Reaction quotient

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In a chemical reaction with certain initial concentrations of reactants and products, it is useful to know if the reaction will shift to the right (increasing the concentrations of the products) or if it will shift to the left (increasing the concentrations of the reactants). For this purpose we define the reaction quotient for reactions of the type:

kA + mB \leftrightarrow nC + pD

where A, B, C, and D are four chemical species involved in this reaction and k, m, n, and p are the coefficients. And the expression for the reaction quotient is:

Q = \frac{\left[C_i\right]^n \left[D_i\right]^p}{\left[A_i\right]^k \left[B_i\right]^m}

where the square brackets denote the activities of the species, and the ' i ' denotes the instantaneous concentration at a certain moment of time. This is crucial in understanding the idea of the Reaction Quotient. The Reaction Quotient is taken at a particular instant, not necessarily the moment when equilibrium is reached.

This reaction quotient is directly related to the Le Chatelier Principle. For a reaction in chemical equilibrium, we define the equilibrium constant as:

K_c = \frac{\left[C\right]^n \left[D\right]^p}{\left[A\right]^k \left[B\right]^m}

where this time the activities are taken at equilibrium. By comparing the values of Q and K, one can determine whether the reaction will shift to the right, to the left, or if the concentrations will remain the same (equilibrium).

  • If Q < K : The reaction will shift to the right
  • If Q > K : The reaction will shift to the left
  • If Q = K : The reaction is at equilibrium

This is a quantitative and more useful alternative to the qualitative La Chatelier's Principle.

The relationship with temperature makes the most sense in terms of the Gibbs energy difference, ΔG = ΔE - TΔS, which represents the total useful work that can be extracted from the system as it develops. At equilibrium ΔG = 0, which gives us

\Delta G = \Delta G_0 + RT \ln {\left(Q\right)}

where ΔG0 is the standard Gibbs energy of reaction.

  • Zumdahl, Steven; Zumdahl, Susan (2003). Chemistry 6th Edition. Houghton Mifflin Company. ISBN 0-618-22158-1. 
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