What is the pH of a 0.5 M solution of NaHCO3? Kb = 2.4x10-8 (base)

To find the pH of a solution of NaHCO3, we need to consider its reaction with water. NaHCO3 is a weak base, so it will undergo hydrolysis in water to release hydroxide ions (OH^-) and bicarbonate ions (HCO3^-).

First, let's write down the balanced chemical equation for the hydrolysis reaction of NaHCO3:

NaHCO3 + H2O ⇌ NaOH + H2CO3

In this equation, NaOH is a strong base and will completely dissociate into Na+ and OH^- ions. H2CO3 is a weak acid formed from the reaction of carbon dioxide (CO2) with water (H2O).

Since Kb (the base dissociation constant) is given as 2.4x10^-8, we can use this value to calculate the concentration of OH^- ions produced from NaHCO3.

The Kb expression for this reaction is:

Kb = [OH^-][H2CO3] / [NaHCO3]

Since NaOH is a strong base, we can assume that its concentration is directly proportional to the hydroxide ion concentration. Thus, [OH^-] = [NaOH].

We can then rearrange the equation to solve for [OH^-]:

[OH^-] = (Kb * [NaHCO3]) / [H2CO3]

Now, we need to determine the concentration of H2CO3 in the solution. Since H2CO3 is a weak acid, it will undergo partial dissociation into bicarbonate ions (HCO3^-) and H+ ions. The equilibrium expression for this reaction is:

Ka = [H+][HCO3^-] / [H2CO3]

Ka is the acid dissociation constant, but it is not provided in the question. However, we can use the relationship between Ka and Kb for the conjugate acid-base pair, H2CO3 and HCO3^-, which is:

Ka * Kb = Kw

Kw is the ionization constant for water (approximated as 1.0x10^-14). Rearranging this equation, we get:

Ka = Kw / Kb

Substituting the given value of Kb (2.4x10^-8) into the equation, we can calculate Ka.

Now, let's solve for [H2CO3] using the given concentration of NaHCO3 (0.5 M) and the equation for Ka:

[H2CO3] = ([H+][HCO3^-]) / Ka

Next, we can substitute the calculated [H2CO3] and [NaHCO3] into the equation to find [OH^-]:

[OH^-] = (Kb * [NaHCO3]) / [H2CO3]

Finally, we can use the relationship between [OH^-] and [H+] to find the pH:

pH = -log[H+]

By following these steps and performing the necessary calculations, you should be able to determine the pH of the 0.5 M solution of NaHCO3.