A 0.050-M solution of the salt NaB has a pH of 9.00 . Calculate the pH of a 0.010-M solution of

A 0.050-M solution of the salt NaB has a pH of 9.00 ....

Key Concepts

pH Calculation Techniques

Calculating the pH of a solution that involves weak acid or weak base equilibria requires setting up the proper equilibrium expressions and often making approximations based on the small degree of ionization. Mastery of these methods enables the prediction of solution pH from the concentrations and strength of the acids or bases present.

Equilibrium Constants in Weak Acid/Base Systems

Equilibrium constants, such as Ka for weak acids and Kb for their conjugate bases, are critical for quantifying the degree of ionization in aqueous solutions. The intrinsic relationship between Ka, Kb, and Kw helps in the accurate calculation of pH in systems involving weak acids and bases.

Salt Hydrolysis

Salt hydrolysis occurs when a salt derived from a weak acid (or weak base) interacts with water. For instance, the anion from the weak acid can react with water to produce hydroxide ions, leading to a basic solution. This concept is essential for understanding how salts like NaB change the pH of the solution.

Conjugate Acid-Base Pairs

This concept involves understanding that a weak acid and its conjugate base are linked by an equilibrium governed by the acid dissociation constant (Ka) and the base hydrolysis constant (Kb). Their relationship, given by Ka × Kb = Kw, helps predict how the species will react in solution, affecting its pH.

Transcript

00:01 So we're told that the sodium salt of some base, b minus, right here, in the concentration of 0 .05 molar, has a ph of 9.

00:11 And we're asked to figure out what the ph is of a 0 .01 molar concentration of hb, which is the conjugate acid of b minus.

00:23 And so the first thing we want to use is this information, the ph being 9 in this concentration, to find, what the kb is of b minus, and then we can use the kb to find the ka, and then do a simple ice table calculation to figure out what the ph is for the contradacin.

00:41 And so we're going to need to find the concentration of oh minus, but first we have to start with finding the concentration of h3o plus, because that's what we can do, because all we have is the ph.

00:55 And so this is a relationship that's very important.

00:57 Just comes from the definition of the relationship between ph and h -2 -o -plus.

01:01 And so we're told that this is 10 to, that this is going to be 9.

01:08 So we're going to find the concentration of h -d -o -plus is 10 to negative 9.

01:14 Then to find the concentration of oh -1, which is what we're looking for, we use this relationship, which equals 10 to negative -14th, the concentration of o -h -minus and h -3 -0 -plus, it's tense to negative -14th, plug in 10 to negative 9th, and you'll find that this equals 10th to negative 5th.

01:36 And so now we can look to write an expression for what kb is.

01:41 And so kb of any sort of base reacting with water is always going to be equal to x squared over the initial concentration, which we're told is 0 .05 minus x, where x is equal to the concentration of oh minus, as well as the concentration.

02:00 Of the conjugate acid.

02:04 And so we are, we just figured out what the concentration of oh minus is, that it's 10 to the negative 5th.

02:12 And so that's really convenient.

02:13 Now we have all these, all the information we need.

02:15 We have x squared.

02:16 We have this x right here.

02:18 Need it to find kb.

02:19 And plugging these values in, we'll find that kb equals 2 times 10 to the 9th, or 10 to the negative ninth, pardon me...