77 Equilibrium Constants
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The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by
the reaction quotient is derived directly from the stoichiometry of the balanced equation as
where the subscript c denotes the use of molar concentrations in the expression. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures:
Note that the reaction quotient equations above are a simplification of more rigorous expressions that use relative values for concentrations and pressures rather than absolute values. For purposes of this introductory text, it will suffice to use the simplified equations and to disregard units when computing Q. In most cases, this will introduce only modest errors in calculations involving reaction quotients.
Writing Reaction Quotient Expressions Write the concentration-based reaction quotient expression for each of the following reactions:
(a) \(3{\text{O}}_{2}\left(g\right)⇌2{\text{O}}_{3}\left(g\right)\)
(b) \({\text{N}}_{2}\left(g\right)+3{\text{H}}_{2}\left(g\right)⇌2{\text{NH}}_{3}\left(g\right)\)
(c) \(4{\text{NH}}_{3}\left(g\right)+7{\text{O}}_{2}\left(g\right)⇌4{\text{NO}}_{2}\left(g\right)+6{\text{H}}_{2}\text{O}\left(g\right)\)
Solution (a) \({Q}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{O}}_{3}\right]}^{2}}{{\left[{\text{O}}_{2}\right]}^{3}}\)
(b) \({Q}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{NH}}_{3}\right]}^{2}}{\left[{\text{N}}_{2}\right]{\left[{\text{H}}_{2}\right]}^{3}}\)
(c) \({Q}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{NO}}_{2}\right]}^{4}\left[{\text{H}}_{2}\text{O}{\right]}^{6}}{{\left[{\text{NH}}_{3}\right]}^{4}\left[{\text{O}}_{2}{\right]}^{7}}\)
Check Your Learning Write the concentration-based reaction quotient expression for each of the following reactions:
(a) \(2{\text{SO}}_{2}\left(g\right)+{\text{O}}_{2}\left(g\right)⇌2{\text{SO}}_{3}\left(g\right)\)
(b) \({\text{C}}_{4}{\text{H}}_{8}\left(g\right)⇌2{\text{C}}_{2}{\text{H}}_{4}\left(g\right)\)
(c) \(2{\text{C}}_{4}{\text{H}}_{10}\left(g\right)+13{\text{O}}_{2}\left(g\right)⇌8{\text{CO}}_{2}\left(g\right)+10{\text{H}}_{2}\text{O}\left(g\right)\)
(a) \({Q}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{SO}}_{3}\right]}^{2}}{{\left[{\text{SO}}_{2}\right]}^{2}\left[{\text{O}}_{2}\right]};\) (b) \({Q}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{C}}_{2}{\text{H}}_{4}\right]}^{2}}{\left[{\text{C}}_{4}{\text{H}}_{8}\right]};\) (c) \({Q}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{CO}}_{2}\right]}^{8}\left[{\text{H}}_{2}\text{O}{\right]}^{10}}{{\left[{\text{C}}_{4}{\text{H}}_{10}\right]}^{2}\left[{\text{O}}_{2}{\right]}^{13}}\)
The numerical value of Q varies as a reaction proceeds towards equilibrium; therefore, it can serve as a useful indicator of the reaction’s status. To illustrate this point, consider the oxidation of sulfur dioxide:
Two different experimental sce