One way to calculate the value of a reaction's equilibrium constant is to
perform the reaction, let it come to equilibrium, measure the concentration of
all the reactants and products, and then plug those concentrations into the
equilibrium constant expression and calculate its value.
(a) A student performs the reaction \(\mathrm{A}(a q)+2 \mathrm{~B}(a q)
\rightleftarrows \mathrm{C}(a q)\) starting with
\(2.0 \mathrm{M} \mathrm{A}\) and \(4.0 \mathrm{M} \mathrm{B}\). He finds that at
equilibrium, the concentrations of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\)
are \(0.020 \mathrm{M}, 0.040 \mathrm{M}\), and \(1.98\) \(\mathrm{M}\),
respectively. What is the value of this reaction's equilibrium constant (write
your answer using scientific notation)?
(b) Next, the student repeats the experiment, but this time he starts with
\(3.0 \mathrm{M} \mathrm{A}\) and 5.0 M B. What value will he get for \(K_{\text
{eq }}\) when he measures the equilibrium concentrations and plugs them into
the equilibrium constant expression? (Hint: Think about why equilibrium
constant is called a constant.)