Problem 19 - Chemistry The Central Science

Question

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. (c) As the value of the equilibrium constant increases, the speed at which a reaction reaches equilibrium increases.

Step-by-Step Solution

Answer

Statement (a) is true, as the equilibrium constant (K) can never be a negative number since it is a ratio of positive concentrations. Statement (b) is false because the equilibrium constant (K) can range from very small to very large positive values, not just close to zero. Statement (c) is also false, as the speed at which a reaction reaches equilibrium is not determined by the equilibrium constant (K) but depends on factors like temperature, concentration, and the presence of a catalyst.

Step 1: Statement (a): The equilibrium constant can never be a negative number.

The equilibrium constant (K) is a dimensionless number that relates the concentrations of the reactants and products at equilibrium. It is defined as the ratio of the multiplication of equilibrium concentrations of the products to the multiplication of equilibrium concentrations of the reactants, each raised to the power of their stoichiometric coefficients. Since concentrations are always positive values, the product of positive concentrations will also be positive. Therefore, the equilibrium constant (K) can never be a negative number. Hence, Statement (a) is true.

Step 2: Statement (b): In reactions that we draw with a single-headed arrow, the equilibrium constant has a value that is very close to zero.

When a reaction is represented by a single-headed arrow, it typically conveys that the reaction mostly proceeds in one direction, either from reactants to products (forward) or from products to reactants (reverse). However, this does not mean that the equilibrium constant (K) will be very close to zero. If a reaction strongly favors the formation of products, K will be much greater than 1. On the other hand, if the reaction strongly favors the formation of reactants, K will be much lesser than 1 but not close to zero. Since equilibrium constants can range from very small to very large positive values, Statement (b) is false.

Step 3: Statement (c): As the value of the equilibrium constant increases, the speed at which a reaction reaches equilibrium increases.

The equilibrium constant (K) provides information about the composition of the reaction mixture at equilibrium and whether the equilibrium position lies towards the reactants or the products. However, K does not provide any information about how fast the reaction reaches equilibrium. The rate of a reaction is determined by the reaction's rate constant and depends on factors like temperature, concentration, and the presence of a catalyst. Therefore, Statement (c) is false, as the equilibrium constant (K) does not determine the speed at which a reaction reaches equilibrium. In conclusion, Statement (a) is true, while Statements (b) and (c) are both false.