Qualitatively plot \(K_{c}\) versus the temperature for an endothermic and an exothermic reaction.

According to the Van't Hoff equation, the following relationship exists: \(K_c = Ae^{-\frac{\Delta H°}{RT}}\), where \(A\) is the pre-exponential factor, \(\Delta H°\) is the standard enthalpy change of the reaction, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. The Van't Hoff equation describes the dependence of the equilibrium constant on temperature. Given that temperature, enthalpy change, and the ideal gas constant are all involved in the relationship, we can infer how \(K_c\) varies with temperature for endothermic and exothermic reactions.

For an endothermic reaction, the enthalpy change \(\Delta H°\) is positive, which means the exponent will be negative. As a result, the equilibrium constant will increase as temperature rises. This indicates that the reaction will favor the products at higher temperatures. For an exothermic reaction, the enthalpy change \(\Delta H°\) is negative, which means that the exponent will be positive. Consequently, the equilibrium constant will decrease as temperature rises. This indicates that the reaction will favor the reactants at higher temperatures.

Now let's qualitatively plot \(K_c\) versus temperature for endothermic and exothermic reactions based on the trends we determined in step 2. For an endothermic reaction, start by plotting a curve that starts from a low \(K_c\) value at low temperature and increases with temperature. The curve will be rising steadily as the temperature increases, indicating that the reaction favors the products even more at higher temperatures. For an exothermic reaction, start by plotting a curve that starts from a high \(K_c\) value at low temperature and decreases with temperature. The curve will be falling steadily as temperature increases, indicating that the reaction favors the reactants more at higher temperatures. In conclusion, the qualitative plot of \(K_c\) versus temperature for endothermic reactions shows a rising curve, while for exothermic reactions, it shows a falling curve. This is due to the different effects of temperature on the equilibrium constant for each type of reaction.