6.2: Acid Equilibria Lab

 

Learning Objectives

Goals: 

• Determine an equilibrium constant from experimental data
• Understand the effect of dilution on percent ionization for a weak acid
• understand the common ion effect and LeChatlier's principle

By the end of this lab, students should be able to:

• Apply the concept of equilibria and equilibrium constants to weak acids (and bases)
• Design and run an experiment using a pH meter to determine the equilibrium constant for a weak acid
• Use an equilibrium constant and pH meter to determine the concentration of an unknown weak acid or base
• Predict the effect on the pH of and acid (or base) by adding the salt of that acid (or base).

Prior knowledge:

• Section 3.5: Neutralization Reactions
• Section 4.5: pH scale for Acids and Bases

Concurrent Reading:

• Section 15.3: Determining an Equilibrium Constant
• Section 15.6: Disturbing Equilibrium (LeChatlier's Principle)

 

 

 

Safety

• Emergency Preparedness
  • Eye protection is mandatory in this lab, and you should not wear shorts or open toed shoes. 
  • Any spills should be cleaned up immediately
• Minimize Risk
  • Label all containers
  • Keep work station clear and neat
• Recognize Hazards
  • Acetic Acid PubChem LCSS
  • All solutions should be considered harmful and care should be taken to avoid contact with your skin or other body tissues. 
  • In event of contact with reagents you should flush contacted area with water and notify instructor immediately.

Figure \(\PageIndex{1}\):OSHA's Chemical Safety Board release on July 27, 2021 fatal accident in Texas involving acetic acid.  Now, this incident involved 100,000 pounds of the acid being released. Glacial acetic acid (anhydrous pure acetic acid) is very dangerous and we are using dilute aqueous solutions. Acetic acid is the common ingredient in vinegar, which you probably have in your kitchen, but you must alert your instructor if you have a spill (Copyright; screen capture by Bob Belford, CC0)

 

 

Equipment and materials needed

Table \(\PageIndex{1}\): Supplies for Experiment 6

Burets	4-250 mL Erlenmeyer flask	50 mL vol flask
1-25 mL pipet	2-10 mL pipets	50 mL beaker
3-100 mL vol flasks	2.00 M Acetic  Acid	2.00 M Sodium Acetate
pH meter	3-buffers at pH=4,7,10	Acetic acid unkown concentration

 

 

Background

Before proceeding read sections 15.2: Equilibrium Constants and 15.3: Determining an Equilibrium Constant.  The generic expression for an equilibrium constant for the reaction \[aA+bB \rightleftharpoons cC+dD \] is: \[ K =\dfrac{[C]^c[D]^d}{[A]^a[B]^b} \; \\ \; \\ \text{(noting all species are at equilibrium concentrations)}\]

Note: The above equation describes the concentrations after the reaction has completed and the system has entered a state of equilibrium.  You can mix reactants in any proportions, and they will react until the above equation equals the equilibrium constant.  The Rice diagram below is used to predict how a reaction will proceed.

Rice Diagram

We typically use a RICE diagram to describe the change in concentration as a reaction proceeds from initial to final (equilibrium) concentrations.  For the above generic reaction, the RICE diagram is:

Table \(\PageIndex{2}\): Generic RICE Diagram

Reactants	aA             +	bB	⇌	cC             +	dD
Initial	[A]Initial	[B]Initial		[C]Initial	[D]Initial
Change	-ax	-bx		+cx	+dx
Equilibrium	[A]Eq	[B]Eq		[C]Eq	[D]Eq

noting that:

\[ \left [ A\right ]_{Eq}=\left [ A\right ]_{Initial}-ax \\ \left [B\right ]_{Eq}=\left [ B\right ]_{Initial}-bx \\ \left [ C\right ]_{Eq}=\left [C\right ]_{Initial}+cx \\ \left [D\right ]_{Eq}=\left [D\right ]_{Initial}+dx \label{15.3.3} \]

where,

x=extent of reaction

and

\[K=\frac{\left [C\right ]_{eq}^{c}\left [D\right ]_{eq}^{d}}{\left [A\right ]_{eq}^{a}\left [B\right ]_{eq}^{b}}\]

