Which of the following statements are true and which are false? (a) The equilibrium constant can never be a negative number. (b) In reactions that we draw with a single-headed arrow, the equilibrium constant has a value that is very close to zero.

Verified step by step guidance

1. Step 1: Understand the concept of the equilibrium constant (K). The equilibrium constant is a ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients. It is expressed as K = [products] / [reactants].
2. Step 2: Evaluate statement (a). The equilibrium constant (K) is derived from concentrations or partial pressures, which are always positive values. Therefore, K itself is always a positive number. Consider why negative concentrations or pressures are not physically meaningful.
3. Step 3: Consider statement (b). A single-headed arrow in a chemical equation typically indicates a reaction that goes to completion, meaning the reactants are fully converted to products. In such cases, the equilibrium constant is not close to zero; instead, it is very large, indicating that the reaction strongly favors the formation of products.
4. Step 4: Reflect on the implications of a very large equilibrium constant. A large K value suggests that at equilibrium, the concentration of products is much higher than that of reactants, which is the opposite of a value close to zero.
5. Step 5: Conclude the truthfulness of each statement based on your understanding of equilibrium constants and the meaning of single-headed arrows in chemical reactions.