Here, we’ll show you how to calculate the initial concentration of a weak acid, given the pH and the Ka of the acid. In this particular example, we’ll use the initial concentration to find initial moles of the acid in the sample pH and K a to Initial Concentration

We’re told that we have a mL sample of oxalic acid (H 2 C 2 O 4 ) with a pH of A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of

And we’re asked how many moles of H 2 C 2 O 4 were initially added to this sample? A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We’ll divide the solution to this problem into 6 main steps. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? Six Steps:

We’re given the pH, and since oxalic acid is a weak acid, we will need an ICE table. We can use hydronium concentration in an ICE table, but not pH. So step 1 is to convert the pH to hydronium ion concentration. Six Steps: 1.Convert pH to [H 3 O + ] A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

In step 2, we write the balanced ionization equation for oxalic acid. Six Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for oxalic acid A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

Next, we draw an ICE table below the equation Six Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for oxalic acid 3.Draw an ICE table below the equation A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We let x equal the initial concentration of the acid, insert known quantities into the ICE table, and determine all the other quantities. Six Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for oxalic acid 3.Draw an ICE table below the equation 4.Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the expression, and solve for x, the initial concentration Six Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for oxalic acid 3.Draw an ICE table below the equation 4.Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities 5.Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

In the last step, we’ll use the concentration and volume of the sample to calculate the number of moles of oxalic acid initially added to the sample. Six Steps: 1.Convert pH to [H 3 O + ] 2.Write the ionization equation for oxalic acid 3.Draw an ICE table below the equation 4.Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities 5.Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We’ll start the process by converting the given pH to hydronium ion concentration. 1.Convert pH to [H 3 O + ] A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We use the equation hydronium concentration equals 10 to the negative pH 1.Convert pH to [H 3 O + ] A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

Which is 10 to the negative Convert pH to [H 3 O + ] A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

This works out to molar 1.Convert pH to [H 3 O + ] A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

So we can state that the hydronium concentration is molar 1.Convert pH to [H 3 O + ] A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

And we’ll make a note of it up here 1.Convert pH to [H 3 O + ] [H 3 O + ] = M A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

In step 2, we write out the ionization equation for oxalic acid. 2.Write the ionization equation for oxalic acid, H 2 C 2 O 4. [H 3 O + ] = M A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We add H2C2O4 to water 2.Write the ionization equation for oxalic acid, H 2 C 2 O 4. [H 3 O + ] = M A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

And it forms H3O plus, 2.Write the ionization equation for oxalic acid, H 2 C 2 O 4. [H 3 O + ] = M A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

And the conjugate base of oxalic acid, the hydrogen oxalate ion, HC2O4 minus 2.Write the ionization equation for oxalic acid, H 2 C 2 O 4. [H 3 O + ] = M A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? The hydrogen oxalate ion

Now, we draw an ICE table below the equation and add a grid so that the columns line up with the substances in the equation. 3.Draw an ICE table [H 3 O + ] = M [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

Water is a liquid, so we ignore its values. We’ll colour its column blue here. 3.Draw an ICE table [H 3 O + ] = M [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We’ll start by adding what we can to the initial concentration row. 3.Draw an ICE table [H 3 O + ] = M [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

We don’t know what the initial concentration of oxalic acid is, so we let it equal 3.Draw an ICE table [H 3 O + ] = M [I]x00 [C] – [E] x – ? A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

x 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities [H 3 O + ] = M [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

And before ionization, the concentrations of hydronium and hydrogen oxalate ions are zero. [H 3 O + ] = M [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

Remember, using the pH, we had determined that the hydronium concentration at equilibrium is molar [H 3 O + ] = M A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample?