We will use the equilibria of a weak acid as our example because we can measure the hydronium ion concentration with a pH meter.

pH and Concentration

In this lab we will use the pH meter to measure the hydronium ion concentration. From section 4.5 (gen chem 1) we know

pH = -log[H₃O⁺]

[H₃O⁺] = 10^-pH = 1/10^pH

Weak Acid Equilibria

From section 3.5.1.2: Acid-Base Reactions we know that the Bronsted-Lowry definition of an acid is a proton donor, which can generically be represented as HA, and in aqueous solutions the proton is donated to water

\[HA(aq)+H_2O(l)⇌H_3O^+(aq)+A^-(aq)\]

At first glance this gives an equilibrium constant of

\[K=\frac{[H_{3}O^{+}]_{eq}[A^{-}]_{eq}}{[HA]_{eq}[H_{2}O]_{eq}}\]

but water is in excess (section 15.2.5) and so this reduces to

\[K_a=\frac{[H_{3}O^{+}]_{eq}[A^{-}]_{eq}}{[HA]_{eq}}\]

The water is typically removed from the equation and implicitly represented, where hydronium is written as H⁺ (implicitly meaning H₃O⁺ ), giving:

\[HA \rightleftharpoons H^+ + A^- \\ \; \\ \text{which results in the equilibrium expression of)} \\ \; \\  K_a=\frac{[H^{+}][A^{-}]}{[HA]} \]

Which results in the following RICE diagram.

Table \(\PageIndex{3}\): Weak Acid RICE Diagram

Reaction	\(HA\)	\(H^+\)	\(A^-\)
Initial	[HA]i	0	0
Change	-x	+x	+x
Equilibrium	[HA]i-x	x	x

Noting that \(x=10^{-pH}\) (at equilibrium) and substituting, gives\[K_a =\frac{(10^{-pH})^2}{[HA]_i-10^{-pH}}\]

So with a pH meter we can study equilibrium problems involving acids (and bases).  We are going to measure the pH of 5 different solutions and perform the following calculations:

1. Calculate K_a knowing [HA]_i (solutions 1-3)
2. Calculate K_a knowing [HA]_i and [NA]_i (solution 4)
3. Calculate [HA]_i knowing Ka (solution 5 - the unknown)  

 

Common Ion Effect

In solution 4 we are mixing equal volumes of 0.1M acetic acid (weak acid) and 0.1M sodium acetate (salt of weak acid section 3.4.2), which have the common ion acetate. Before mixing we would expect little of the acid to dissociate and all the salt to be dissociated.  So before mixing we expect

\[\begin{align}HC_2H_3O_2  &\rightleftharpoons  H^+ + C_2H_3O_2^- \\  NaC_2H_3O_2  &\rightarrow Na^+ + C_2H_3O_2^- \end{align}\]

According to LeChatlier's principle (section 15.6), a system shifts its equilibrium to consume a chemical species involved in a reaction if it is added to a system at equilibrium. If we add sodium acetate to the weak acidic acid we would expect the weak acid equilibria to shift to the left, and thus the common ion (acetate) inhibits the ionization of the weak acid (acetic acid). 

 

Table \(\PageIndex{4}\): Weak Acid and its salt RICE Diagram

Reaction	\(HA\)	\(H^+\)	\(A^-\)
Initial	[HA]i	0	[NaA]i
Change	-x	+x	+x
Equilibrium	[HA]i-x	x	[NaA]i+x

\[K_a=\frac{x\left ( [NaA]_i+x] \right )}{[HA]_i-x} \; \\  \; \\ \; =\frac{x\left ( [NaA]_i] \right )}{[HA]_i}\]

This is saying that the common ion (A^-) added by the salt pushes the equilibrium of the acid (HA) to the left and inhibits the ionization of the acid, driving the pH up. 

