Here, we’ll show you how to calculate the value of the acid ionization constant, Ka, for a weak acid of a given concentration. pH and Acid Concentration to K a

We’re told that a M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of 1.13.

And we’re asked to use this information to calculate the value of Ka for dichloroacetic acid. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Using this information, calculate the K a value for dichloroacetic acid.

There are 4 main steps we can take to solve this type of problem. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4 Steps:

The first thing we do is convert the given pH into hydronium ion concentration. We’ll be using an ICE table and we need concentrations for that. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4 Steps: 1.Convert pH to [H 3 O + ] 1

The second step is to write the ionization equation for the given weak acid. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4 Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for the weak acid 2

The third step is to draw an ICE table under the ionization equation and use it to calculate the equilibrium concentration of the acid and its conjugate base. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4 Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for the weak acid 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base 3

In Step 4, we insert the equilibrium concentrations into the Ka expression and calculate its value. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4 Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for the weak acid 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a 4

So we’ll start by converting pH to hydronium ion concentration. We use the formula the concentration of H3O + equals 10 to the negative pH (or antilog of negative pH) A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 1.Convert pH to [H 3 O + ]

Which is equal to 10 to the negative 1.13 A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 1.Convert pH to [H 3 O + ]

And that comes out to Even though the pH had 2 significant figures, we’ll use 1 extra significant figure for this value and our calculations, then round to 2 significant figures at the end of the problem. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 1.Convert pH to [H 3 O + ]

So we can say the [H3O+] is M. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 1.Convert pH to [H 3 O + ]

We’ll make a note of that up here. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 1.Convert pH to [H 3 O + ] [ H 3 O + ] = M

The second step is to write the ionization equation for the weak acid, CHCl2COOH A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. [ H 3 O + ] = M 2.Write the ionization equation for the weak acid CHCl 2 COOH

To write the ionization equation we add water to the acid, and on the product side we write H3O+ and the conjugate base of the weak acid. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 2.Write the ionization equation for the weak acid CHCl 2 COOH [ H 3 O + ] = M Conjugate base of CHCl 2 COOH

The formula for the conjugate base is obtained by removing a proton, or one H and one + charge from the acid. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 2.Write the ionization equation for the weak acid CHCl 2 COOH [ H 3 O + ] = M

This gives us CHCl2COO minus. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 2.Write the ionization equation for the weak acid CHCl 2 COOH [ H 3 O + ] = M

And this is called the dichloroacetate ion. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 2.Write the ionization equation for the weak acid CHCl 2 COOH [ H 3 O + ] = M Dichloroacetate ion

The third step is to use an ICE table to find the equilibrium concentration of the acid and its conjugate base. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. [ H 3 O + ] = M 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base

[I] [C] – [E] – So we draw an ICE table under the equation. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M

[I] [C] – [E] – And draw a grid so that the columns line up nicely under the substances in the equation. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M

[I] [C] – [E] – Because water is a liquid, we’ll put an X through the column underneath it. We’ll colour it blue here. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M

[I] [C] – [E] – We can start filling in the row for initial concentrations. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M

The initial concentration of the acid is M, so we insert in here. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

Some teachers prefer you to use the unit Molarity for entries inside of ICE table. If this is the case, make sure you include these units in your work. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] – M

In the ICE table in our examples, we’ll just write the values for the concentrations and we’ll assume that all entries are molar concentrations. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

The square brackets around the I, C, and E indicate that all values are molar concentrations. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

Before any ionization occurs, the concentration of hydronium is 1.0 × M, its concentration in neutral water. This is insignificant compared to what it will be after ionization, so we’ll just call it zero here. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

Before ionization, the concentration of the dichloroacetate ion is also zero A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

Because the concentrations of the products are initially zero (click), the reaction will move to the right as equilibrium is established. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] – Move to the Right

At this point, we recall that the equilibrium concentration of hydronium is M A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

So we write in the cell for the equilibrium concentration of hydronium. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [ H 3 O + ] = M [I] [C] – [E] –

Now we’ll focus on the column under the hydronium ion. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

The concentration of hydronium started out as 0 Molar A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

And reached M at equilibrium A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

So we know that as the ionization occurred, the concentration of hydronium must have increased by Molar, so we write in the change in concentration row under the hydronium ion. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M

We can use this, along with the coefficients in the ionization equation, to determine the changes in concentration of the other two species as ionization occurs. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M

The dichloroacetate ion is a product, so its concentration will increase as the ionization occurs. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M

And the coefficients on the hydronium ion and the dichloroacetate ion are both 1 A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M 11

So we know that the concentration of dichloroacetate increases by Molar, just like the hydronium. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M

Because dichloroacetic acid is a reactant in the ionization equation, its concentration will go down as ionization occurs and the reaction moves to the right. So we’ll write a minus sign here. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M

The coefficients on dichloroacetic acid and hydronium are both 1, A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – Move to the Right [ H 3 O + ] = M 1 1

[I] [C] – [E] – So as the ionization occurs, the concentration of dichloroacetic acid goes down by molar. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base Move to the Right [ H 3 O + ] = M 1 1

Now, we can fill in the row for the equilibrium concentrations of all the species. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

We’ll start with the dichloroacetate ion over on the right A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

Its concentration started out as zero A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

And increased by M, A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

So its equilibrium concentration is 0 plus , which is equal to Molar. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

Now we’ll go over to the dichloroacetic acid on the left. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

It started out as M A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

And went down by Molar. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M

So it’s equilibrium concentration will be minus A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] – [ H 3 O + ] = M –

Which comes out to M. This is written to more significant figures than the final answer can have, but we’ll use this number and round to the correct number of significant figures at the end of the calculations. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] [ H 3 O + ] = M –

We now have the equilibrium concentrations of all three species A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 3.Use an ICE table to determine the equilibrium concentrations of the acid and its conjugate base [I] [C] – [E] [ H 3 O + ] = M

We now have what’s necessary to carry out step 4. We’ll insert the equilibrium concentrations into the Ka expression A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression

and calculate the value of Ka. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a

The Ka expression is the concentrations of products over the concentration of the reactant, A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a products reactant

Which is the concentration of hydronium times the concentration of dichloroacetate A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a

Over the concentration of dichloroacetic acid. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a

The equilibrium concentrations of hydronium and dichloroacetate are both M, so their product in the Ka expression, is squared. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a

And the equilibrium concentration of dichloroacetic acid is M, so we substitute that in here. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a

squared divided by comes out to 4.4 × when rounded to 2 significant figures. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a

The reason we’re rounding to 2 significant figures is the original pH was given to 2 decimal places, which is 2 significant figures. A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a 2 significant figures

So our final answer is, the value of Ka for dichloroacetic acid is 4.4 × A M solution of dichloroacetic acid (CHCl 2 COOH) has a pH of Calculate the K a for dichloroacetic acid. 4.Insert equilibrium concentrations into the K a expression and calculate the value of K a The value of K a for CHCl 2 COOH is 4.4 × 10 –2