 
        • In the reaction above, the reaction mixture is pale brown as it consists of mostly `N_2O_4`. As the reaction approaches equilibrium, the concentration of `NO_2` increases, making the mixture appear browner.
        • When the reaction reaches a dynamic equilibrium, the concentration of `NO_2` and `N_2O_4` remain constant, so the colour of the mixture stays unchanged. This is used as an indication that the reaction has reached equilibrium.

        Effect of Changes in Concentration on Equilibrium

        Collision theory is useful in explaining the effect on a reaction at equilibrium when the concentration of a chemical species changes. 

        Let's consider the following equilibrium:

        $$N_2O_4(g) \rightleftharpoons 2NO_2(g)$$

         

         
        If `[N_2O_4]` increases, collision between reactants increases which in turn increases the forward reaction rate. Now that the forward reaction rate is greater than the reverse reaction rate (reaction is no longer at equilibrium), `[NO_2]` will gradually increase, and `[N_2O_4]` will gradually decrease. 
         

        As the concentrations change, the forward and reverse reaction rates will decrease and increase respectively, until they become equal. At this instance, the reaction reaches a new equilibrium.

        Effect of Changes in Pressure/Volume on Equilibrium

        Pressure changes affect the collision rate between gas molecules which in turn affects reaction rate. The effect of changes in pressure affect the rate of the reaction that has more gaseous reactants. 

        Let's consider the following equilibrium.

        $$2NO_2(g) \rightleftharpoons N_2O_4(g)$$

         

         

        • There are more gaseous reactants than products. Thus, changes in pressure would affect the rate of the forward reaction more.
        • If pressure is increased, the rates of both forward and reverse reaction will increase but the forward rate will increase more than the reverse rate (reaction no longer at equilibrium). Since the forward reaction is faster than the reverse reaction, `[N_2O_4]` will increase and `[NO_2]` will decrease. As these concentrations change, the reverse and forward reaction rates will increase and decrease respectively, until they become equal again, at a new equilibrium.
        • If pressure is decreased, the rates of both forward and reverse reaction will decrease but the forward rate will decrease more than the reverse rate. This will cause `[N_2O_4]` will decrease and `[NO_2]` to increase. As these concentrations change, the reverse and forward reaction rates will decrease and increase respectively, until they become equal again, at a new equilibrium.

        Effect of Changes in Temperature on Equilibrium

        Changes in temperature affects reaction rate by:

        1. changing the average kinetic energy and hence collision rate between particles
        2. changing the proportion of particles or molecules that has energy greater than the activation energy of the reaction

        While changes in temperature affect rates of both forward and reverse reactions, it also affects the endothermic reaction rate more due to its greater activation energy.

         

        The Maxwell-Boltzmann energy distribution curves demonstrate the effects of changing temperature on the molecular energy of a chemical system. The greater activation energy of the endothermic reaction means its reactants would be more affected by changes in kinetic energy i.e. temperature.

        Let's consider the following exothermic reaction at equilibrium:

        $$2NO_2(g) \rightleftharpoons N_2O_4(g) \hspace{1 cm} \Delta H < 0$$

         

         

        • If temperature is increased, the rates of both forward and reverse reactions will increase, but the reverse reaction rate (endothermic) will increase more than the forward reaction. Since the reverse reaction is now faster, `[2NO_2]` will gradually increase, and `[N_2O_4]` will gradually decrease. As these concentrations change, the rates of forward and reverse reactions will increase and decrease respectively, until they become equal again, at a new equilibrium.
        • If temperature is decreased, the rates of both forward and reverse reactions will decrease, but the reverse reaction rate (endothermic) will decrease more than the forward reaction. Since the forward reaction is now faster, `[2NO_2]` will gradually decrease, and `[N_2O_4]` will gradually increase. As these concentrations change, the rates of forward and reverse reactions will decrease and increase respectively, until they become equal again, at a new equilibrium.

        Effect of Catalyst on Equilibrium


        Figure: catalysts reduce the activation energy of both forward and reverse reactions.
         

        • Addition of catalyst(s) increases the rate of both forward and reverse reactions by reducing their respective activation energies.

         

        Catalysts do not disturb chemical equilibria

        Figure: addition of catalyst at the 10-minute mark increases the rate of both forward and reverse reaction. The equilibrium is not disturbed.
         
        • Adding a catalyst to a reaction at equilibrium increases the forward and reverse reaction rates to the same extent. As a result, the reaction rates remain equal and equilibrium is not disturbed. 

         

        Reactions reach equilibrium faster

        Figure: addition of a catalyst allows the equilibrium to be reached faster.

         

        In the presence of a catalyst, a reversible reaction reaches equilibrium faster. In the rate versus time graph above, note the following:

        The catalysed reaction compared to the uncatalysed reaction

        • has a higher initial reaction rate
        • reaches equilibrium (equal reaction rates) faster, at an earlier time point
        • both forward and reverse reaction rates are higher (but remains equal) at equilibrium