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That a reaction quotient always assumes the same value at equilibrium can be expressed as:
This equation is a mathematical statement of the law of mass action : When a reaction has attained equilibrium at a given temperature, the reaction quotient for the reaction always has the same value.
When 0.10 mol NO 2 is added to a 1.0-L flask at 25 °C, the concentration changes so that at equilibrium, [NO 2 ] = 0.016 M and [N 2 O 4 ] = 0.042 M .
(a) What is the value of the reaction quotient before any reaction occurs?
(b) What is the value of the equilibrium constant for the reaction?
(b) At equilibrium, the value of the equilibrium constant is equal to the value of the reaction quotient. At equilibrium, The equilibrium constant is 1.6 10 2 .
Note that dimensional analysis would suggest the unit for this K c value should be M −1 . However, it is common practice to omit units for K c values computed as described here, since it is the magnitude of an equilibrium constant that relays useful information. As will be discussed later in this module, the rigorous approach to computing equilibrium constants uses dimensionless quantities derived from concentrations instead of actual concentrations, and so K c values are truly unitless.
K c = 4.3
The magnitude of an equilibrium constant is a measure of the yield of a reaction when it reaches equilibrium. A large value for K c indicates that equilibrium is attained only after the reactants have been largely converted into products. A small value of K c —much less than 1—indicates that equilibrium is attained when only a small proportion of the reactants have been converted into products.
Once a value of K c is known for a reaction, it can be used to predict directional shifts when compared to the value of Q c . A system that is not at equilibrium will proceed in the direction that establishes equilibrium. The data in [link] illustrate this. When heated to a consistent temperature, 800 °C, different starting mixtures of CO, H 2 O, CO 2 , and H 2 react to reach compositions adhering to the same equilibrium (the value of Q c changes until it equals the value of K c ). This value is 0.640, the equilibrium constant for the reaction under these conditions.
It is important to recognize that an equilibrium can be established starting either from reactants or from products, or from a mixture of both. For example, equilibrium was established from Mixture 2 in [link] when the products of the reaction were heated in a closed container. In fact, one technique used to determine whether a reaction is truly at equilibrium is to approach equilibrium starting with reactants in one experiment and starting with products in another. If the same value of the reaction quotient is observed when the concentrations stop changing in both experiments, then we may be certain that the system has reached equilibrium.
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