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    • Overview
    • Key points
    • Introduction: reversible reactions and equilibrium
    • How do we calculate Kc‍ ?
    • What does the magnitude of Kc‍  tell us about the reaction at equilibrium?
    • Part 1: Calculating Kc‍  from equilibrium concentrations
    • Part 2: Using the reaction quotient Q‍  to check if a reaction is at equilibrium
    • Example 2: Using Kc‍  to find equilibrium compositions
    • Summary

    Reversible reactions, equilibrium, and the equilibrium constant K. How to calculate K, and how to use K to determine if a reaction strongly favors products or reactants at equilibrium.

    •A reversible reaction can proceed in both the forward and backward directions.

    •Equilibrium is when the rate of the forward reaction equals the rate of the reverse reaction. All reactant and product concentrations are constant at equilibrium.

    •Given a reaction aA+bB⇌cC+dD‍ , the equilibrium constant Kc‍ , also called K‍  or Keq‍ , is defined as follows:

    Kc=[C]c[D]d[A]a[B]b‍ 

    •For reactions that are not at equilibrium, we can write a similar expression called the reaction quotient Q‍ , which is equal to Kc‍  at equilibrium.

    •A reversible reaction can proceed in both the forward and backward directions.

    •Equilibrium is when the rate of the forward reaction equals the rate of the reverse reaction. All reactant and product concentrations are constant at equilibrium.

    •Given a reaction aA+bB⇌cC+dD‍ , the equilibrium constant Kc‍ , also called K‍  or Keq‍ , is defined as follows:

    Kc=[C]c[D]d[A]a[B]b‍ 

    •For reactions that are not at equilibrium, we can write a similar expression called the reaction quotient Q‍ , which is equal to Kc‍  at equilibrium.

    •Kc‍  and Q‍  can be used to determine if a reaction is at equilibrium, to calculate concentrations at equilibrium, and to estimate whether a reaction favors products or reactants at equilibrium.

    A reversible reaction can proceed in both the forward and backward directions. Most reactions are theoretically reversible in a closed system, though some can be considered to be irreversible if they heavily favor the formation of reactants or products. The double half-arrow sign we use when writing reversible reaction equations, ⇌‍ , is a good visual reminder that these reactions can go either forward to create products, or backward to create reactants. One example of a reversible reaction is the formation of nitrogen dioxide, NO2‍ , from dinitrogen tetroxide, N2O4‍ :

    N2O4(g)⇌2NO2(g)‍ 

    Imagine we added some colorless N2O4(g)‍  to an evacuated glass container at room temperature. If we kept our eye on the vial over time, we would observe the gas in the ampoule changing to a yellowish orange color and gradually getting darker until the color stayed constant. We can graph the concentration of NO2‍  and N2O4‍  over time for this process, as you can see in the graph below.

    Initially, the vial contains only N2O4‍ , and the concentration of NO2‍  is 0 M. As N2O4‍  gets converted to NO2‍ , the concentration of NO2‍  increases up to a certain point, indicated by a dotted line in the graph to the left, and then stays constant. Similarly, the concentration of N2O4‍  decreases from the initial concentration until it reaches the equilibrium concentration. When the concentrations of NO2‍  and N2O4‍  remain constant, the reaction has reached equilibrium.

    All reactions tend towards a state of chemical equilibrium, the point at which both the forward process and the reverse process are taking place at the same rate. Since the forward and reverse rates are equal, the concentrations of the reactants and products are constant at equilibrium. It is important to remember that even though the concentrations are constant at equilibrium, the reaction is still happening! That is why this state is also sometimes referred to as dynamic equilibrium.

    Based on the concentrations of all the different reaction species at equilibrium, we can define a quantity called the equilibrium constant Kc‍ , which is also sometimes written as Keq‍  or K‍ . The c‍  in the subscript stands for concentration since the equilibrium constant describes the molar concentrations, in molL‍ , at equilibrium for a specific temperature. The equilibrium constant can help us understand whether the reaction tends to have a higher concentration of products or reactants at equilibrium. We can also use Kc‍  to determine if the reaction is already at equilibrium.

