Which of the following statements is true of a solution at pH 7?

A. Kw and Kb are equal.
B. Kw and Ka are equal.
C. Kw, Ka and Kb are equal.
D. Ka and Kb are equal.

D. Ka and Kb are equal

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Kw = Ka x Kb

For pH = 7 => Kw = 10^-14 @ 25-deg Celcius
Therefore, for Ka x Kb = 10^-14 => Ka = Kb = 10^-7
=> (10^-7)(10^-7)= 10^-14

The correct answer is D. Ka and Kb are equal.

In a water solution at pH 7, the concentrations of hydrogen ions (H+) and hydroxide ions (OH-) are equal. At this pH, water acts as a neutral solution. The equilibrium constant for the ionization of water, known as Kw, remains constant at all pH levels and is equal to 1.0 x 10^-14. This equation can be represented as follows:

H2O ⇌ H+ + OH-

When an acid is added to water, it increases the concentration of H+ ions and shifts the equilibrium to the left. When a base is added, it increases the concentration of OH- ions and shifts the equilibrium to the right. The dissociation of water can be represented using equilibrium constants for acids (Ka) and bases (Kb), which are related to each other in the following equation:

Kw = Ka x Kb

Since Ka and Kb are both equal to Kw, the correct statement is that Ka and Kb are equal in a solution at pH 7.

To determine which of the statements is true of a solution at pH 7, we need to understand the concepts of pH, Kw, Ka, and Kb.

pH is a measure of the acidity or alkalinity of a solution. A pH value of 7 indicates a neutral solution, where the concentration of hydrogen ions (H+) is equal to the concentration of hydroxide ions (OH-).

Kw is the ionization constant for water. It represents the equilibrium constant for the reaction of water dissociating into hydrogen ions and hydroxide ions: H2O ⇌ H+ + OH-. At 25°C, the value of Kw is approximately 1.0 x 10^-14.

Ka represents the acid dissociation constant, which is a measure of the extent to which an acid dissociates in water. It quantifies the equilibrium constant for the reaction of an acid, HA, dissociating into its conjugate base, A-, and a hydrogen ion: HA ⇌ H+ + A-.

Kb represents the base dissociation constant, which is similar to Ka but for bases. It quantifies the equilibrium constant for the reaction of a base, B, accepting a hydrogen ion from water to form the conjugate acid, BH+: B + H2O ⇌ BH+ + OH-.

Now, let's evaluate which statement is true for a solution at pH 7:

(A) Kw and Kb are equal: This statement is not true. Kw represents the ionization constant for water, while Kb represents the base dissociation constant. They are two different concepts and not equal to each other.

(B) Kw and Ka are equal: This statement is also not true. Kw represents the ionization constant for water, whereas Ka represents the acid dissociation constant. Again, these are different concepts and not equal.

(C) Kw, Ka, and Kb are equal: This statement is not true as well because Kw, Ka, and Kb represent different equilibria in water and are therefore not equal to each other.

(D) Ka and Kb are equal: This statement is true for a solution at pH 7. In a neutral solution (pH 7), the concentrations of hydrogen ions (H+) and hydroxide ions (OH-) are equal. Consequently, any acid-base equilibrium reactions that involve these ions, such as the dissociation of an acid (HA) or a base (B), will have equal Ka and Kb values in a neutral solution.

So, the correct answer is (D) Ka and Kb are equal.