So we’ll write in the cell for the equilibrium concentration of hydronium, down here. [H 3 O + ] = M [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

Now we’ll focus on the column for hydronium. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

The hydronium ion concentration started out as 0 molar and went up to molar at equilibrium, so its change in concentration is an increase of molar. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

Hydronium and hydrogen oxalate both have a coefficient of 1 in the ionization equation. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities 11

So we can say that the concentration of hydrogen oxalate also increased by molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities 11

Because concentrations of the products increased, we can see that the reaction (click) has moved to the right in order to establish equilibrium [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities Moved to the Right

Therefore, we can say that the concentration of oxalic acid on the left must have decreased. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities Moved to the Right

And because the coefficients on oxalic acid and hydronium are both 1 [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities 11

We can say that the concentration of oxalic acid went down by molar, the same as the hydronium ion increased by. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities 11

Now we can fill in the row for equilibrium concentrations. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

We’ll start with the hydrogen oxalate ion on the right. It’s concentration started out as 0 molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

And increased by molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

So its equilibrium concentration is molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

Now we’ll move over to the oxalic acid on the left. It’s concentration started out as x molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

And it went down by molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

So its equilibrium concentration is x minus molar [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

So now we have equilibrium concentrations for all three species. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities

Our task now is to determine the value of x. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 4. Let x equal the initial concentration of oxalic acid, insert known quantities into the ICE table, and determine the other quantities ? ?

We do this by inserting these equilibrium concentrations into the Ka expression for oxalic acid as set out in Step 5 of our plan. [I]x00 [C] – [E] x – A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

We start by using the ionization equation to write the Ka expression for oxalic acid. It is products over reactants, A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

Which is the concentration of hydronium times the concentration of hydrogen oxalate over the concentration of oxalic acid. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

Looking up oxalic acid on the acid table, it tells us that it’s Ka value is 5.9 × A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

To save space, we’ll write this as a decimal number. 5.9 × is the same as A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration K a = 0.059

We can now substitute this value for Ka in our Ka expression. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration K a = 0.059

Like this A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration K a = 0.059

We substitute in for both hydronium and hydrogen oxalate, and their product in the Ka expression is squared. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

And we’ll substitute x in for the equilibrium concentration of H2C2O4. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

So now we have the equation equals squared over x minus A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

We’ll rearrange this equation to solve for x minus , and we get x minus equals squared over A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

squared over works out to We’ll leave this as 4 significant figures for now and round our answer to the correct number of significant figures at the end of the calculation. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

So at this point, we know that x minus is equal to A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

Adding to both sides of the equation, gives us x is equal to plus A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

Which is A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

Remember that x was set as the initial concentration of oxalic acid, H2C2O4. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

So we can say that the initial concentration of H2C2O4 was molar. We added the unit M because this is a molar concentration. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration

We’ll make a note of it up here. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 5. Write the K a expression for oxalic acid, look up the K a value, insert equilibrium concentrations into the K a expression, and solve for x, the initial concentration [H 2 C 2 O 4 ] initial = M

We now know the initial concentration of the oxalic acid. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? [H 2 C 2 O 4 ] initial = M We know the initial concentration

But the question asks us to find the number of moles of Oxalic acid. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? [H 2 C 2 O 4 ] initial = M We know the initial concentration

So in Step 6, we’ll use the concentration and volume to calculate the number of moles of oxalic acid initially added to the sample. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added [H 2 C 2 O 4 ] initial = M

The moles of H2C2O4 A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added [H 2 C 2 O 4 ] initial = M

Is equal to moles of H2C2O4 per litre A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added [H 2 C 2 O 4 ] initial = M

Times the volume of the sample, L A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added

Equals moles of H2C2O4. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added

So we can say that the number of moles of H2C2O4 initially added to the sample was moles. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added

This final answer is rounded to 2 significant figures. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added 2 significant figures

This is because the Ka value we obtained from the acid table was only 2 significant figures. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added 2 significant figures

2 is the lowest number of significant figures in the data we used, so we round our final answer to 2 significant figures. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added 2 significant figures

So to summarize, the final answer is moles of oxalic acid, H 2 C 2 O 4 was initially added to the mL sample. A mL sample of oxalic acid (H 2 C 2 O 4 ) has a pH of How many moles of H 2 C 2 O 4 were initially added to the sample? 6.Using the concentration and volume, calculate the number of moles of oxalic acid initially added moles of H 2 C 2 O 4 was initially added to the mL sample.