Question

What is the ${K_{eq}}$ of the following reaction?

A. $1.7$
B. $0.17$
C. $17$
D. None of these

Answer 1

Hint: If the value of change in Gibbs free energy under standard condition is negative then the value of the equilibrium constant will be greater than one which implies that the reaction is spontaneous and the reaction will proceed in forward direction but if the value of change in Gibbs free energy under standard condition is less than zero then the reaction will proceed in reverse direction.

Complete answer:
Step 1: Gathering the values from the question:
According to the question \[\Delta {G^\circ } = - 0.010{\text{ kJ mo}}{{\text{l}}^{ - 1}}\]
The reaction proceeds at room temperature therefore the temperature at Celsius is ${27^ \circ }C$
 while the temperature in Kelvin is \[273 + 27 = {\text{ }}300K.\]
The value of universal gas constant R in \[kJ{\text{ }}mo{l^{ - 1}}\] is \[8.314kJ{\text{ }}mo{l^{ - 1}}\].
Step 2: Substituting the values in the equation:
If the value of Gibbs free energy change is known for a chemical process at a known temperature the value of equilibrium constant can be calculated from the equation mentioned below.
$\Delta {G^\circ } = 2.303{\text{ RT log }}{{\text{K}}_{eq}}$
$\log {\text{ }}{{\text{K}}_{eq}} = \dfrac{{\Delta {G^\circ }}}{{2.303RT{\text{ log}}}}$
$\log {\text{ }}{{\text{K}}_{eq}} = \dfrac{{ - 0.010}}{{2.303 \times 8.314 \times 300}}$
Step 3: solving the equation:
$\log {\text{ }}{{\text{K}}_{eq}} = \dfrac{{ - 0.010}}{{19.147 \times {\text{300}}}}$
$\log {\text{ }}{{\text{K}}_{eq}} = \dfrac{{ - 0.010}}{{5744.1}}$
$\log {\text{ }}{{\text{K}}_{eq}} = - 1.74 \times {10^{ - 6}}$
\[{K_{eq}} = {\text{ }}0.999\;\]
Therefore, ${K_{eq}}$ is approximately equal to 1.

Note:
In an exergonic process the energy will be releases while the Gibbs free energy is less than zero while at equilibrium Gibbs free energy is equal to zero and no net changes occur in the system and in endergonic process energy is required and work is done on the system while the Gibbs free energy is more than zero. If the value of \[{K_{eq}}\] under standard condition is more than one then the reaction will proceed in forward direction but when the value of \[{K_{eq}}\] under standard condition is less than one the reaction will proceed in backward direction.