Note, the special case for equimolar mixtures of an acid and its conjugate base (where the acetate ion concentration equals the acetic acid concentration ) gives an easy way to measure the equilibrium constant.

\[K_a=\frac{x\left (\cancel{[NaA]_i]} \right )}{\cancel{[HA]_i}} = x = 10^{-pH} \\ \; \\ \underbrace{K_a = 10^{-pH}}_{when \; [HA] = [A^-]}\]

So we have a very easy way to measure the acid ionization constant of a weak acid.

Experimental Procedures

In this lab we are going to measure the pH of five solutions.  Three are solutions of acetic acid (HA), one of an unknown and one is an equimolar solution of acetic acid and its salt.

Preparing Reagents

1. Solution 1: Calculate the volume of 2.00 M acetic acid that will make 100 ml of 0.100 M acetic acid, transfer that volume to a 100 mL volumetric flask and dilute to volume with DI water. You will measure the pH of this solution and use it to make three other solutions.
2. Solution 2: Using a volumetric pipette transfer 25 mL of solution 1 to a 50 mL Volumetric flask and dilute to volume. 
3. Solution 3: Using a volumetric pipette transfer 10 mL of solution 1 to a 100 mL Volumetric flask and dilute to volume
4. Solution 4: Using volumetric pipettes transfer 10 mL of solution 1 (0.100 M acetic acid) and 10 mL of 0.100 M sodium acetate to a small beaker
5. Solution 5: Unknown (add enough to a small beaker to submerge the pH probe tip).

Measuring pH

1. Set up pH meter as instructed in the general information page, section 0.4.4 (pH Meter under Instrumentation)
2. Test pH meter with buffers and if required, calibrate.
3. Measure pH of each of the 5 solutions and record values in the data sheet. 

 

Data Analysis

Cover Page

As always, fill out the cover page of your Google Workbook

Solutions

The material in light brown represents data or values you used in making the solutions (like the concentration of a reagent you diluted, and the volume you diluted it to).  The stuff in blue represents calculations you do with the data.  Some of these you will use in other sheets of this workbook.

Figure \(\PageIndex{1}\): Solutions worksheet of the acid equilibrium workbook. (Bob Belford CC-0)

Remember, you can use formulas in worksheets.  For example you wish to find the initial volume of concentrated acetic acid from the dilution formula.  So you know that

\[M_iV_i=M_fV_f\] and can solve for the volume you need with the spreadsheet, and then use that volume in the lab.  So in the cell B4 you can type 

=(Z1*Z2)/Z3

where Z1, Z2 and Z3 are the cells of your sheet that have the data you wish to use in your calculation.
 

Data Analysis

Once again, you can use functions or work the data up by hand.

Figure \(\PageIndex{1}\): Copy and Paste Caption here. (Copyright; author via source)

• Row 2 for solutions 1-4 are the molarities of the solutions created in the solutions worksheet (you can cut and paste values). 
• Row 3 has the pH values for each of the solutions you measured and recorded in your data sheet. 
• Calculate hydronium ion concentration from pH (weak acid equilibria above).
• For solutions 1-3
  • Calculate acetate ion concentration from hydronium ion concentration (Table \(\PageIndex{3}\) above)
  • Calculate undissociated acid concentration at equilibrium from the initial concentration and the extent of reaction (Table \(\PageIndex{3}\) above)
  • Calculate K_a from equilibrium acid, hydronium and acetate concentrations
  • Calculate percent ionization from initial acid concentration and extent of reaction (x) in (Table \(\PageIndex{3}\) 
• For solution 4 insert values but calculate K_a from just the pH measurement  (see eq. 6.2.13)
• The unknown is acetic acid and you are using the pH meter to determine its concentration.  Use the average K_a from the four solutions you prepared.