    Consider the balanced reversible reaction below:

    aA+bB⇌cC+dD‍ 

    If we know the molar concentrations for each reaction species, we can find the value for Kc‍  using the relationship

    Kc=[C]c[D]d[A]a[B]b‍ 

    where [C]‍  and [D]‍  are equilibrium product concentrations; [A]‍  and [B]‍  are equilibrium reactant concentrations; and a‍ , b‍ , c‍ , and d‍  are the stoichiometric coefficients from the balanced reaction. The concentrations are usually expressed in molarity, which has units of molL‍ .

    There are some important things to remember when calculating Kc‍ :

    The magnitude of Kc‍  can give us some information about the reactant and product concentrations at equilibrium:

    •If Kc‍  is very large, ~1000 or more, we will have mostly product species present at equilibrium.

    •If Kc‍  is very small, ~0.001 or less, we will have mostly reactant species present at equilibrium.

    •If Kc‍  is in between 0.001 and 1000, we will have a significant concentration of both reactant and product species present at equilibrium.

    Let's take a look at the equilibrium reaction that takes place between sulfur dioxide and oxygen to produce sulfur trioxide:

    2SO2(g)+O2(g)⇌2SO3(g)‍ 

    The reaction is at equilibrium at some temperature, T‍ , and the following equilibrium concentrations are measured:

    [SO2]=0.90M[O2]=0.35M[SO3]=1.1M‍ 

    We can calculate Kc‍  for the reaction at temperature T‍  by solving following expression:

    Kc=[SO3]2[SO2]2[O2]‍ 

    Now we know the equilibrium constant for this temperature: Kc=4.3‍ . Imagine we have the same reaction at the same temperature T‍ , but this time we measure the following concentrations in a different reaction vessel:

    [SO2]=3.6M[O2]=0.087M[SO3]=2.2M‍ 

    We would like to know if this reaction is at equilibrium, but how can we figure that out? When we aren't sure if our reaction is at equilibrium, we can calculate the reaction quotient, Q‍ :

    Q=[SO3]2[SO2]2[O2]‍ 

    At this point, you might be wondering why this equation looks so familiar and how Q‍  is different from Kc‍ . The main difference is that we can calculate Q‍  for a reaction at any point whether the reaction is at equilibrium or not, but we can only calculate Kc‍  at equilibrium. By comparing Q‍  to Kc‍ , we can tell if the reaction is at equilibrium because Q=Kc‍  at equilibrium.

    If we calculate Q‍  using the concentrations above, we get:

    Let's consider an equilibrium mixture of N2‍ , O2‍  and NO‍ :

    N2(g)+O2(g)⇌2NO(g)‍ 

    We can write the equilibrium constant expression as follows:

    Kc=[NO]2[N2][O2]‍ 

    We know the equilibrium constant is 3.4×10−21‍  at a particular temperature, and we also know the following equilibrium concentrations:

    [N2]=[O2]=0.1M‍ 

    •A reversible reaction can proceed in both the forward and backward directions.

    •Equilibrium is when the rate of the forward reaction equals the rate of the reverse reaction. All reactant and product concentrations are constant at equilibrium.

    •Given an equation aA+bB⇌cC+dD‍ , the equilibrium constant Kc‍ , also called K‍  or Keq‍ , is defined using molar concentration as follows:

    Kc=[C]c[D]d[A]a[B]b‍ 

    •For reactions that are not at equilibrium, we can write a similar expression called the reaction quotient Q‍ , which is equal to Kc‍  at equilibrium.

    •Kc‍  can be used to determine if a reaction is at equilibrium, to calculate concentrations at equilibrium, and to estimate whether a reaction favors products or reactants at equilibrium.

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