Four grams of a monoprotic weak acid are dissolved in water...

Four grams of a monoprotic weak acid are dissolved in water to make $250.0 \mathrm{~mL}$ of solution with a $\mathrm{pH}$ of $2.56 .$ The solution is divided into two equal parts, $A$ and $B$. Solution $A$ is titrated with strong base to its equivalence point. Solution $\mathrm{B}$ is added to solution $\mathrm{A}$ after solution $\mathrm{A}$ is neutralized. The $\mathrm{pH}$ of the resulting solution is $4.26 .$ What is the molar mass of the acid?

Key Concepts

Mole Concept and Molar Mass Calculation

The mole concept is fundamental in chemistry for relating the mass of a substance to the number of particles it contains. Molar mass is calculated by dividing the mass of the compound by the number of moles present. In titration problems, where the amount of substance is determined from the reaction stoichiometry, the mole concept is crucial for converting between the measured mass and the chemical amount.

Buffer System

A buffer system is formed when a weak acid and its conjugate base are present together in solution. This system resists changes in pH upon the addition of small amounts of acid or base. The pH of the buffer can be effectively described using the Henderson–Hasselbalch equation, which links the acid-base ratio to the pH of the solution.

Titration and Equivalence Point

Titration is an analytical technique in which a solution of known concentration (titrant) is added to a solution containing an analyte until the reaction reaches the equivalence point, where stoichiometrically equivalent amounts of acid and base have reacted. In the context of a weak acid titration, reaching the equivalence point allows for the determination of the total amount of acid present by measuring the volume and concentration of the titrant used.

Henderson–Hasselbalch Equation

This equation provides a relationship between the pH of a solution, the pKa of a weak acid, and the ratio of the concentrations of the conjugate base and acid. It is especially useful in buffer solutions where both the weak acid and its conjugate base are present, allowing for the prediction or calculation of pH changes upon the addition of acid or base.

Acid Dissociation Equilibrium

This concept involves the process by which a weak acid partially dissociates in solution into its constituent hydrogen ion and conjugate base. The degree of dissociation is described by the acid dissociation constant (Ka), which, together with the pH of the solution, helps determine the concentration of all species present according to equilibrium principles.

Transcript

00:01 So we have a solution with a ph of 2 .56.

00:07 That gives us a hydrogen ion concentration of 2 .75 times 10 to negative 3 molar.

00:18 So we know that this is our original solution, and we're going to divide it in half.

00:27 So in one solution, we've got 1 .375 times 10 to negative 3 molar, and the same thing over here, because we've split it in half.

00:42 So we're going to react the same amount of oh minus here, and this is going to produce that same amount of our a minus, our weak base.

01:03 So over here, now we've got a weak acid, and we're going to combine these two solutions here.

01:11 So now we have equal amounts of a weak acid and its conjugate base, so we have a buffer.

01:17 And we have a buffer with equal concentrations.

01:20 So if we have a buffer with equal concentrations, we know that h plus equals ka.

01:30 And ka.

01:32 So that's going to be equal to 10 to the negative 4 .26 because they said that final ph was 4 .26.

01:40 So if we do that out, we'll get 5 .5 times 10 of the negative 5.

01:47 So now let's take our weak acid and write the reaction for it ionizing.

01:52 So h plus plus a minus.

02:00 I'm going to set up an ice box here.

02:04 I don't know how much of this i started with, but i know that at equilibrium i have 2 .75 times 10 of the minus 3.

02:17 Okay? we calculated that above...

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