Final answer:
The detailed answer provided addresses equilibrium constants in chemical reactions and their impact on chemical concentration changes. It also relates to the pressure-volume relationship in gases, which is another context for the use of a constant k. However, the matter of k in an equation with no solution is a mathematical question.
Step-by-step explanation:
It seems there is a misunderstanding as the detailed information provided pertains to equilibrium constants in chemical reactions, and not to solving equations with no solution in the mathematical sense. In chemistry, when the equilibrium constant (K) is very small (K ≤ 10⁻³) or very large (K ≥ 10³), it suggests that there is negligible change in the concentration of reactants and products at equilibrium. As such, in these cases, the concentrations remain essentially unchanged, and this simplifies calculations regarding the reaction. However, the question of what value of a constant k makes an equation have no solution would be a question more suited to mathematics, specifically algebra, and would generally depend on the form of the equation itself.
Considering pressure and volume relationships in a gas, which follows the Ideal Gas Law (PV = nRT), the product of pressure and volume is also a constant (k) for a given amount of gas at a constant temperature, highlighting a different context where the concept of a constant k is used.